- Email: [email protected]
Design and 3D printing of adjustable modulus porous structures for customized diabetic foot insoles
Accepted Manuscript Design and 3D printing of adjustable modulus porous structures for customized diabetic foot insoles Zheng Ma, Jiacheng Lin, Xiaoyue Xu, Ziwei Ma, Lei Tang, Changning Sun, Dichen Li, Chaozong Liu, Yongming Zhong, Ling Wang PII:
S2588-8404(18)30047-7
DOI:
https://doi.org/10.1016/j.ijlmm.2018.10.003
Reference:
IJLMM 31
To appear in:
International Journal of Lightweight Materials and Manufacture
Received Date: 2 June 2018 Revised Date:
22 October 2018
Accepted Date: 22 October 2018
Please cite this article as: Z. Ma, J. Lin, X. Xu, Z. Ma, L. Tang, C. Sun, D. Li, C. Liu, Y. Zhong, L. Wang, Design and 3D printing of adjustable modulus porous structures for customized diabetic foot insoles, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/ j.ijlmm.2018.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Design and 3D printing of adjustable modulus porous structures for customized diabetic foot insoles Zheng Ma1,2, Jiacheng Lin1,2, Xiaoyue Xu1,2, Ziwei Ma1,2, Lei Tang1,2, Changning Sun1,2, Dichen Li1,2, Chaozong Liu3, Yongming Zhong4, *Ling Wang1,2 State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, 710054,
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Xi'an, Shaanxi, China
School of Mechanical Engineering, Xi’an Jiaotong University, 710054, Xi’an, Shaanxi, China
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John Scale Centre for Biomedical Engineering, University College London, Royal National
Orthopaedic Hospital, Stanmore, HA74LP, HK
Shandong Weigao Pharmaceutical Co., Limited. No.20 Xingshan Road, Hi-tech District, Weihai,
Shandong, China *Corresponding Author Associate Prof. Ling Wang Email: [email protected]
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Design and 3D printing of adjustable modulus porous structures for
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customized diabetic foot insoles
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Abstract Designs with adjustable gradient modulus have become necessary for
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applications with special demands such as diabetic insole, in which the contact stress
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between the foot and insole is a critical factor for ulcers development. However, since
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the adjustment of elastic modulus on certain regions of insole can hardly be achieved
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via materials selection, a porous structural unit with varying porosity becomes a
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feasible way. Therefore, porous structural units associated with adjustable effective
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modulus and porosity can be employed to construct such insoles by 3D printing
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manufacturing technology. This paper presents a study on the porous structural units
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in terms of the geometrical parameters, porosity, and their correlations with the
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effective modulus. To achieve this goal, finite element analyses were carried out on
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porous structural units, and mechanical tests were carried out on the 3D printed
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samples for validation purposes. In this case, the mathematical relationships between
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the effective modulus and the key geometrical parameters were derived and
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subsequently employed in the construction of an insole model. This study provides a
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generalized foundation of porous structural design and adjustable gradient modulus in
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application of diabetic insole, which can be equally applied to other designs with
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similar demands.
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Keywords: Adjustable gradient modulus; Porous structures; Diabetic insoles; 3D
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printing;
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1. Introduction
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Nowadays, designs with adjustable gradient modulus has become necessary for
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applications with special demands such as diabetic insole since the contact stress
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between foot and insole is a critical factor for ulcer development [1-3]. It has been
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found that the symptoms of diabetic foot are significantly alleviated by reducing and
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uniformly distributing plantar pressure, which can be achieved by the customized
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of insoles should be assigned with different modulus for localized support. Traditional
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methods, such as molding and machining, are only applicable to manufacture insoles
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with homogeneous mechanical property, which hinders the effectiveness of insoles for
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slowing down the development of ulcers [7]. Besides, such insoles are relatively
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high-cost due to the demanding requirements of selecting materials and relatively
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long designing and manufacturing period, which is hard to afford for the majority of
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patients [3,7]. Since the adjustment of modulus can hardly be achieved by materials
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selection, a porous structure with adjustable mechanical properties (effective modulus)
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becomes a feasible way.
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3D printing techniques are now widely used for the freedom of manufacturing
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materials with complex geometry [8-10], which makes them capable of
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manufacturing porous structural units for customized diabetic insoles. Among all
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kinds of 3D printing techniques, the material extrusion technique (MEX) is the most
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commonly used technique due to its low cost in instruments and materials, which
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makes it a fairly good candidate for fabrication [11]. Nevertheless, common flexible
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materials, like thermoplastic polyurethane (TPU) and thermoplastic elastomer (TPE),
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have effective moduli that are beyond the demand of alleviating plantar pressure
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[4,7,12]. In this case, porous structural units were utilized to yield lower effective
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modulus with flexible, MEX-supported materials as desired.
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Many researchers have been working on the manufacturing of customized diabetic
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insoles with 3D printing techniques. Miguel et al. presented a CAD methodology to
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design and manufacture therapeutic insoles by MEX. Feasibility of this methodology
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was verified both practically and economically by several prototypes in their latest
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paper [13]. Telfer et al. enrolled twenty participants in the comparison of 3D-printed
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insoles and subtractive milled insoles. Results show that the use of 3D-printed insoles
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yields lower peak pressures in 88% of the plantar regions of interests [14]. Though
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many studies have provided feasible methods in this field, few of them focusing on
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porous structural units (size, geometric parameter, porosity and effective modulus).
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Therefore, it’s necessary to provide a general methodology of studying porous
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structural units, in order to map customized diabetic insoles and other possible
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applications. To achieve this goal, a typical porous structural unit was selected. Based on this
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porous structural unit, a FE model was constructed to calculate its effective modulus
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[15]. The feasibility of FE model was validated by carrying out compressive tests on
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the 3D-printed porous structures. Then both compressive tests and FEA simulations
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were employed to measure the effective modulus of the porous structure. For further
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analyses in mechanical properties, orthogonal experiments were carried out to
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determine geometric parameters that are sensitive to the effective modulus of units.
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When the sensitive geometric parameters were determined, further study was carried
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out to obtain the mathematical relationships between the sensitive parameters and the
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effective modulus of porous structural units. Meanwhile, mathematical relationships
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between porosity and geometric parameters were also presented.
