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Computer modeling and testing of structural metamaterials
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Procedia online Computer 00 (2019) 000–000 Available at Science www.sciencedirect.com Procedia Computer Science 00 (2019) 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Computer Science 159 (2019) 2543–2550
23rd International Conference on Knowledge-Based and Intelligent Information & Engineering 23rd International Conference on Knowledge-Based Systems and Intelligent Information & Engineering Systems
Computer modeling and testing of structural metamaterials Computer modeling and testing of structural metamaterials T. Krolikowskiaa*, R. Knitteraa, A. Blazejewskiaa T. Krolikowski *, R. Knitter , A. Blazejewski FTaE, Koszalin University of Technology, Koszalin 75-453, Poland FTaE, Koszalin University of Technology, Koszalin 75-453, Poland
a
a
Abstract Abstract The experiments and computer research on the issue of metamaterials [6-9,11,14] allow a dedicated parts or even whole devices The experiments and computer research the issue of metamaterials [6-9,11,14] allow a dedicated parts or even whole devices designing using 3D CAD technology andon Finite Element Methods. Research and their effects aim at replacing the mechanisms by designing using 3D perform CAD technology andtechnology Finite Element and their effects replacing the by means of elements by additive withMethods. different Research internal geometry in termsaim of atdimensions andmechanisms shapes, while means of elements by additive different internal geometry in order terms to of do dimensions and shapes, while maintaining identicalperform dimensions in suchtechnology a way that with the desired abbreviated motion. In that the adequate computer maintaining identical dimensions in such prototyping a way that the desired The abbreviated motion. In order doisthat the adequate computer model [15-24] using for fast and effective is desired. initial steps to achieve thistoaim shown in this work. model [15-24] using for fast and effective prototyping is desired. The initial steps to achieve this aim is shown in this work. © 2019 The Author(s). Published by Elsevier B.V. © 2019 2019 The Authors. Published by Elsevier B.V. © The Author(s). Published Elsevier B.V. This is an open access article underbythe CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. Peer-review under responsibility of KES International. Peer-review under responsibility of KES International. Keywords: metamaterial, structrure, stand, numerical methods, FEM Keywords: metamaterial, structrure, stand, numerical methods, FEM
1. Introduction 1. Introduction The fused deposition modeling (FDM) technology is included in the family of incremental manufacturing The fused Its deposition modeling (FDM) included the family of incremental manufacturing technologies. development began with the technology invention ofisStatasys Ltd.,inpatented in 1989 [10]. The FDM technology technologies. Its development- began theproduction invention of Statasys Ltd.,widespread, patented in 1989 [10].on The technology uses polymer thermoplastics plasticswith of the class, the most available theFDM market in many uses polymer thermoplastics - plastics of the production class, the most widespread, available on the market many varieties and colors is poly (acrylonitrile-co-butadiene-co-styrene) (ABS). The rapid development of this in method varieties the anduse colors is poly (acrylonitrile-co-butadiene-co-styrene) (ABS). Theor rapid this method allowed of new materials such as PET-G, PLA, PVA, TPU, PEEK HIPSdevelopment used for theofproduction of allowed in themore use complex of new materials supports models. such as PET-G, PLA, PVA, TPU, PEEK or HIPS used for the production of supports more complex models. is very popular, the effect is, among others, availability on the market of cheap In the in present, FDM technology In the present, FDM[1-5], technology verynot popular, the effect is, among others, availability on the cheap consumer 3D printers whichisdoes diminish its usability in industrial applications. Themarket pursuitof of the consumer 3D printers [1-5], which does not diminish its usability in industrial applications. The pursuit of the
* Corresponding author. Tel.: +48 601959023; fax: +48 94 342-59-63. address:author. [email protected] * E-mail Corresponding Tel.: +48 601959023; fax: +48 94 342-59-63. E-mail address: [email protected] 1877-0509 © 2019 The Author(s). Published by Elsevier B.V. This is an open access underPublished the CC BY-NC-ND 1877-0509 © 2019 Thearticle Author(s). by Elsevier license B.V. (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 10.1016/j.procs.2019.09.429
