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Mechanical characterisation of Dacron graft: Experiments and numerical simulation
Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Mechanical characterisation of Dacron graft: Experiments and numerical simulation Claudio A. Bustos a, Claudio M. García-Herrera a,n, Diego J. Celentano b a b
Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, USACH, Av. Bernardo O'Higgins 3363, Santiago de Chile, Chile Departamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago de Chile, Chile
art ic l e i nf o
a b s t r a c t
Article history: Accepted 10 November 2015
Experimental and numerical analyses focused on the mechanical characterisation of a woven Dacron vascular graft are presented. To that end, uniaxial tensile tests under different orientations have been performed to study the anisotropic behaviour of the material. These tests have been used to adjust the parameters of a hyperelastic anisotropic constitutive model which is applied to predict through numerical simulation the mechanical response of this material in the ring tensile test. The obtained results show that the model used is capable of representing adequately the nonlinear elastic region and, in particular, it captures the progressive increase of the rigidity and the anisotropy due to the stretching of the Dacron. The importance of this research lies in the possibility of predicting the graft's mechanical response under generalized loading such as those that occur under physiological conditions after surgical procedures. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Dacron graft Biomechanical model Numerical simulation
1. Introduction The aorta is the central artery of the cardiovascular system in charge of dampening the pulsating pressure coming from the left ventricle of the heart. Among the different diseases that can affect it, we find ascending aortic aneurysms which consist in focalized dilations of the arterial wall. For that reason, the pathological tissue must be replaced by a vascular prosthesis, generally artificial, the first implants being reported in 1958 by DeBakey and Cooley with Dacron grafts. Repairing the damaged tissue involves replacement with a Dacron graft (De Paulis et al., 2008). Over the years, Dacron has been used as a substitute in the ascending aorta region because of its good post-operative performance and ease of insertion during the replacement surgery. The prostheses consist of a cylindrical structure made of orthogonally oriented polyethylene terephthalate (PET) fibres that have great resistance and rigidity, in addition to biocompatibility with the medium. Research has shown that differences between the mechanical properties of the graft and the native tissue generate adverse effects on the functioning of the cardiovascular cycle, altering the pressure wave due to the different distensibility in the anastomosis (Berger and Sauvage, 1981; AbuRahman and DeLuca, 1995; Zilla and Bezuidenhout, 2007) but, n
Corresponding author. E-mail address: [email protected] (C.M. García-Herrera).
to date, the real stress state that is generated in the aortic arch is unknown. In the literature, there is a limited number of papers related to the mechanical characterisation of Dacron. Hasegawa and Azuma (1979) and Lee and Wilson (1986) carried out in-vitro tensile and relaxation tests on woven and knitted Dacron grafts for circumferential and longitudinal specimens. Their results show differences depending on orientation, showing a clear anisotropic response according to the direction of the fibres, attributing it mainly to the fabric's configuration and the corrugation present in the prosthesis. More recent studies like that of Tremblay et al. (2009) indicate, from biaxial tests, that grafts of this kind have considerable differences, reaching 24 times greater rigidity than that of human aorta. Yet none of the work that has been done has proposed a realistic constitutive model considering the directions of the material's fibres and their nonlinear response. However, in papers like those by Vardoulis et al. (2011) and Hajjaji et al. (2012), on the basis of assumptions of isotropic linear elasticity, comparisons with respect to the geometric configuration and the influence on hemodynamics in numerical models have been respectively established considering a Dacron graft. The objective of the present paper is to characterise and model the mechanical response of Dacron. The methodology of this study includes the following stages: (1) Realisation of uniaxial tensile tests under different orientations in order to assess the anisotropic effects due to the material composition, (2) proposal of a hyperelastic anisotropic constitutive model, (3) adjustment of the parameters of the constitutive model by numerical simulation of
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Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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the uniaxial tensile tests, (4) realisation of ring tensile tests, (5) validation of the model by comparing the experimental and numerical values of the ring tensile test. The materials and methods considered are presented in Section 2, where Section 2.1 includes the experimental procedure and Section 2.2 summarises the proposed constitutive model that describes the material's anisotropic response. The experimental and numerical results are given in Section 3. Specifically, the adjustment of the model's parameters by means of the uniaxial tensile tests is detailed in Section 3.1. Moreover, Section 3.2 presents the measured and computed results for the ring tensile test. Finally, the experimental and numerical results are discussed in Section 4 where a satisfactory validation of the model with respect to the experimental data, as well as the complex tensional state generated by the stress to which it is subjected, is achieved in both tests.