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2. Materials and methods
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2.1 Preparation of Porous Structural Units
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Initially, porous structural units were designed by parametric modeling. Among
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all units, the ellipsoidal structural unit (Fig.1(a).) was employed in this study because
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of its relatively satisfying 3D-printing quality and resilience under compression. By
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adjusting the geometric parameters, it can achieve a wide range of effective elastic
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modulus, which is necessary for customized diabetic insoles. In the construction of
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ellipsoidal structural units, geometric parameters were determined based on the
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character of ellipsoid structure (‘A’, the length of long axis of ellipsoidal cross section.
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‘B’, the length of short axis of ellipsoidal cross section. ‘T’, the thickness of wall of
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the hollow ellipsoid. ‘H’, the thickness of plate between layers). The side lengths of
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units vary from 4.4mm to 8.1mm and the heights of units vary from 3.3mm to 5.1mm.
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The porosity of units is in the range of 30.91% to 46.97%. For the convenience of
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printing and compressive tests, samples were arrayed of 5×5×5 replications of a single
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unit as Fig1 (b). Several printed samples are shown as Fig.1(c).
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(b)
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Fig.1. (a) Cutaway view of ellipsoidal structural unit; (b) Sketch of arrayed samples (5×5×5);
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(c) MEX printed TPE samples.
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2.2 Manufacturing Porous Structures with MEX
The desktop MEX printer used in this study is 3DP-300B (Shaanxi Hengtong
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Intelligent Machine Co., Ltd.). The printing precision is 0.4mm. Slicing files were
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generated in Cura 15.04 (Ultimaker, Netherlands). Printing settings were as fellow:
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nozzle temperature of 235℃, nozzle diameter of 0.4mm, layer thickness of 0.2mm,
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printing speed of 30mm/min, and filling rate of 100%. TPE filament (eLastic ,
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Shenzhen Esun Industrial Co., Ltd ) with diameter of 1.75mm±0.05mm was used in
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this study.
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2.3 Compressive Test
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Compressive tests were conducted with electromechanical universal testing
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machine (ETM103A from Shenzhen Wance Testing Machine Co.). During
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compression, samples were compressed at a constant speed of 1mm/min, with a
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sampling frequency of 120Hz. Tests were terminated when the force reached the
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upper limitation of 200N, in order to keep the samples within linear elastic range and
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avoid plastic deformation or internal structure interference. Three samples (N=3) were
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tested for each group, and the average value was determined. Average length of each
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sample was measured with caliper. The experimental effective elastic modulus of the
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samples can be obtained from the slop of stress-strain curves, which is expressed in
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Eq. (1).
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The equation [16] employed in effective modulus calculation:
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# 1 111
where F is the external loading, A is the nominal cross-sectional area, h is the original
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height,
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the stress-strain curve.
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2.4 Finite Element Analysis (FEA)
h is the compressive displacement and k is the slope of the elastic range in
Compression testing simulations of various porous structure models were carried
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out via FEA method in ABAQUS 6.14-4 (Dassault, France), as shown in Fig.2.
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Models were created in SolidWorks 2017 SP4.0 (Dassault, France) and converted into
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IGES format before imported into ABAQUS. Each porous structural unit was
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free-meshed by tetrahedral element with an approximate global size of 2mm [17].
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According to the simulation of ordinary walking [12], the stresses of plantar were
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within the linear elastic range of TPE material. Therefore, the material in FEA model
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can be considered as an elastomer with two key factors, Young’s modulus and Poisson
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ratio. According to the compression testing standard ASTM D695 [18], solid cylinders
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with diameter of 12.7mm, height of 25.4mm were printed under the printing settings
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listed above, in order to determine the mechanical property of TPE material. After
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calculation, the Young’s modulus of TPE is 14.525MPa and Poisson’s ration is 0.3.
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To authentically simulate the compressive tests, the boundary and loading
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conditions of the FE model were consistent with those applied in the compressive
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tests [12,15]. Since the base of the porous structural unit was fully constrained for any
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degree of freedom during the compressive test, the boundary condition of the bottom
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layer was set up accordingly as fully constrained (Encastre) for the FE model. The
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surface of the porous structural unit was coupled with the reference point (RP1) that is
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located at the center. An axial compressive load of 200N, perpendicular to the surface,
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was applied via RP1. Thus, every point on the surface was under the same
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compressive load as RP-1, which is equal to a uniformly distributed load of 200N
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over the surface. Finally, the general compressive displacement that was parallel to
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the load was calculated. With the results of deforming displacement, the effective
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modulus of porous structural units was calculated by Eq. (1).
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Fig.2 FE model set-up as representative of the effective model of the porous structural units
2.5 Orthogonal Experiments
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In order to find out the sensitive factors that could have dominating influence on
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mechanical properties, orthogonal experiments were carried out at first. Based on the
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guidelines for orthogonal experiments [19,20], four factors (wall thickness ‘T’, long
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axis ‘A’, short axis’ B’ and plate thickness ‘H’) were chosen as geometrical
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parameters from the cutaway view in Fig.1.(a). And 3 levels were set for each factor,
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as shown in Table.1. Orthogonal experiments were arranged according to L9 (3^4).
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Table.1 Level settings in orthogonal experiments (wall thickness ‘T’, long axis ‘A’, short axis’ B’
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and plate thickness ‘H’)
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Factors
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T/mm
0.4
0.6
0.8
A/mm
3.5
4.5
5.5
B/mm
2.5
3
3.5
H/mm
0.4
0.6
0.8
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Levels
All samples were printed using the mentioned printing settings and effective
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modulus was determined from both the compressive tests and the FEA simulations.
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By gathering and analyzing all testing results, the level of sensitivity of each factor
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was determined by the range, calculated from Eq. (2) - (4).
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The dominating equations [19] are listed below (i, j=1,2,3) ,
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the value of factor i level j # 2
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$, (
repetition of level i
# 3
)*+,$ ," , $ ,- , $ , . / )01 $ ," , $ ,- , $ , # 4
denotes the estimating value for the level j of factor i; $ , represents the
where
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overall mean value for the level j of factor i; ( stands for the range of overall mean
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value for factor i.
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2.6 Parametrical Study
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Based on the previous tests, two of the most effective factors, wall thickness ‘T’
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and long axis ‘A’, were chosen as the sensitive factors in the following study, and
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their effects were investigated thoroughly in sequential manner. The range of ‘T’ was
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set from 0.4mm to 0.9mm at an interval of 0.1mm to generate six wall thickness
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sequential models; likewise, the range of ‘A’ was set from 3.5mm to 6.5mm at an
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interval of 0.5mm to generate 7 long axis sequential models. All generated models
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were printed out under the same printing settings and were put into mechanical testes
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to determine the effective modulus.