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possibility of producing utility objects with them forces the development of methods and computational tools that allow the anticipation or design of desired product features. In recent years, many papers have been published regarding the testing of mechanical properties of structures manufactured in FDM technology from polymeric materials. Dawoud M. et al. [5] compared the mechanical properties of standard samples produced by means of injection molding and incremental technology. The authors have broadly discussed the influence of both positive or negative values of the gap between adjacent fibers of the material and the angle determining the direction of material application, distinguishing between individual layers of the product. Similar research has been published by Sood A.K. and co-workers [12,13]. In their abdications, they also took into account the height of the layer and the orientation of the produced sample in the working space of the machine, however, they did not take into account the negative values of the gap between adjacent fibers. The authors [12] used the answer surface method, using the results of the planned experiment. The same team of authors [13] also presented a different approach to prediction of mechanical properties, based on neural networks, and demonstrated their greater ability to model non-linear features of the product. Casavola C. et al. [4] used the classic theory of laminates to prepare the structure model produced in FDM technology. In the studies, they confirmed the orthotropic character of the strength properties of the products. The aim of this work is to initiate discussions on metamaterial mechanisms carried out with the additive method and to develop and verify a parametric numerical model to predict the mechanical properties of structures developed and designed thanks to advanced CAD and FEM methods. The development of the method of designing metamaterial structures in the model will contribute to the growth of industry demand for elements made using 3D printing to replace the classic mechanical assemblies using printed models with developed properties. 2. Test sample geometry and material characteristics In the first phase of the research, it was necessary to examine the material and confirm the hypothesis about the influence of internal structures on mechanical properties. The samples made of TPU rubber-like material with the following properties: Table 1. Specification of material used for testing Properties
ASTM No
Units
Material
Hardness Density Water Absorption Mold Shrinkage Tensile Stress at 10% Strain Tensile Stress at break Elongation at break Flexural Modulus Tear strength Izod impact strenth/notcher Resilience Melting point HDT Resistance to Surface abrasion
D2240 D570 D955 D638 D638 D638 D790 D1004 D256 D2632 D3418 D648 D1044 (wheel H-19)
Shore D g/cm3 % % kg/cm2 kg/cm2 % kg/cm2 kN/m kg*cm/cm % OC OC Mg
40 1,16 0,6 0,8 44 270 680 680 115 N.B. 57 157 70 95
T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550
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Fig. 1. Samples intended for testing a) full sample b) sample with metamaterial structure.
Fig. 2. Tensile strength diagram of a sample printed using FDM technology with a metamaterial structure and a full infill.
Because the geometric structure created in FDM technology exhibits orthotropic properties, according to Hooke's generalized law, constitutive equations determining the mechanical properties of this structure can be written in the form of the following matrix equation:
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T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
(1)
where: σ ij and τij - components of the stress vector, ε ij and γ ij - components of the strain vector (i and j can take the values 1, 2 or 3), and the stiffness matrix is a symmetric matrix containing 12 independent quantities: three Young modules: E11, E22, E33, three Kirchhoff modules: G23, G31, G12, and six Poisson modules: v21, v31, v12, v32, v13, v23, where for FDM technology: v12 = v21, v13 = v31, v23 = v32. 3. Computer model of the samples The computer model, which has been prepared using FEM method [. The material properties introduce in the model is not reflect orthotropic properties directly. It results from the lack of information about values of Young, Kirchhoff and Poison module. Therefore, it is assumed linear elastic isotropic material model. The plasticity of this material is assumed in order to get strength diagram with two ranges (Fig. 2). First range assume that the material is linear isotropic with one Young module value and second range with different Young modulus value. These modules are calculated according with following formula [8]: E1=exp(((H+50)0.0235)-0.6403) And the second as follow [8]: E2= ((0.0981(56+7.62336H))/(0.137505(254-2.54*H))) Where H is a hardness of material gives by producer. In this case the material with hardness H=40 is applied. The Poison module value is assumed about 0.4. The initial yield stress (von Mises stress) is 7e6 MPa. Tensile stress at break for this particular material, gives by the producer, is 2.7e7 Pa. In the computer model above parameters is introduced and the experiment results are compared. Tensile strength diagram in the case of metamaterial structure probe (honey sample) and 100% infill probe introduced in the model shows Fig. 3. The dash lines indicate elongation at break takes from experiments (compare also Table 1).