Fig. 2. Detail of the corrugation of the tested Dacron prosthesis (sizes in mm).
2. Materials and methods 2.1. Experimental procedure 2.1.1. Material The material used for all the tests was a Boston Scientific Hemashield Platinum woven Dacron prosthesis. It has a straight corrugated tubular configuration formed with fibres (PET) covered with a double layer impregnated with bovine collagen (matrix); see Fig. 1. The black longitudinal line observed at the bottom of the prosthesis serves to align the graft during the surgery. Specimens for the uniaxial and ring tensile tests were obtained from it. Fig. 2 shows the configuration of the corrugation folds, which were obtained digitally using an optical microscope. 2.1.2. Uniaxial tensile test The purpose of this test is to get the relation between the force and the stretching of the material subjected to a uniaxial load, which makes it possible to determine the mechanical properties and the rupture limits. The anisotropic degree of the material can also be determined by testing specimens in different orientations. Since the material is composed of various filaments, the results will be considered until the first drop of the load registered in the test which represents an evident rupture of some of the threads that make up the prosthesis. The tested specimens were cut mechanically with a die in two directions following the weave of the prosthesis, defining the circumferential (90°) and longitudinal (0°) directions with respect to its axis, and some specimens were also cut at 45° (bias direction). It should be noted that the corrugated structure was conserved during the extraction, allowing the evaluation of its influence on the mechanical response. Fig. 3 shows the sizes of the test specimens obtained. The sizes of the test pieces at 45° were cut with a rectangular scalpel (16 6 mm) keeping the corrugated structure. The tests were performed immersed in water conditioned at a temperature of 37 7 1 °C in an acrylic cell. All the tests were performed at a constant loading cell speed of 0.03 mm/s to preclude viscous effects. Before each test, the specimens were subjected to loading–unloading conditioning cycles up to a force equal to 5% of the maximum load. The specimens were then tested to rupture, recording the displacement between the jaws and the axial force directly from the testing machine with precisions of 7 1 μm and 7 0.01 N, respectively. In this context the
Fig. 3. Sample used in the tensile test. The sizes of the test specimens in mm are depicted in (A)–(C) that show the cross sections of the circumferential and longitudinal orientations. axial stretch is defined as λ ¼ l=l0 with l and l0 being the instantaneous sample axial lengths. Because of the low rigidity of the specimens at the beginning of the test, it is not apparent to determine the initial length of each sample with the axial load at the instant at which its rate changes significantly, particularly in the test specimens oriented in the longitudinal and bias directions. For this reason, a digital camera was set up configured at 10 images per second to record the displacement between two points separated by a known distance (defined as l0 ¼ 4 mm in this study). Therefore, the beginning of the test is set at the time at which the separation between the points and the reference length become equal. 2.1.3. Ring tensile test As in the previous test, the ring tensile test allows the evaluation of the mechanical properties, specifically for the overall behaviour of the material. The test consists in applying tension through two pins inserted in a ring-shaped test specimen under the hypothesis that the initial bending is negligible and there is no friction between the specimen and the pins. Several rings were cut with a scalpel following the direction of the circumferential fibres between the folds. Each specimen was approximately 4 mm thick, corresponding to two folds of the corrugated structure (see Fig. 2). The temperature control system used in this test was the same as that of the uniaxial tensile test. Special jaws were used to tension the ring specimens. First, the jaws were set up in the testing machine by means of a ball joint attached to a 500 N loading cell. The initial distance between the jaw pins was adjusted to 17 mm. Then, the ring specimen was introduced between the pins and the assembly was finished with the filling of the test cell. Before each test, three loading–unloading cycles to 5% of the maximum rupture load were carried out. Then the test was performed at a loading cell speed of 0.03 mm/s, recording continually the force and the displacement. 2.2. Constitutive modelling The constitutive model analyzed in this work, which is an extension of that proposed by Planas et al. (2007), considers a deformable matrix reinforced by a dispersion of fibres. This model proposes a macroscopic approximation equivalent to the microscopic description of the reinforcing fibres, obtained by equating the mechanical deformation work of the fibres with the work of the effective continuum medium per unit volume in the reference configuration. Thus, the Second Piola–Kirchhoff stress tensor of the fibres S fibres is m f Θ sΘ X f f
S fibres ¼
Θ¼1
Fig. 1. General view of the analysed Dacron prosthesis.