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3. Results
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Mechanical tests and FEA simulations were conducted according to the design of
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orthogonal experiment and parametrical study. Typical result of one instance with the
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largest deformation is presented in Fig.3(a) as a comparison between the mechanical
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test and FEA simulation. Displacement nephogram of FEA model under ultimate load
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condition is expressed in Fig.3(b). The original height of sample (h) is 17.4mm. The
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compressive displacement of compressive test ( h) is 4.95mm and the compressive
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displacement of FEA simulation ( h’) is 5.81mm. Fairly good agreement has been
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achieved in both methods in terms of the maximum displacement.
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(a)
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Fig.3 (a) Contrasts between compressive tests and FEM simulations; (b) Displacement nephogram
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under ultimate load condition
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Table.2. Effective modulus results of FEA simulations and compression tests of orthogonal models
Effective modulus from compressive tests
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1.964
0.782
0.489
3.975
2.472
1.483
5.768
4.216
2.261
0.427
±0.16 ±0.06 ±0.04 ±0.33 ±0.18 ±0.11 ±0.41 ±0.35 ±0.13 ±0.03 1.083
0.511
0.342
2.204
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0.759
3.684
2.779
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Effective modulus from FEA
The effective modulus of FEA simulations and compression tests for orthogonal
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models are compared in Table.2. Calculated from Eq. (2) - (4), the range of each
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factor from two methods was determined and portrayed in Fig.4. As indicated in the
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diagram, the order of sensitivity for the four factors was: wall thickness ‘T ’> long
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axis ‘A’ > plate thickness ‘H’ > short axis ‘B’. The optimized result [19] associated
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with the smallest effective modulus was determined as well. Orthogonal model No.10
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denotes the optimized model set-up (A=5.5mm, B=3mm, T=0.4mm, H=0.4mm).
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Geometric Parameters
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T
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1.0
1.5
2.0
2.5
3.0
3.5
Ranges
Fig.4. Factor ranges in orthogonal experiments
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0.5
(Plate thickness ‘H’; Short axis ‘B’; Long axis ‘A’; Wall thickness ‘T’)
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From the contrasts between two methods’ results of orthogonal models, results
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can be summarized that: 1) These two sensitivity sequences of ellipsoidal models’
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parameters in descending order are completely identical. 2) Orthogonal model No.10
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has been proved to possess the smallest effective modulus among all orthogonal series
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models via FEA simulation or compressive test.
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Based on the conclusion of orthogonal experiments, two geometric parameters,
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wall thickness ‘T’ and long axis ‘A’, were chosen to conduct parametrical study.
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Stress-strain curves of ‘T’ sequential models are shown in Fig.5(a). Images of
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samples under different strain conditions in compression are expressed in Fig.5(b). 0.15 kT=0.8=1.279
kT=0.6=0.620
Strain
0.05
0.1
0.2
0.4
0.09
T=0.4
kT=0.4=0.215 0.06
T=0.6
Unit with T=0.4mm Unit with T=0.6mm Unit with T=0.8mm Liner Fitting
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T=0.8
0 0.1
0.2
0.3
Strain
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Fig.5.(a) Stress –stain curves of ‘T’ sequential models; (b) Images of the ellipsoidal models under
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different strain conditions
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After data fitting, the mathematical relationships between wall thickness and
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effective modulus were obtained, as shown in Fig.6(a). In the same way, the effect of
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the long axis A was also investigated in Fig.6(b). Porosity for various parametrical
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model was also determined and correlated to the effective modulus, as presented in
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Fig.7(a) and Fig.7(b).
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y=3.8x2-1.9x+0.4 R²=0.9991
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y=3.6x2-2.4x+0.6 R²=0.9996
0.2
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0.4
0.6
Effective Modulus (MPa)
Mechanical Compressive Test
0.0
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1.5
FEA simulation
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Effective Modulus (MPa)
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FEA Simulation Mechanical Compressive Test
1.0
y=0.1x2-1.6x+5.1 R²=0.9836
0.5
y=0.1x2-1.4x+4.7 R²=0.9746 0.0
0.8
Wall Thickness 'T' (mm)
1
3
3.5
4
4.5
5
5.5
6
6.5
7
Long Axis 'A' (mm)
(a)
(b)
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Fig.6 (a) The mathematical relationship between wall thickness ‘T’ and effective modulus (‘T’ is
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changeable while other parameters are A=6.5mm, B=3mm, H=0.5mm); (b) The mathematical
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relationship between long axis ‘A’ and effective modulus (‘A’ is changeable while other
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parameters are T=0.4mm, B=3mm, H=0.5mm)
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45% y=-0.034x2+0.37x+0.17
1.2
R²=0.9982
40%
0.8
35% y=3.8x2-1.9x+0.4 R²=0.9991
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30%
0.0
25%
Porosity 1.6
45%
1.2
40% y=0.004x2-0.06x+0.5 R²= 0.9981
0.8 0.4
35% 30%
y=0.1x2-1.6x+4.7 R²=0.9746
0.0
25%
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
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50%
Porosity
Porosity 1.6
Effective Modulus
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Effective modulus(MPa)
Effective Modulus
Porosity
Effective modulus(MPa)
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Wall Thickness 'T' (mm)
Long Axia 'A' (mm)
(a)
(b)
Fig.7 (a) The mathematical relationships between wall thickness ‘T’ and mechanical properties
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(porosity and effective modulus). (b) The mathematical relationships between long axis ‘A’ and
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mechanical properties (porosity and effective modulus).
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4. Discussion
In this study, a FE model was developed to study the mechanical properties of
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porous structural units. Mesh convergence study was carried out first to guarantee the
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accuracy in FE calculation [15]. Since it is a static process, time integration is
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irrelevant to the result. Focus should be paid on the meshing size. In the analysis, the
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approximate global size ranges from 0.5mm to 3.0mm with an interval of 0.5mm.
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Relative errors of these six groups are less than 5%. Because the proper setting of
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meshing size is determined by the trade-off between accuracy and time span, the
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approximate global size of 2.0mm is a feasible option.