T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
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Fig. 3. Tensile strength diagram of metamaterial structure probe and 100% infill probe drown using computer model.
The computer model gives the opportunity to calculate many more parameters than experiment. It is true within the verified model range, as it is done above (Fig. 3.). The dash lines indicate in Fig.3 the visible linear ranges of the tensile strength characteristics show in Fig.2. Beyond this range the characteristics show force-elongation fluctuation (material flow). The example results, such as: von Mises stress and maximal elongation are show in the below figures. In the Fig. 4 and Fig. 5, there are results in the case infill probe and in Fig. 6 and Fig.7 honey structure probe.
Fig. 4. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of 100% infill probe
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et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, T. R.Krolikowski Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
Fig. 5. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of 100% infill probe.
Fig. 6. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of honey structure probe.
T. R. Krolikowski al. / Procedia Computer ScienceScience 159 (2019) 2543–2550 T. Krolikowski, Knitter, A.etBlazejewski/ Procedia Computer 00 (2019) 000–000
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Fig. 7. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of honey structure probe.
In the figures Fig. 4,5 and Fig. 6,7 the applied forces Fn in N, acting in the direction X (see axes in figures), are chosen increasingly. The force values Fn are selected from the range, where tensile strength diagram is linear. The deformation in a form of displacement in mm are shown in real scale. The point of maximal displacement is additionally indicated as abbreviation max: with the particular value of this displacement. The right-side colour bar shows values of stress in Pa 4. Conclusions The computer modelling using FEM method and the experimental test show that metamaterials can be introduce relatively easy in designing process, even though these materials properties are described as the orthotropic. Linear elastic properties with plasticity give acceptable results. The tensile strength diagrams both, in case of the experiments and modelling, are converged, considering their values and the shapes. Some problems arise, when the material flow range is reached in the model. In this work it is taken from experiments and marked as the dash line. This specific area modelling in the tensile strength problems is under the further consideration. References [1] A. Mix and A. (2011) Giacomin, "Standardized Polymer Durometry" Journal of Testing and Evaluation 39 (4): 696-705., Journal of Testing and Evaluation, 39 (4): 1–10. [2] Vinay H. Ba, Govindarajub H.K., Prashanth Banakarc. 2017 “AMMMT 2016 Experimental Study on Mechanical Properties of Polymer Based Hybrid Composite Materials Today”: Proceedings. 