where ff
Θ
λΘ f
ðN Θ N Θ Þ
is the volume fraction of the different m families of the fibres
ð1Þ
Θ, so that
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
C.A. Bustos et al. / Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Pm
3
Θ
Θ
Θ ¼ 1 f f ¼ 1, NΘ is the direction of the family of fibres Θ and sf is the nominal stress that relates the mechanical behaviour of the fibres Θ with the respective ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Θ stretching λf ¼ CN Θ N Θ . In addition, C ¼ F T F is the Cauchy–Green tensor, where F is the deformation gradient tensor with J ¼ detF. The Second Piola–Kirchhoff stress tensor of the composite material (fibres þ matrix) under the incompressibility hypothesis (J ¼1) is
S ¼ S fibres þ 2
∂W matrix ∂C
ð2Þ
where Wmatrix is the strain energy function of the hyperelastic material of the matrix. The constitutive elastic tensor that can be derive from Eq. (2) is 2 3 Θ m 2 X ∂sΘ ff 4 f sΘ 1 5ðN Θ N Θ N Θ N Θ Þ þ 4∂ W matrix ð3Þ C¼ 2 f Θ Θ Θ ∂C ∂C ∂ λf λf Θ ¼ 1 λf In this work the following definitions are adopted: Θ
Θ sΘ f ¼ s f ðλ f Þ ¼
3 X
Θ
K i ðλf 1Þi
ð4Þ Fig. 4. Experimental data of force versus stretch for the three directions analyzed.
i¼1
W matrix ¼ μðI1 3Þ=2
ð5Þ
where Ki are positive material parameters of the fibres, μ is the material parameter of the matrix and I1 is the first invariant of the Cauchy–Green tensor C. This constitutive model was implemented in an in-house finite element code extensively validated in many biomechanical applications (García-Herrera and Celentano, 2013).
3. Results 3.1. Uniaxial tensile test 3.1.1. Experimental measurements The average experimental force–stretching curves corresponding to the specimens oriented in the circumferential, longitudinal and bias directions are plotted in Fig. 4 (the vertical bars represent the standard deviation). Table 1 shows the rupture limits for the stretching, λrupt, and force, Frupt, according to the corresponding direction. It should be mentioned that there is not necessarily a relation between the values related to the longitudinal and bias specimens because, as already mentioned in Section 2.1, their sizes and shapes are different. 3.1.2. Fitting model parameters According to the model of Section 2.2, the constitutive equation characterises the material with a total of six positive constants: μ (matrix), K 1 , K 2 and K 3 (fibres), and the volumetric fractions fcirc and flong respectively associated with the circumferential and longitudinal PET fibres of the Dacron fabric. Due to the complex geometric distribution of the fibres present in this fabric, fcirc and flong can be considered in this constitutive model as stress weighting factors associated to both directions. In this context, these factors account for the braided character of the fibres and their frictional interaction since these effects are not explicitly addressed. Because of the corrugated geometry of the specimens, the generated stresses and strains do not present a homogeneous state and, therefore, the obtaining of the material parameters must be accomplished via numerical simulation of the tensile test considering a mesh according to the size of the specimens (see Figs. 2 and 3) with boundary conditions equivalent to the test making use of the problem's symmetries. As a basis for the calibration of the model, μ has been fitted by least squares of the test in the bias direction up to a sample stretch λ ¼ 1:30, because the response in this stretch range is due exclusively to the deformation caused by the stretching of the corrugate oriented at 45° and not to the direct tension of the fibres. Therefore, it is reasonable to expect up to this stretching that the response will represent completely the material's structure and rigidity. On the other hand, the constants K 1 , K 2 and K 3 of Eq. (4)
Table 1 Rupture limits of the Dacron specimens. Limit
Circumferential
Longitudinal
Bias
λrupt Frupt (N)
1.836 70.080 37.250 7 4.484
2.390 7 0.067 28.853 7 2.566
1.592 7 0.050 7.755 7 1.669