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Compressive tests and FEA simulations were conducted in parallel, in order to
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correlate the porous structural design to the effective modulus. Overall, the effective
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moduli determined from the FEA simulation vary from 0.27MPa to 3.68MPa, which
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are 40.5%±10.3% lower than those derived from compressive tests. This may due to
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the following reasons: 1) The actual Young’s modulus of TPE material is higher than
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the value that was assigned in FE model for the material property. As mentioned in
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2.4, the effective modulus of solid cylinder is used to represent the Young’s modulus
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in FE model. Confined by the principle of MEX [11,21-23], however, the solid
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cylinder is not an ideal one with 0% porosity and it may yield a lower modulus than
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ACCEPTED MANUSCRIPT the material itself. 2) Interference inside the porous structural unit occurs in the
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compressive test. As the load increases, the internal structures (Fig.1(b)) gradually
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expand and touch the surroundings [23,24]. Then the internal structures pile up,
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resulting in a larger cross sectional area and therefore a higher effective modulus.
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While in FEA model, the interference is not considered because of its algorithm. 3)
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Confined by the MEX, fracture, cracks and other flaws are inevitable in the printed
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samples. These flaws are not possible to be replicated in the FEA model [25]. 4) The
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constrains in the FEA model are not identical to the compressive test. An ideal
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encastre as in the FEA model (Fig.2) is impossible in practice. It needs to be noted
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that 3) and 4) can only prove a mismatch between the compressive tests and FEA
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simulations. Whether the results of FEA simulations are lower than those from
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compressive tests or not has not been strongly proved by 3) and 4) yet. Whatsoever,
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the tendencies shown by FEA simulations are in accordance with those of mechanical
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testing, which indicates that FEA can still be a very good candidate for parametrical
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optimization at fairly low cost and more convenience.
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As the orthogonal experiment shows, wall thickness ‘T’ and long axis ‘A’ are
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among the most sensitive factor to the effective modulus of porous structural unit
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while short axis ‘B’ and plate thickness ‘H’ impose relatively rare influence on its
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mechanical property. Several reasons contribute to this conclusion: 1) Wall thickness
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‘T’ can significantly affect the effective sectional area in porous structural units. The
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increase in wall thickness will generate more area within porous structural units to
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bear the load, which consequently yields a bigger effective modulus [26]. 2) Wall
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thickness is closely related with the printing quality via MEX technique. Since TPE
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material is flexible and sticky during the depositing process, porous structural units
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with thin wall (less than one or two times of the diameter of nozzle) are susceptible to
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the crack or flaw while porous structural units with thick wall (more than two times of
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the diameter of nozzle) are more tolerant [22]. 3) Mechanical properties of spherical
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or ellipsoid structure are remarkable influenced by eccentricity. By increasing the long
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axis ‘A’, the porous structural units will become flatter and decentralize the pressure
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concentration, which indirectly reduces the effective modulus and form a softer unit. 4)
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instead of bearing load, just transmits the load internally to the lower part. Therefore,
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the plate thickness “H” has little effect on the stress distribution, which makes it
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rather irrelevant compared with the other two parameters like the wall thickness “T”
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and the long axis “A”. In summary, geometric parameters that affect the effective
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sectional area and the internal stress distribution will significantly affect the effective
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modulus as well.
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In addition to the instruction of porous structural design, the orthogonal
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experiment also provides an optimized porous structural unit with low effective
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modulus, the orthogonal model No.10. Since porous structural units were employed to
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reduce the effective modulus of material to satisfy the demand of mapping diabetic
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foot insoles [12,13,15], the orthogonal model No.10 is one of the best option.
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In parametrical study, mathematical relationships between effective modulus and
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key geometric parameters were constructed from both the FEA simulations and
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compressive tests. Practical applications of mathematical relationships are listed as
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follow. 1) The range of effective modulus for the porous structure units was
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determined, varying from 0.21MPa to 1.76MPa, which meets the demand of reducing
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effective modulus to construct diabetic foot insoles [4,12,15]. 2) The mathematical
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relationships could be nested in a database, which is used to predict the effective
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modulus when geometric parameters are known or to generate geometric parameters
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when certain effective modulus is required. 3) Porosity is also an essential indicator of
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the density and effective modulus when compared with other porous structural units.
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Focusing on the property of ellipsoidal porous structural units, evaluation could
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be summarized. 1) The elliptical unit possesses flexibility in adjusting its geometric
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size as well as its effective modulus, which enables this porous structural unit to
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satisfy both geometric and mechanical demands of designing the diabetic insoles or
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other possible applications 2) The ellipsoidal unit could remain its linear elasticity
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under normal plantar stress conditions [12], as shown in the stress-strain curves of
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sequential models. For this reason, this porous structural unit possesses a stable
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mechanical property as an elastomer. 3) The yield strength of ellipsoidal unit is far
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[4,12]. With the increase of load, the internal structures pile up and the effective
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modulus increases, like the latter range of stress-strain curves in Fig.5(a). It is
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reasonable to assume that if the load keeps increasing, the effective modulus will
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increase along with it until it reaches the threshold of the material strength of TPE.
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This study provides a generalized foundation of porous structural design for
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adjustable gradient modulus in application of diabetic insole, which can be equally
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applicable to other designs with similar demands. In the future, emphasis will be put
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on establishing database about the mechanical properties and key geometric
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parameters of porous structural units. Next, customized diabetic foot insoles can be
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constructed by selecting the corresponding porous structural units according to the
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demanded modulus via assembly procedure, as shown in Fig.8(a) [27].
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(a)
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(b)
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Fig.8 (a) Diagram of filling customized diabetic foot insoles (without the coverage of external
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sphere); (b) Diagram of manufactured customized diabetic foot insole (with the coverage of
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external sphere)
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The cost of one pair of insole is 27 US dollars approximately, which includes
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expenses on materials (7$), equipment depreciation and maintenance (10$), labor
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(10$) etc. The cost is a lot less than the commercially available products in the market
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(80-100 dollars), which indicates good marketing opportunity of such a technique in
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the application of diabetic insole manufacturing. The major limitation of this study is that only single type of structural unit was
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studied. Further study should expand the choices of other structural units in order to
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provide more flexibility of low modulus structural design, which will be suitable for a
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wider range of application.
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5. Conclusion
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This study presents a study on the porous structural units in terms of the
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geometrical parameters and their correlation with the porosity as well as the effective
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mechanical properties. Finite element analyses were carried out on porous structural
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units, and mechanical tests were carried out on the 3D printed samples for validation
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purposes. The mathematical relationships between the effective modulus and the key
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geometrical parameters were derived and subsequently employed in the construction
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of an insole model. This study also provides a generalized foundation of porous
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structural design for adjustable gradient modulus in application of diabetic insole,
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which can be equally applicable to other designs with similar demands.