4 (2017): s. 10904–10912. [3] Campbell I., Bourell D., Gibson I. (2012) “Additive manufacturing: rapid prototyping comes of age” Rapid Prototyping Journal 18 (4): 255258. [4] Casavola C., Cazzato A., Moramarco V. 2016 “Orthotropic mechanical properties of fused deposition modelling parts described by classical laminate theory” Materials & Design 90: 453-458. [5] Dawoud M., Taha I., Ebeid S.J. 2016 “Mechanical behaviour of ABS: An experimental study using FDM and injection moulding techniques” Journal of Manufacturing Processes 21: 39-45. [6] Ion A., Frohnhofen J., Wall L., Kovacs R., Alistar M., Lindsay J., Lopes P., Chen H., Baudisch P., Hasso 2016 “Metamaterial Mechanisms” UIST '16, October 16 - 19, 2016, Tokyo, Japan 529-539 [7] Kinsler Paul., McCall Martin W. 2015 “The futures of transformations and metamaterials” Photonic and Nanostructures – Fundamentals and Applications 15: 10-23 [8] Knitter R., Królikowski T., (2018) „Metamateriały mechaniczne wytwarzane w sposób przyrostowy” Mechanik 7 :502-504
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[9] Novakova-Marcincinova L., Novak-Marcincin J. 2012 “Testing of Materials for Rapid Prototyping Fused Deposition Modelling Technology” International Journal of Industrial and Manufacturing Engineering 6 (10): 2082-2085. [10] Pat. US 5 121 329 (1989). [11] Qi, H. J., Joyce, K., Boyce, M. C. (2003), Durometer hardness and the stress-strain behavior of elastomeric materials, Rubber Chemistry and Technology, 76(2), pp. 419–435. [12] Sood A.K., Ohdar R.K., Mahapatra S.S. 2012 “Experimental investigation and empirical modelling of FDM process for compressive strength improvement” Journal of Advanced Research 3 (1): 81-90. [13] Sood A.K., Ohdar R.K., Mahapatra S.S. 2010 “Parametric appraisal of mechanical property of fused deposition modelling processed parts” Materials & Design 31 (1): 287-295. [14] Xianglong Yu, Ji Zhou,Haiyi Liang,Zhengyi Jiang, Lingling Wu, Mechanical metamaterials associated with stiffness, rigidity and compressibility:a brief review, JMPS 486, 12/2017, Progress in Material Science [15] P. Stepien, B. Balasz, T. Szatkiewicz, T. Krolikowski. (2006) „Application of Artificial Intelligence Algorithms for the Modeling of the Surfaces of Abrasive Grains” 4th International Industrial Simulation Conference 2006, ISC 2006: 265-277 [16] B. Balasz, T. Krolikowski. (2007) “Advanced kinematic-geometrical model of grinding processes” 5th International Industrial Simulation Conference 2007, ISC 2007: 137-141 [17] Jankowski, J., Hamari, J., & Wątróbski, J. (2019). A gradual approach for maximising user conversion without compromising experience with high visual intensity website elements. Internet Research, 29 (1): 194-217 [18] 2 Karczmarczyk, A., Jankowski, J., & Wątróbski, J. (2018). Multi-criteria decision support for planning and evaluation of performance of viral marketing campaigns in social networks. PloS one, 13 (12), e0209372. [19] Wątróbski, J., Ziemba, E., Karczmarczyk, A., & Jankowski, J. (2018). An index to measure the sustainable information society: the Polish households case. Sustainability, 10 (9): 3223. [20] Jankowski, J., Zioło, M., Karczmarczyk, A., & Wątróbski, J. (2017). Towards sustainability in viral marketing with user engaging supporting campaigns. Sustainability, 10 (1): 15. [21] Wątróbski, J. (2016). Outline of multicriteria decision-making in green logistics. Transportation Research Procedia, 16: 537-552. [22] Faizi, S., Rashid, T., Sałabun, W., Zafar, S., & Wątróbski, J. (2018). Decision making with uncertainty using hesitant fuzzy sets. International Journal of Fuzzy Systems, 20 (1): 93-103. [23] Faizi, S., Sałabun, W., Rashid, T., Wątróbski, J., & Zafar, S. (2017). Group decision-making for hesitant fuzzy sets based on characteristic objects method. Symmetry, 9 (8): 136. [24] Sałabun, W., & Piegat, A. (2017). Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome. Artificial Intelligence Review, 48 (4): 557-571.