have been fitted from the circumferential test, since the behaviour for this direction is directly related to the response of the Dacron fibres and involves a simpler geometry. Finally, the simultaneous consideration of the circumferential and longitudinal responses allows the refitting of Ki and the derivation of the fractions fcirc and flong in an iterative manner. Fig. 5 shows the numerical results of the force compared to the experimental measurements using the parameters of the final fitting. The responses were plotted up to the first section of the curve (inflection point), approximately λcirc C 1:08 and λlong C 1:50 for each direction. 3.2. Ring tensile test 3.2.1. Geometry and boundary conditions The 3D ring model considered in the numerical simulation consists of 1/8 of the tested geometry in order to make use of the symmetry planes of the problem. Fig. 6 shows schematically the boundary conditions used in the analysis. The geometric configuration has an inner radius of 12 mm and a width of 2 mm, equivalent to one wave (as shown in Fig. 2). The pin that stretches the ring is defined as a rigid surface with a diameter of 6.35 mm. The circumferential and axial dimensions of the pin have been selected in order to guarantee an adequate contact during the whole deformation process. For the numerical model the mesh considered six elements along the thickness, 40 elements for the wave in the longitudinal direction distributed with greater density in the supports toward the pin, and 110 elements for the 90° sector in the circumferential direction, where 40 elements were used to mesh the zone that would be in contact with the pin (approximately 25°), for a total of 26,400 hexahedral elements with 31,857 nodes. Since this simulation involves large displacements and deformations, it is necessary to use a contact mesh between the pin and the Dacron ring whose nodes do not spatially coincide. The contact surface of the ring has a total of 1600 quadrilateral elements with 1681 nodes (green dots in Fig. 6). For the pin, on the other hand, the mesh considers 40 elements for the 120° sector and 95 elements for the length defined as having a greater density in the ring support zones, with a total of 3800 quadrilateral elements with 3895 nodes (red dots in Fig. 6). It should be noted that the numerical analysis assumes frictionless contact conditions.
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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Fig. 5. Experimental measurements and numerical results of force versus stretch along the circumferential (90°) and longitudinal (0°) directions in the tensile test. Final fitted material parameters: μ¼ 60.596 kPa; K 1 ¼ 10:234 kPa; K 2 ¼ 1:852 10 3 kPa; K 3 ¼ 1:420 107 kPa; f circ ¼ 0:95; f long ¼ 0:05.
Fig. 6. Geometry and boundary conditions in the ring tensile test simulation. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
3.2.2. Numerical results and principal stress contours Fig. 7 shows the experimental and computed force versus displacement of the jaws curves up to 14 mm. Although not shown, the experimental data of the ring tensile test reach rupture values of displacement 35.271.3 mm and force 91.6717.5 N, giving a curve with the same shape as that of the circumferential tensile tests. The principal Cauchy stresses in the final deformed configuration are shown in Fig. 8, which includes symmetries for better visualization. The principal directions follow the contours of the deformed geometry, i.e., the first, second and third principal directions approximately are oriented along the circumferential, axial and thickness directions, respectively. It should be noted that the mesh used in the computations is the result of a previous convergence study of the numerical response to different discretisations.
4. Discussion The experimental force–stretching curves of Fig. 4 show the anisotropic behaviour manifested by the material. In general, the shape of the curves of the circumferential and longitudinal specimens shows a similar trend with two sections: an elastic portion
Fig. 7. Experimental measurements and numerical results of force versus displacement of the jaws for the ring tensile test.