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6. Acknowledgements
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The work was supported by the National Key R&D Program of China
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[2018YFB1107000] and the Key Program of international cooperation in Shaanxi
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Province [grant number 2017KW-ZD-02].
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S2588-8404(18)30047-7
DOI:
https://doi.org/10.1016/j.ijlmm.2018.10.003
Reference:
IJLMM 31
To appear in:
International Journal of Lightweight Materials and Manufacture
Received Date: 2 June 2018 Revised Date:
22 October 2018
Accepted Date: 22 October 2018
Please cite this article as: Z. Ma, J. Lin, X. Xu, Z. Ma, L. Tang, C. Sun, D. Li, C. Liu, Y. Zhong, L. Wang, Design and 3D printing of adjustable modulus porous structures for customized diabetic foot insoles, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/ j.ijlmm.2018.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Design and 3D printing of adjustable modulus porous structures for customized diabetic foot insoles Zheng Ma1,2, Jiacheng Lin1,2, Xiaoyue Xu1,2, Ziwei Ma1,2, Lei Tang1,2, Changning Sun1,2, Dichen Li1,2, Chaozong Liu3, Yongming Zhong4, *Ling Wang1,2 State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, 710054,
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Xi'an, Shaanxi, China
School of Mechanical Engineering, Xi’an Jiaotong University, 710054, Xi’an, Shaanxi, China
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John Scale Centre for Biomedical Engineering, University College London, Royal National
Orthopaedic Hospital, Stanmore, HA74LP, HK
Shandong Weigao Pharmaceutical Co., Limited. No.20 Xingshan Road, Hi-tech District, Weihai,
Shandong, China *Corresponding Author Associate Prof. Ling Wang Email: [email protected]
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Tel.: +86 29 83395382
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Design and 3D printing of adjustable modulus porous structures for
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customized diabetic foot insoles
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Abstract Designs with adjustable gradient modulus have become necessary for
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applications with special demands such as diabetic insole, in which the contact stress
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between the foot and insole is a critical factor for ulcers development. However, since
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the adjustment of elastic modulus on certain regions of insole can hardly be achieved
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via materials selection, a porous structural unit with varying porosity becomes a
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feasible way. Therefore, porous structural units associated with adjustable effective
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modulus and porosity can be employed to construct such insoles by 3D printing
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manufacturing technology. This paper presents a study on the porous structural units
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in terms of the geometrical parameters, porosity, and their correlations with the
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effective modulus. To achieve this goal, finite element analyses were carried out on
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porous structural units, and mechanical tests were carried out on the 3D printed
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samples for validation purposes. In this case, the mathematical relationships between
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the effective modulus and the key geometrical parameters were derived and
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subsequently employed in the construction of an insole model. This study provides a
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generalized foundation of porous structural design and adjustable gradient modulus in
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application of diabetic insole, which can be equally applied to other designs with
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similar demands.
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Keywords: Adjustable gradient modulus; Porous structures; Diabetic insoles; 3D
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printing;
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1. Introduction
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Nowadays, designs with adjustable gradient modulus has become necessary for
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applications with special demands such as diabetic insole since the contact stress
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between foot and insole is a critical factor for ulcer development [1-3]. It has been
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found that the symptoms of diabetic foot are significantly alleviated by reducing and
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uniformly distributing plantar pressure, which can be achieved by the customized
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of insoles should be assigned with different modulus for localized support. Traditional
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methods, such as molding and machining, are only applicable to manufacture insoles
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with homogeneous mechanical property, which hinders the effectiveness of insoles for
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slowing down the development of ulcers [7]. Besides, such insoles are relatively
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high-cost due to the demanding requirements of selecting materials and relatively
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long designing and manufacturing period, which is hard to afford for the majority of
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patients [3,7]. Since the adjustment of modulus can hardly be achieved by materials
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selection, a porous structure with adjustable mechanical properties (effective modulus)
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becomes a feasible way.
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3D printing techniques are now widely used for the freedom of manufacturing
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materials with complex geometry [8-10], which makes them capable of
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manufacturing porous structural units for customized diabetic insoles. Among all
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kinds of 3D printing techniques, the material extrusion technique (MEX) is the most
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commonly used technique due to its low cost in instruments and materials, which
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makes it a fairly good candidate for fabrication [11]. Nevertheless, common flexible
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materials, like thermoplastic polyurethane (TPU) and thermoplastic elastomer (TPE),
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have effective moduli that are beyond the demand of alleviating plantar pressure
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[4,7,12]. In this case, porous structural units were utilized to yield lower effective
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modulus with flexible, MEX-supported materials as desired.
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Many researchers have been working on the manufacturing of customized diabetic
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insoles with 3D printing techniques. Miguel et al. presented a CAD methodology to
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design and manufacture therapeutic insoles by MEX. Feasibility of this methodology
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was verified both practically and economically by several prototypes in their latest
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paper [13]. Telfer et al. enrolled twenty participants in the comparison of 3D-printed
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insoles and subtractive milled insoles. Results show that the use of 3D-printed insoles
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yields lower peak pressures in 88% of the plantar regions of interests [14]. Though
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many studies have provided feasible methods in this field, few of them focusing on
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porous structural units (size, geometric parameter, porosity and effective modulus).
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Therefore, it’s necessary to provide a general methodology of studying porous
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structural units, in order to map customized diabetic insoles and other possible
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applications. To achieve this goal, a typical porous structural unit was selected. Based on this
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porous structural unit, a FE model was constructed to calculate its effective modulus
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[15]. The feasibility of FE model was validated by carrying out compressive tests on
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the 3D-printed porous structures. Then both compressive tests and FEA simulations
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were employed to measure the effective modulus of the porous structure. For further
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analyses in mechanical properties, orthogonal experiments were carried out to
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determine geometric parameters that are sensitive to the effective modulus of units.
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When the sensitive geometric parameters were determined, further study was carried
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out to obtain the mathematical relationships between the sensitive parameters and the
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effective modulus of porous structural units. Meanwhile, mathematical relationships
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between porosity and geometric parameters were also presented.
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2. Materials and methods
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2.1 Preparation of Porous Structural Units
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Initially, porous structural units were designed by parametric modeling. Among
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all units, the ellipsoidal structural unit (Fig.1(a).) was employed in this study because
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of its relatively satisfying 3D-printing quality and resilience under compression. By
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adjusting the geometric parameters, it can achieve a wide range of effective elastic
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modulus, which is necessary for customized diabetic insoles. In the construction of
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ellipsoidal structural units, geometric parameters were determined based on the
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character of ellipsoid structure (‘A’, the length of long axis of ellipsoidal cross section.