ScienceDirect ScienceDirect
Procedia online Computer 00 (2019) 000–000 Available at Science www.sciencedirect.com Procedia Computer Science 00 (2019) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Computer Science 159 (2019) 2543–2550
23rd International Conference on Knowledge-Based and Intelligent Information & Engineering 23rd International Conference on Knowledge-Based Systems and Intelligent Information & Engineering Systems
Computer modeling and testing of structural metamaterials Computer modeling and testing of structural metamaterials T. Krolikowskiaa*, R. Knitteraa, A. Blazejewskiaa T. Krolikowski *, R. Knitter , A. Blazejewski FTaE, Koszalin University of Technology, Koszalin 75-453, Poland FTaE, Koszalin University of Technology, Koszalin 75-453, Poland
a
a
Abstract Abstract The experiments and computer research on the issue of metamaterials [6-9,11,14] allow a dedicated parts or even whole devices The experiments and computer research the issue of metamaterials [6-9,11,14] allow a dedicated parts or even whole devices designing using 3D CAD technology andon Finite Element Methods. Research and their effects aim at replacing the mechanisms by designing using 3D perform CAD technology andtechnology Finite Element and their effects replacing the by means of elements by additive withMethods. different Research internal geometry in termsaim of atdimensions andmechanisms shapes, while means of elements by additive different internal geometry in order terms to of do dimensions and shapes, while maintaining identicalperform dimensions in suchtechnology a way that with the desired abbreviated motion. In that the adequate computer maintaining identical dimensions in such prototyping a way that the desired The abbreviated motion. In order doisthat the adequate computer model [15-24] using for fast and effective is desired. initial steps to achieve thistoaim shown in this work. model [15-24] using for fast and effective prototyping is desired. The initial steps to achieve this aim is shown in this work. © 2019 The Author(s). Published by Elsevier B.V. © 2019 2019 The Authors. Published by Elsevier B.V. © The Author(s). Published Elsevier B.V. This is an open access article underbythe CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. Peer-review under responsibility of KES International. Peer-review under responsibility of KES International. Keywords: metamaterial, structrure, stand, numerical methods, FEM Keywords: metamaterial, structrure, stand, numerical methods, FEM
1. Introduction 1. Introduction The fused deposition modeling (FDM) technology is included in the family of incremental manufacturing The fused Its deposition modeling (FDM) included the family of incremental manufacturing technologies. development began with the technology invention ofisStatasys Ltd.,inpatented in 1989 [10]. The FDM technology technologies. Its development- began theproduction invention of Statasys Ltd.,widespread, patented in 1989 [10].on The technology uses polymer thermoplastics plasticswith of the class, the most available theFDM market in many uses polymer thermoplastics - plastics of the production class, the most widespread, available on the market many varieties and colors is poly (acrylonitrile-co-butadiene-co-styrene) (ABS). The rapid development of this in method varieties the anduse colors is poly (acrylonitrile-co-butadiene-co-styrene) (ABS). Theor rapid this method allowed of new materials such as PET-G, PLA, PVA, TPU, PEEK HIPSdevelopment used for theofproduction of allowed in themore use complex of new materials supports models. such as PET-G, PLA, PVA, TPU, PEEK or HIPS used for the production of supports more complex models. is very popular, the effect is, among others, availability on the market of cheap In the in present, FDM technology In the present, FDM[1-5], technology verynot popular, the effect is, among others, availability on the cheap consumer 3D printers whichisdoes diminish its usability in industrial applications. Themarket pursuitof of the consumer 3D printers [1-5], which does not diminish its usability in industrial applications. The pursuit of the
* Corresponding author. Tel.: +48 601959023; fax: +48 94 342-59-63. address:author. [email protected] * E-mail Corresponding Tel.: +48 601959023; fax: +48 94 342-59-63. E-mail address: [email protected] 1877-0509 © 2019 The Author(s). Published by Elsevier B.V. This is an open access underPublished the CC BY-NC-ND 1877-0509 © 2019 Thearticle Author(s). by Elsevier license B.V. (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 10.1016/j.procs.2019.09.429
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T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