(detailed in Fig. 5) up to λ C 1:08 in the circumferential case and λ C 1:50 in the longitudinal direction, and another one that involves viscous and plastic effects until the rupture of the material. Comparatively, a great difference is seen between orientations, the circumferential response becoming about twice rigid as illustrated by the slopes in Fig. 5. These differences can be explained due to the different filaments that compose the threads and their number in the fabric according to each direction (King et al., 2013) and, in addition, to the longitudinal corrugation that displaces the curve due to its stretching. The stretchings and rupture forces given in Table 1 show the great resistance of the PET fibres that constitute the Dacron prosthesis and, considering the sizes of the test specimens, values around 74 MPa and 72 MPa for the Cauchy stress (σ ¼ F=A, where F is the axial force and A is the cross section at the rupture stage) are obtained for the circumferential and longitudinal directions, respectively. According to the results reported by García-Herrera et al. (2012) and García-Herrera and Celentano (2013) for the aortic tension in the circumferential direction, a rupture Cauchy stress of about 2 MPa is obtained, resulting in 35 times smaller than that of the Dacron. In this relation, the graft would exhibit a high stiffness for damping the pressure wave and it would eventually modify the functioning of the cardiovascular cycle (de Tullio et al., 2011; Vardoulis et al., 2011). However, in the longitudinal direction the flexibility induced by the corrugated wall in the prosthesis would contribute to smooth this phenomenon and also prevent the collapse caused by the motion due to the arterial pressure. As seen in Fig. 5, the constitutive model correlates adequately the response of the material up to the considered stretchings, describing the progressive rigidization and the anisotropic characteristic of the fabric. Although not shown, the maximum principal stresses have values of 5.96 MPa for the circumferential case and 12.03 MPa for the longitudinal case in the mean transversal plane of the simulated geometry, following the direction of the loaded fibres and producing a nonuniform distribution with a concentration of stress toward the inner radii of the corrugated prosthesis. Regarding the performance of the model, in general terms it can be said that it describes the orthogonal interaction between the fibres, making the activation of the anisotropy directions occur for tensile stretching (λ 4 1). The above is confirmed because the narrowing across the width does not exceed 1%, compared to 25% for the thickness and, consequently, that the volume changes restrict the deformation to favour it through the thickness due to the rigidity of the fibres themselves. Also, this effect is shown
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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one, i.e., when the sides of the ring in the deformed configuration are parallel. In this way, from the numerical results it is possible to validate the parameters of the constitutive model fitted by means of the uniaxial tensile tests, because a geometry representative of the prosthesis with boundary conditions identical to the experimental test is considered. The stress concentration that can be seen in Fig. 8a toward the edges of the ring, and similarly in the symmetry plane as well as in the free end, reaches a maximum value of 16.76 MPa near the perpendicular to the tensile direction (zone A in Fig. 8a) and in the symmetry in contact with the pin values of 19.01 MPa (zone B in Fig. 8a). The above shows the high stress levels that the Dacron can achieve without breaking. However, a large part of the central zone of the folds does not exceed 0.54 MPa, attributing the resistance to the tension only to the circumferential fibres of the inner radii of the corrugated (edges) and, therefore, the deformation does not propagate to the smooth zone tensioned by the pin. The stresses plotted in Fig. 8b and c exhibit a marked compression zone in the inner part of the ring, with a value of 1.11 MPa along the deformed width and of 1.39 MPa through the thickness. This effect can be explained by the sliding and tension of the ring over the pin. In spite of this, the surface obtained by the tension achieves a uniform and flat shape defined according to the geometry of the pin, and even then the simulation can be improved by increasing the number of contact elements, but the numerical gain would increase considerably the computing time. The shear stresses (not shown) achieve maximum values of 9.02 MPa and 1.21 MPa in the zone where the contact between the ring and the pin stops (zone C in Fig. 8a). This generates a complex deformation field, distorting the free edge of the ring and inducing instability in the material due to the low rigidity of the matrix. Finally, it should be pointed out that the mechanical characterisation of the Dacron with the proposed model is limited to a quasi static condition, since the material has a marked viscous dependence which, according to studies like those of Hasegawa and Azuma (1979) and Lee and Wilson (1986), can be assimilated to the response of the canine proximal aorta. Furthermore, the work of Etz et al. (2007) determined that the grafts tend to dilate their diameter a mean of 19% one and a half years after the replacement surgery.