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‘B’, the length of short axis of ellipsoidal cross section. ‘T’, the thickness of wall of
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the hollow ellipsoid. ‘H’, the thickness of plate between layers). The side lengths of
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units vary from 4.4mm to 8.1mm and the heights of units vary from 3.3mm to 5.1mm.
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The porosity of units is in the range of 30.91% to 46.97%. For the convenience of
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printing and compressive tests, samples were arrayed of 5×5×5 replications of a single
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unit as Fig1 (b). Several printed samples are shown as Fig.1(c).
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(a)
(b)
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Fig.1. (a) Cutaway view of ellipsoidal structural unit; (b) Sketch of arrayed samples (5×5×5);
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(c) MEX printed TPE samples.
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2.2 Manufacturing Porous Structures with MEX
The desktop MEX printer used in this study is 3DP-300B (Shaanxi Hengtong
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Intelligent Machine Co., Ltd.). The printing precision is 0.4mm. Slicing files were
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generated in Cura 15.04 (Ultimaker, Netherlands). Printing settings were as fellow:
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nozzle temperature of 235℃, nozzle diameter of 0.4mm, layer thickness of 0.2mm,
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printing speed of 30mm/min, and filling rate of 100%. TPE filament (eLastic ,
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Shenzhen Esun Industrial Co., Ltd ) with diameter of 1.75mm±0.05mm was used in
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this study.
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2.3 Compressive Test
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Compressive tests were conducted with electromechanical universal testing
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machine (ETM103A from Shenzhen Wance Testing Machine Co.). During
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compression, samples were compressed at a constant speed of 1mm/min, with a
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sampling frequency of 120Hz. Tests were terminated when the force reached the
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upper limitation of 200N, in order to keep the samples within linear elastic range and
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avoid plastic deformation or internal structure interference. Three samples (N=3) were
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tested for each group, and the average value was determined. Average length of each
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sample was measured with caliper. The experimental effective elastic modulus of the
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samples can be obtained from the slop of stress-strain curves, which is expressed in
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Eq. (1).
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The equation [16] employed in effective modulus calculation:
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# 1 111
where F is the external loading, A is the nominal cross-sectional area, h is the original
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height,
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the stress-strain curve.
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2.4 Finite Element Analysis (FEA)
h is the compressive displacement and k is the slope of the elastic range in
Compression testing simulations of various porous structure models were carried
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out via FEA method in ABAQUS 6.14-4 (Dassault, France), as shown in Fig.2.
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Models were created in SolidWorks 2017 SP4.0 (Dassault, France) and converted into
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IGES format before imported into ABAQUS. Each porous structural unit was
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free-meshed by tetrahedral element with an approximate global size of 2mm [17].
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According to the simulation of ordinary walking [12], the stresses of plantar were
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within the linear elastic range of TPE material. Therefore, the material in FEA model
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can be considered as an elastomer with two key factors, Young’s modulus and Poisson
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ratio. According to the compression testing standard ASTM D695 [18], solid cylinders
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with diameter of 12.7mm, height of 25.4mm were printed under the printing settings
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listed above, in order to determine the mechanical property of TPE material. After
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calculation, the Young’s modulus of TPE is 14.525MPa and Poisson’s ration is 0.3.
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To authentically simulate the compressive tests, the boundary and loading
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conditions of the FE model were consistent with those applied in the compressive
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tests [12,15]. Since the base of the porous structural unit was fully constrained for any
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degree of freedom during the compressive test, the boundary condition of the bottom
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layer was set up accordingly as fully constrained (Encastre) for the FE model. The
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surface of the porous structural unit was coupled with the reference point (RP1) that is
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located at the center. An axial compressive load of 200N, perpendicular to the surface,
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was applied via RP1. Thus, every point on the surface was under the same
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compressive load as RP-1, which is equal to a uniformly distributed load of 200N
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over the surface. Finally, the general compressive displacement that was parallel to
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the load was calculated. With the results of deforming displacement, the effective
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modulus of porous structural units was calculated by Eq. (1).
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Fig.2 FE model set-up as representative of the effective model of the porous structural units
2.5 Orthogonal Experiments
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In order to find out the sensitive factors that could have dominating influence on
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mechanical properties, orthogonal experiments were carried out at first. Based on the
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guidelines for orthogonal experiments [19,20], four factors (wall thickness ‘T’, long
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axis ‘A’, short axis’ B’ and plate thickness ‘H’) were chosen as geometrical
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parameters from the cutaway view in Fig.1.(a). And 3 levels were set for each factor,
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as shown in Table.1. Orthogonal experiments were arranged according to L9 (3^4).
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Table.1 Level settings in orthogonal experiments (wall thickness ‘T’, long axis ‘A’, short axis’ B’
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and plate thickness ‘H’)
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Factors
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2
3
T/mm
0.4
0.6
0.8
A/mm
3.5
4.5
5.5
B/mm
2.5
3
3.5
H/mm
0.4
0.6
0.8
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Levels
All samples were printed using the mentioned printing settings and effective
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modulus was determined from both the compressive tests and the FEA simulations.
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By gathering and analyzing all testing results, the level of sensitivity of each factor
153
was determined by the range, calculated from Eq. (2) - (4).
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The dominating equations [19] are listed below (i, j=1,2,3) ,
!"
the value of factor i level j # 2
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$, (
repetition of level i
# 3
)*+,$ ," , $ ,- , $ , . / )01 $ ," , $ ,- , $ , # 4
denotes the estimating value for the level j of factor i; $ , represents the
where
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overall mean value for the level j of factor i; ( stands for the range of overall mean
157
value for factor i.
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2.6 Parametrical Study
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Based on the previous tests, two of the most effective factors, wall thickness ‘T’
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and long axis ‘A’, were chosen as the sensitive factors in the following study, and
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their effects were investigated thoroughly in sequential manner. The range of ‘T’ was
162
set from 0.4mm to 0.9mm at an interval of 0.1mm to generate six wall thickness
163
sequential models; likewise, the range of ‘A’ was set from 3.5mm to 6.5mm at an
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interval of 0.5mm to generate 7 long axis sequential models. All generated models
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were printed out under the same printing settings and were put into mechanical testes
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to determine the effective modulus.