possibility of producing utility objects with them forces the development of methods and computational tools that allow the anticipation or design of desired product features. In recent years, many papers have been published regarding the testing of mechanical properties of structures manufactured in FDM technology from polymeric materials. Dawoud M. et al. [5] compared the mechanical properties of standard samples produced by means of injection molding and incremental technology. The authors have broadly discussed the influence of both positive or negative values of the gap between adjacent fibers of the material and the angle determining the direction of material application, distinguishing between individual layers of the product. Similar research has been published by Sood A.K. and co-workers [12,13]. In their abdications, they also took into account the height of the layer and the orientation of the produced sample in the working space of the machine, however, they did not take into account the negative values of the gap between adjacent fibers. The authors [12] used the answer surface method, using the results of the planned experiment. The same team of authors [13] also presented a different approach to prediction of mechanical properties, based on neural networks, and demonstrated their greater ability to model non-linear features of the product. Casavola C. et al. [4] used the classic theory of laminates to prepare the structure model produced in FDM technology. In the studies, they confirmed the orthotropic character of the strength properties of the products. The aim of this work is to initiate discussions on metamaterial mechanisms carried out with the additive method and to develop and verify a parametric numerical model to predict the mechanical properties of structures developed and designed thanks to advanced CAD and FEM methods. The development of the method of designing metamaterial structures in the model will contribute to the growth of industry demand for elements made using 3D printing to replace the classic mechanical assemblies using printed models with developed properties. 2. Test sample geometry and material characteristics In the first phase of the research, it was necessary to examine the material and confirm the hypothesis about the influence of internal structures on mechanical properties. The samples made of TPU rubber-like material with the following properties: Table 1. Specification of material used for testing Properties
ASTM No
Units
Material
Hardness Density Water Absorption Mold Shrinkage Tensile Stress at 10% Strain Tensile Stress at break Elongation at break Flexural Modulus Tear strength Izod impact strenth/notcher Resilience Melting point HDT Resistance to Surface abrasion
D2240 D570 D955 D638 D638 D638 D790 D1004 D256 D2632 D3418 D648 D1044 (wheel H-19)
Shore D g/cm3 % % kg/cm2 kg/cm2 % kg/cm2 kN/m kg*cm/cm % OC OC Mg
40 1,16 0,6 0,8 44 270 680 680 115 N.B. 57 157 70 95
T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550
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Fig. 1. Samples intended for testing a) full sample b) sample with metamaterial structure.
Fig. 2. Tensile strength diagram of a sample printed using FDM technology with a metamaterial structure and a full infill.
Because the geometric structure created in FDM technology exhibits orthotropic properties, according to Hooke's generalized law, constitutive equations determining the mechanical properties of this structure can be written in the form of the following matrix equation:
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T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
(1)
where: σ ij and τij - components of the stress vector, ε ij and γ ij - components of the strain vector (i and j can take the values 1, 2 or 3), and the stiffness matrix is a symmetric matrix containing 12 independent quantities: three Young modules: E11, E22, E33, three Kirchhoff modules: G23, G31, G12, and six Poisson modules: v21, v31, v12, v32, v13, v23, where for FDM technology: v12 = v21, v13 = v31, v23 = v32. 3. Computer model of the samples The computer model, which has been prepared using FEM method [. The material properties introduce in the model is not reflect orthotropic properties directly. It results from the lack of information about values of Young, Kirchhoff and Poison module. Therefore, it is assumed linear elastic isotropic material model. The plasticity of this material is assumed in order to get strength diagram with two ranges (Fig. 2). First range assume that the material is linear isotropic with one Young module value and second range with different Young modulus value. These modules are calculated according with following formula [8]: E1=exp(((H+50)0.0235)-0.6403) And the second as follow [8]: E2= ((0.0981(56+7.62336H))/(0.137505(254-2.54*H))) Where H is a hardness of material gives by producer. In this case the material with hardness H=40 is applied. The Poison module value is assumed about 0.4. The initial yield stress (von Mises stress) is 7e6 MPa. Tensile stress at break for this particular material, gives by the producer, is 2.7e7 Pa. In the computer model above parameters is introduced and the experiment results are compared. Tensile strength diagram in the case of metamaterial structure probe (honey sample) and 100% infill probe introduced in the model shows Fig. 3. The dash lines indicate elongation at break takes from experiments (compare also Table 1).