5. Conclusions
Fig. 8. Contour fill of principal Cauchy stresses at the final deformed (MPa).
when the stress generated in the radii of the specimens is considered, because the elements in that part work at a lower load, with values of 0.97 kPa for the circumferential tension and 5.67 kPa for the longitudinal tension, depending on the maximum principal stress. However, it should be mentioned that the model, because of its formulation, does not consider the interaction due to friction between the fibres (rotation and sliding among themselves) but, due to the acting loads and boundary conditions under which the graft would be working, this effect may be neglected. In Fig. 7, it is seen that the simulation represents properly the mechanical response for the whole evaluated range, with the circumferential fibres becoming loaded when the stretching approaches
Experimental and numerical results aimed at characterising the anisotropic mechanical response of a woven Dacron graft have been presented. The experimental data of the uniaxial tensile tests have been used to determine the parameters of the proposed constitutive model by means of a mixed methodology that simultaneously accounts for the simulated responses for both the circumferential and longitudinal samples directions. Furthermore, the constitutive model has been validated in the simulation of the ring tensile test, showing a complex stress state and a high resistance of the Dacron fabric. In particular, the application of this methodology is an original contribution of this research. The capacities and limitations of this model have also been discussed. In general, the characterisation made in this work gives a reasonable description of the mechanical behaviour under a static condition, representing adequately the directions of the fibres and considering the corrugated geometry of the material. The limitations of this work should be tackled in future research relaxing restrictive assumptions in the constitutive modelling (for example, by incorporating the viscous response and the interaction bet ween fibres) and complementing the validation by means of tests
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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that mimics the loading physiological conditions (e.g., the pressurisation test).
Conflict of interest The authors have no conflicting interests regarding this paper.
Acknowledgements The supports provided by the DICYT Project no. 051415GH of the Universidad de Santiago de Chile (USACH) and the FONDECYT project number 1151119 of the Chilean Council for Research and Technology (CONICYT) are gratefully acknowledged.
References AbuRahman, A.F., DeLuca, J.A., 1995. Multiple nonanastomotic aneurysms in an external velour ringed Dacron femoropopliteal vascular prosthesis. Ann. Vasc. Surg. 9 (5), 493–496. Berger, K., Sauvage, L.R., 1981. Late fiber deterioration in Dacron arterial grafts. Ann. Surg. 193 (4), 477–491. De Paulis, R., Scaffa, R., Maselli, D., Salica, A., Bellisario, A., Welter, L., 2008. A third generation of ascending aorta Dacron graft: preliminary experience. Ann. Thorac. Surg. 85 (1), 305–309. De Tullio, M.D., Afferrante, L., Demelio, G., Pascazio, G., Verzicco, R., 2011. Fluid– structure interaction of deformable aortic prostheses with a bileaflet mechanical valve. J. Biomech. 44, 1684–1690.
Etz, C.D., Homann, T., Silovitz, D., Bodian, C.A., Luhuer, M., Di Luozzo, G., Konstadinos, A.P., Griepp, R.B., 2007. Vascular graft replacement of the ascending and descending aorta: do Dacron grafts grow?. Ann. Thorac. Surg. 84 (4), 1206–1213. García-Herrera, G.M., Celentano, D.J., Cruchaga, M.A., Rojo, F.J., Atienza, J.M., Guinea, G.V., Goicolea, J.M., 2012. Mechanical characterisation of the human thoracic descending aorta: experiments and modelling. Comput. Methods Biomech. Biomed. Eng. 15 (2), 185–193. García-Herrera, G.M., Celentano, D.J., 2013. Modelling and numerical simulation of the human aortic arch under in vivo conditions. Biomech. Model. Mechanobiol. 12 (6), 1143–1154. Hajjaji, R., Ben Abdessalem, S., Ganghofferb, J.F., 2012. The influence of textile vascular prosthetis crimping on graft longitudinal elasticity and flexibilily. J. Mech. Behav. Biomed. Mater. 16, 73–80. Hasegawa, M., Azuma, T., 1979. Mechanical properties of synthetic arterial grafts. J. Biomech. 12 (7), 509–517. King, M.W., Chung, S., 2013. Medical fibers and biotextiles. In: Ratner, B., Hoffman, A., Schoen, J., Lemons, J. (Eds.), Biomaterials Science: An Introduction to Materials in Medicine, thrid edition. Academic Press, pp. 301–320. Lee, J.M., Wilson, G.J., 1986. Anisotropic tensile viscoelastic properties of vascular graft material tested at low strain rates. Biomaterials 7 (6), 423–431. Planas, J., Guinea, G.V., Elices, M., 2007. Constitutive model for fiber-reinforced materials with deformable matrices. Phys. Rev. E 76 (4), 041903–041909. Tremblay, D., Zigras, T., Cartier, R., Leduc, L., Butany, J., Mongrain, R., Leask, R.L., 2009. A comparison of mechanical properties of materials used in aortic arch reconstruction. Ann. Thorac. Surg. 88 (5), 1484–1491. Vardoulis, O., Coppens, E., Martin, B., Reymon, P., Tozzi, P., Stergiopulos, N., 2011. Impact of aortic grafts on arterial pressure: a computational fluid dynamics study. Eur. J. Vasc. Endovasc. Surg. 42 (5), 704–710. Zilla, P., Bezuidenhout, D., Human, P., 2007. Prosthetic vascular grafts: wrong model, wrong questions and no healing. Biomaterials 28 (34), 5009–5027.