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3. Results
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Mechanical tests and FEA simulations were conducted according to the design of
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orthogonal experiment and parametrical study. Typical result of one instance with the
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largest deformation is presented in Fig.3(a) as a comparison between the mechanical
171
test and FEA simulation. Displacement nephogram of FEA model under ultimate load
172
condition is expressed in Fig.3(b). The original height of sample (h) is 17.4mm. The
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compressive displacement of compressive test ( h) is 4.95mm and the compressive
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displacement of FEA simulation ( h’) is 5.81mm. Fairly good agreement has been
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achieved in both methods in terms of the maximum displacement.
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(a)
(b)
Fig.3 (a) Contrasts between compressive tests and FEM simulations; (b) Displacement nephogram
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under ultimate load condition
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Table.2. Effective modulus results of FEA simulations and compression tests of orthogonal models
Effective modulus from compressive tests
1
2
3
4
5
6
7
8
9
10
1.964
0.782
0.489
3.975
2.472
1.483
5.768
4.216
2.261
0.427
±0.16 ±0.06 ±0.04 ±0.33 ±0.18 ±0.11 ±0.41 ±0.35 ±0.13 ±0.03 1.083
0.511
0.342
2.204
1.101
0.759
3.684
2.779
1.449
0.275
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Effective modulus from FEA
The effective modulus of FEA simulations and compression tests for orthogonal
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models are compared in Table.2. Calculated from Eq. (2) - (4), the range of each
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factor from two methods was determined and portrayed in Fig.4. As indicated in the
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diagram, the order of sensitivity for the four factors was: wall thickness ‘T ’> long
185
axis ‘A’ > plate thickness ‘H’ > short axis ‘B’. The optimized result [19] associated
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with the smallest effective modulus was determined as well. Orthogonal model No.10
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denotes the optimized model set-up (A=5.5mm, B=3mm, T=0.4mm, H=0.4mm).
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Geometric Parameters
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T
0.0
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1.0
1.5
2.0
2.5
3.0
3.5
Ranges
Fig.4. Factor ranges in orthogonal experiments
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0.5
(Plate thickness ‘H’; Short axis ‘B’; Long axis ‘A’; Wall thickness ‘T’)
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From the contrasts between two methods’ results of orthogonal models, results
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can be summarized that: 1) These two sensitivity sequences of ellipsoidal models’
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parameters in descending order are completely identical. 2) Orthogonal model No.10
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has been proved to possess the smallest effective modulus among all orthogonal series
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models via FEA simulation or compressive test.
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Based on the conclusion of orthogonal experiments, two geometric parameters,
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wall thickness ‘T’ and long axis ‘A’, were chosen to conduct parametrical study.
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Stress-strain curves of ‘T’ sequential models are shown in Fig.5(a). Images of
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samples under different strain conditions in compression are expressed in Fig.5(b). 0.15 kT=0.8=1.279
kT=0.6=0.620
Strain
0.05
0.1
0.2
0.4
0.09
T=0.4
kT=0.4=0.215 0.06
T=0.6
Unit with T=0.4mm Unit with T=0.6mm Unit with T=0.8mm Liner Fitting
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Fig.5.(a) Stress –stain curves of ‘T’ sequential models; (b) Images of the ellipsoidal models under
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different strain conditions
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After data fitting, the mathematical relationships between wall thickness and
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effective modulus were obtained, as shown in Fig.6(a). In the same way, the effect of
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the long axis A was also investigated in Fig.6(b). Porosity for various parametrical
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model was also determined and correlated to the effective modulus, as presented in
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Fig.7(a) and Fig.7(b).
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y=3.8x2-1.9x+0.4 R²=0.9991
0.5
y=3.6x2-2.4x+0.6 R²=0.9996
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0.4
0.6
Effective Modulus (MPa)
Mechanical Compressive Test
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1.5
FEA simulation
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FEA Simulation Mechanical Compressive Test
1.0
y=0.1x2-1.6x+5.1 R²=0.9836
0.5
y=0.1x2-1.4x+4.7 R²=0.9746 0.0
0.8
Wall Thickness 'T' (mm)
1
3
3.5
4
4.5
5
5.5
6
6.5
7
Long Axis 'A' (mm)
(a)
(b)
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Fig.6 (a) The mathematical relationship between wall thickness ‘T’ and effective modulus (‘T’ is
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changeable while other parameters are A=6.5mm, B=3mm, H=0.5mm); (b) The mathematical
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relationship between long axis ‘A’ and effective modulus (‘A’ is changeable while other
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parameters are T=0.4mm, B=3mm, H=0.5mm)
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45% y=-0.034x2+0.37x+0.17
1.2
R²=0.9982
40%
0.8
35% y=3.8x2-1.9x+0.4 R²=0.9991
0.4
30%
0.0
25%
Porosity 1.6
45%
1.2
40% y=0.004x2-0.06x+0.5 R²= 0.9981
0.8 0.4
35% 30%
y=0.1x2-1.6x+4.7 R²=0.9746
0.0
25%
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
215 216
50%
Porosity
Porosity 1.6
Effective Modulus
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Effective modulus(MPa)
Effective Modulus
Porosity
Effective modulus(MPa)
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Wall Thickness 'T' (mm)
Long Axia 'A' (mm)
(a)
(b)
Fig.7 (a) The mathematical relationships between wall thickness ‘T’ and mechanical properties
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(porosity and effective modulus). (b) The mathematical relationships between long axis ‘A’ and
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mechanical properties (porosity and effective modulus).
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4. Discussion
In this study, a FE model was developed to study the mechanical properties of
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porous structural units. Mesh convergence study was carried out first to guarantee the
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accuracy in FE calculation [15]. Since it is a static process, time integration is
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irrelevant to the result. Focus should be paid on the meshing size. In the analysis, the
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approximate global size ranges from 0.5mm to 3.0mm with an interval of 0.5mm.
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Relative errors of these six groups are less than 5%. Because the proper setting of
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meshing size is determined by the trade-off between accuracy and time span, the
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approximate global size of 2.0mm is a feasible option.
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Compressive tests and FEA simulations were conducted in parallel, in order to
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correlate the porous structural design to the effective modulus. Overall, the effective
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moduli determined from the FEA simulation vary from 0.27MPa to 3.68MPa, which
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are 40.5%±10.3% lower than those derived from compressive tests. This may due to
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the following reasons: 1) The actual Young’s modulus of TPE material is higher than
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the value that was assigned in FE model for the material property. As mentioned in
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2.4, the effective modulus of solid cylinder is used to represent the Young’s modulus
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in FE model. Confined by the principle of MEX [11,21-23], however, the solid
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cylinder is not an ideal one with 0% porosity and it may yield a lower modulus than
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ACCEPTED MANUSCRIPT the material itself. 2) Interference inside the porous structural unit occurs in the
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compressive test. As the load increases, the internal structures (Fig.1(b)) gradually
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expand and touch the surroundings [23,24]. Then the internal structures pile up,
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resulting in a larger cross sectional area and therefore a higher effective modulus.