T. Krolikowski et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, R. Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
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Fig. 3. Tensile strength diagram of metamaterial structure probe and 100% infill probe drown using computer model.
The computer model gives the opportunity to calculate many more parameters than experiment. It is true within the verified model range, as it is done above (Fig. 3.). The dash lines indicate in Fig.3 the visible linear ranges of the tensile strength characteristics show in Fig.2. Beyond this range the characteristics show force-elongation fluctuation (material flow). The example results, such as: von Mises stress and maximal elongation are show in the below figures. In the Fig. 4 and Fig. 5, there are results in the case infill probe and in Fig. 6 and Fig.7 honey structure probe.
Fig. 4. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of 100% infill probe
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et al. / Procedia Computer Science 159 (2019) 2543–2550 T. Krolikowski, T. R.Krolikowski Knitter, A. Blazejewski/ Procedia Computer Science 00 (2019) 000–000
Fig. 5. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of 100% infill probe.
Fig. 6. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of honey structure probe.
T. R. Krolikowski al. / Procedia Computer ScienceScience 159 (2019) 2543–2550 T. Krolikowski, Knitter, A.etBlazejewski/ Procedia Computer 00 (2019) 000–000
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Fig. 7. Chosen parameters values essential to tensile strength, obtained using computer model, in the case of honey structure probe.
In the figures Fig. 4,5 and Fig. 6,7 the applied forces Fn in N, acting in the direction X (see axes in figures), are chosen increasingly. The force values Fn are selected from the range, where tensile strength diagram is linear. The deformation in a form of displacement in mm are shown in real scale. The point of maximal displacement is additionally indicated as abbreviation max: with the particular value of this displacement. The right-side colour bar shows values of stress in Pa 4. Conclusions The computer modelling using FEM method and the experimental test show that metamaterials can be introduce relatively easy in designing process, even though these materials properties are described as the orthotropic. Linear elastic properties with plasticity give acceptable results. The tensile strength diagrams both, in case of the experiments and modelling, are converged, considering their values and the shapes. Some problems arise, when the material flow range is reached in the model. In this work it is taken from experiments and marked as the dash line. This specific area modelling in the tensile strength problems is under the further consideration. References [1] A. Mix and A. (2011) Giacomin, "Standardized Polymer Durometry" Journal of Testing and Evaluation 39 (4): 696-705., Journal of Testing and Evaluation, 39 (4): 1–10. [2] Vinay H. Ba, Govindarajub H.K., Prashanth Banakarc. 2017 “AMMMT 2016 Experimental Study on Mechanical Properties of Polymer Based Hybrid Composite Materials Today”: Proceedings. 4 (2017): s. 10904–10912. [3] Campbell I., Bourell D., Gibson I. (2012) “Additive manufacturing: rapid prototyping comes of age” Rapid Prototyping Journal 18 (4): 255258. [4] Casavola C., Cazzato A., Moramarco V. 2016 “Orthotropic mechanical properties of fused deposition modelling parts described by classical laminate theory” Materials & Design 90: 453-458. [5] Dawoud M., Taha I., Ebeid S.J. 2016 “Mechanical behaviour of ABS: An experimental study using FDM and injection moulding techniques” Journal of Manufacturing Processes 21: 39-45. [6] Ion A., Frohnhofen J., Wall L., Kovacs R., Alistar M., Lindsay J., Lopes P., Chen H., Baudisch P., Hasso 2016 “Metamaterial Mechanisms” UIST '16, October 16 - 19, 2016, Tokyo, Japan 529-539 [7] Kinsler Paul., McCall Martin W. 2015 “The futures of transformations and metamaterials” Photonic and Nanostructures – Fundamentals and Applications 15: 10-23 [8] Knitter R., Królikowski T., (2018) „Metamateriały mechaniczne wytwarzane w sposób przyrostowy” Mechanik 7 :502-504
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