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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Mechanical characterisation of Dacron graft: Experiments and numerical simulation Claudio A. Bustos a, Claudio M. García-Herrera a,n, Diego J. Celentano b a b
Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, USACH, Av. Bernardo O'Higgins 3363, Santiago de Chile, Chile Departamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago de Chile, Chile
art ic l e i nf o
a b s t r a c t
Article history: Accepted 10 November 2015
Experimental and numerical analyses focused on the mechanical characterisation of a woven Dacron vascular graft are presented. To that end, uniaxial tensile tests under different orientations have been performed to study the anisotropic behaviour of the material. These tests have been used to adjust the parameters of a hyperelastic anisotropic constitutive model which is applied to predict through numerical simulation the mechanical response of this material in the ring tensile test. The obtained results show that the model used is capable of representing adequately the nonlinear elastic region and, in particular, it captures the progressive increase of the rigidity and the anisotropy due to the stretching of the Dacron. The importance of this research lies in the possibility of predicting the graft's mechanical response under generalized loading such as those that occur under physiological conditions after surgical procedures. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Dacron graft Biomechanical model Numerical simulation
1. Introduction The aorta is the central artery of the cardiovascular system in charge of dampening the pulsating pressure coming from the left ventricle of the heart. Among the different diseases that can affect it, we find ascending aortic aneurysms which consist in focalized dilations of the arterial wall. For that reason, the pathological tissue must be replaced by a vascular prosthesis, generally artificial, the first implants being reported in 1958 by DeBakey and Cooley with Dacron grafts. Repairing the damaged tissue involves replacement with a Dacron graft (De Paulis et al., 2008). Over the years, Dacron has been used as a substitute in the ascending aorta region because of its good post-operative performance and ease of insertion during the replacement surgery. The prostheses consist of a cylindrical structure made of orthogonally oriented polyethylene terephthalate (PET) fibres that have great resistance and rigidity, in addition to biocompatibility with the medium. Research has shown that differences between the mechanical properties of the graft and the native tissue generate adverse effects on the functioning of the cardiovascular cycle, altering the pressure wave due to the different distensibility in the anastomosis (Berger and Sauvage, 1981; AbuRahman and DeLuca, 1995; Zilla and Bezuidenhout, 2007) but, n
Corresponding author. E-mail address: [email protected] (C.M. García-Herrera).
to date, the real stress state that is generated in the aortic arch is unknown. In the literature, there is a limited number of papers related to the mechanical characterisation of Dacron. Hasegawa and Azuma (1979) and Lee and Wilson (1986) carried out in-vitro tensile and relaxation tests on woven and knitted Dacron grafts for circumferential and longitudinal specimens. Their results show differences depending on orientation, showing a clear anisotropic response according to the direction of the fibres, attributing it mainly to the fabric's configuration and the corrugation present in the prosthesis. More recent studies like that of Tremblay et al. (2009) indicate, from biaxial tests, that grafts of this kind have considerable differences, reaching 24 times greater rigidity than that of human aorta. Yet none of the work that has been done has proposed a realistic constitutive model considering the directions of the material's fibres and their nonlinear response. However, in papers like those by Vardoulis et al. (2011) and Hajjaji et al. (2012), on the basis of assumptions of isotropic linear elasticity, comparisons with respect to the geometric configuration and the influence on hemodynamics in numerical models have been respectively established considering a Dacron graft. The objective of the present paper is to characterise and model the mechanical response of Dacron. The methodology of this study includes the following stages: (1) Realisation of uniaxial tensile tests under different orientations in order to assess the anisotropic effects due to the material composition, (2) proposal of a hyperelastic anisotropic constitutive model, (3) adjustment of the parameters of the constitutive model by numerical simulation of
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Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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the uniaxial tensile tests, (4) realisation of ring tensile tests, (5) validation of the model by comparing the experimental and numerical values of the ring tensile test. The materials and methods considered are presented in Section 2, where Section 2.1 includes the experimental procedure and Section 2.2 summarises the proposed constitutive model that describes the material's anisotropic response. The experimental and numerical results are given in Section 3. Specifically, the adjustment of the model's parameters by means of the uniaxial tensile tests is detailed in Section 3.1. Moreover, Section 3.2 presents the measured and computed results for the ring tensile test. Finally, the experimental and numerical results are discussed in Section 4 where a satisfactory validation of the model with respect to the experimental data, as well as the complex tensional state generated by the stress to which it is subjected, is achieved in both tests.