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While in FEA model, the interference is not considered because of its algorithm. 3)
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Confined by the MEX, fracture, cracks and other flaws are inevitable in the printed
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samples. These flaws are not possible to be replicated in the FEA model [25]. 4) The
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constrains in the FEA model are not identical to the compressive test. An ideal
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encastre as in the FEA model (Fig.2) is impossible in practice. It needs to be noted
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that 3) and 4) can only prove a mismatch between the compressive tests and FEA
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simulations. Whether the results of FEA simulations are lower than those from
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compressive tests or not has not been strongly proved by 3) and 4) yet. Whatsoever,
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the tendencies shown by FEA simulations are in accordance with those of mechanical
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testing, which indicates that FEA can still be a very good candidate for parametrical
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optimization at fairly low cost and more convenience.
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As the orthogonal experiment shows, wall thickness ‘T’ and long axis ‘A’ are
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among the most sensitive factor to the effective modulus of porous structural unit
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while short axis ‘B’ and plate thickness ‘H’ impose relatively rare influence on its
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mechanical property. Several reasons contribute to this conclusion: 1) Wall thickness
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‘T’ can significantly affect the effective sectional area in porous structural units. The
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increase in wall thickness will generate more area within porous structural units to
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bear the load, which consequently yields a bigger effective modulus [26]. 2) Wall
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thickness is closely related with the printing quality via MEX technique. Since TPE
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material is flexible and sticky during the depositing process, porous structural units
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with thin wall (less than one or two times of the diameter of nozzle) are susceptible to
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the crack or flaw while porous structural units with thick wall (more than two times of
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the diameter of nozzle) are more tolerant [22]. 3) Mechanical properties of spherical
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or ellipsoid structure are remarkable influenced by eccentricity. By increasing the long
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axis ‘A’, the porous structural units will become flatter and decentralize the pressure
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concentration, which indirectly reduces the effective modulus and form a softer unit. 4)
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instead of bearing load, just transmits the load internally to the lower part. Therefore,
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the plate thickness “H” has little effect on the stress distribution, which makes it
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rather irrelevant compared with the other two parameters like the wall thickness “T”
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and the long axis “A”. In summary, geometric parameters that affect the effective
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sectional area and the internal stress distribution will significantly affect the effective
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modulus as well.
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In addition to the instruction of porous structural design, the orthogonal
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experiment also provides an optimized porous structural unit with low effective
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modulus, the orthogonal model No.10. Since porous structural units were employed to
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reduce the effective modulus of material to satisfy the demand of mapping diabetic
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foot insoles [12,13,15], the orthogonal model No.10 is one of the best option.
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In parametrical study, mathematical relationships between effective modulus and
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key geometric parameters were constructed from both the FEA simulations and
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compressive tests. Practical applications of mathematical relationships are listed as
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follow. 1) The range of effective modulus for the porous structure units was
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determined, varying from 0.21MPa to 1.76MPa, which meets the demand of reducing
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effective modulus to construct diabetic foot insoles [4,12,15]. 2) The mathematical
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relationships could be nested in a database, which is used to predict the effective
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modulus when geometric parameters are known or to generate geometric parameters
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when certain effective modulus is required. 3) Porosity is also an essential indicator of
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the density and effective modulus when compared with other porous structural units.
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Focusing on the property of ellipsoidal porous structural units, evaluation could
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be summarized. 1) The elliptical unit possesses flexibility in adjusting its geometric
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size as well as its effective modulus, which enables this porous structural unit to
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satisfy both geometric and mechanical demands of designing the diabetic insoles or
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other possible applications 2) The ellipsoidal unit could remain its linear elasticity
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under normal plantar stress conditions [12], as shown in the stress-strain curves of
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sequential models. For this reason, this porous structural unit possesses a stable
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mechanical property as an elastomer. 3) The yield strength of ellipsoidal unit is far
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[4,12]. With the increase of load, the internal structures pile up and the effective
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modulus increases, like the latter range of stress-strain curves in Fig.5(a). It is
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reasonable to assume that if the load keeps increasing, the effective modulus will
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increase along with it until it reaches the threshold of the material strength of TPE.
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This study provides a generalized foundation of porous structural design for
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adjustable gradient modulus in application of diabetic insole, which can be equally
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applicable to other designs with similar demands. In the future, emphasis will be put
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on establishing database about the mechanical properties and key geometric
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parameters of porous structural units. Next, customized diabetic foot insoles can be
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constructed by selecting the corresponding porous structural units according to the
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demanded modulus via assembly procedure, as shown in Fig.8(a) [27].
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Fig.8 (a) Diagram of filling customized diabetic foot insoles (without the coverage of external
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sphere); (b) Diagram of manufactured customized diabetic foot insole (with the coverage of
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external sphere)
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The cost of one pair of insole is 27 US dollars approximately, which includes
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expenses on materials (7$), equipment depreciation and maintenance (10$), labor
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(10$) etc. The cost is a lot less than the commercially available products in the market
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(80-100 dollars), which indicates good marketing opportunity of such a technique in
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the application of diabetic insole manufacturing. The major limitation of this study is that only single type of structural unit was
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studied. Further study should expand the choices of other structural units in order to
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provide more flexibility of low modulus structural design, which will be suitable for a
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wider range of application.
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5. Conclusion
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This study presents a study on the porous structural units in terms of the
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geometrical parameters and their correlation with the porosity as well as the effective
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mechanical properties. Finite element analyses were carried out on porous structural
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units, and mechanical tests were carried out on the 3D printed samples for validation
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purposes. The mathematical relationships between the effective modulus and the key
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geometrical parameters were derived and subsequently employed in the construction
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of an insole model. This study also provides a generalized foundation of porous
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structural design for adjustable gradient modulus in application of diabetic insole,
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which can be equally applicable to other designs with similar demands.
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6. Acknowledgements
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The work was supported by the National Key R&D Program of China
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[2018YFB1107000] and the Key Program of international cooperation in Shaanxi
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Province [grant number 2017KW-ZD-02].
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