Fig. 2. Detail of the corrugation of the tested Dacron prosthesis (sizes in mm).
2. Materials and methods 2.1. Experimental procedure 2.1.1. Material The material used for all the tests was a Boston Scientific Hemashield Platinum woven Dacron prosthesis. It has a straight corrugated tubular configuration formed with fibres (PET) covered with a double layer impregnated with bovine collagen (matrix); see Fig. 1. The black longitudinal line observed at the bottom of the prosthesis serves to align the graft during the surgery. Specimens for the uniaxial and ring tensile tests were obtained from it. Fig. 2 shows the configuration of the corrugation folds, which were obtained digitally using an optical microscope. 2.1.2. Uniaxial tensile test The purpose of this test is to get the relation between the force and the stretching of the material subjected to a uniaxial load, which makes it possible to determine the mechanical properties and the rupture limits. The anisotropic degree of the material can also be determined by testing specimens in different orientations. Since the material is composed of various filaments, the results will be considered until the first drop of the load registered in the test which represents an evident rupture of some of the threads that make up the prosthesis. The tested specimens were cut mechanically with a die in two directions following the weave of the prosthesis, defining the circumferential (90°) and longitudinal (0°) directions with respect to its axis, and some specimens were also cut at 45° (bias direction). It should be noted that the corrugated structure was conserved during the extraction, allowing the evaluation of its influence on the mechanical response. Fig. 3 shows the sizes of the test specimens obtained. The sizes of the test pieces at 45° were cut with a rectangular scalpel (16 6 mm) keeping the corrugated structure. The tests were performed immersed in water conditioned at a temperature of 37 7 1 °C in an acrylic cell. All the tests were performed at a constant loading cell speed of 0.03 mm/s to preclude viscous effects. Before each test, the specimens were subjected to loading–unloading conditioning cycles up to a force equal to 5% of the maximum load. The specimens were then tested to rupture, recording the displacement between the jaws and the axial force directly from the testing machine with precisions of 7 1 μm and 7 0.01 N, respectively. In this context the
Fig. 3. Sample used in the tensile test. The sizes of the test specimens in mm are depicted in (A)–(C) that show the cross sections of the circumferential and longitudinal orientations. axial stretch is defined as λ ¼ l=l0 with l and l0 being the instantaneous sample axial lengths. Because of the low rigidity of the specimens at the beginning of the test, it is not apparent to determine the initial length of each sample with the axial load at the instant at which its rate changes significantly, particularly in the test specimens oriented in the longitudinal and bias directions. For this reason, a digital camera was set up configured at 10 images per second to record the displacement between two points separated by a known distance (defined as l0 ¼ 4 mm in this study). Therefore, the beginning of the test is set at the time at which the separation between the points and the reference length become equal. 2.1.3. Ring tensile test As in the previous test, the ring tensile test allows the evaluation of the mechanical properties, specifically for the overall behaviour of the material. The test consists in applying tension through two pins inserted in a ring-shaped test specimen under the hypothesis that the initial bending is negligible and there is no friction between the specimen and the pins. Several rings were cut with a scalpel following the direction of the circumferential fibres between the folds. Each specimen was approximately 4 mm thick, corresponding to two folds of the corrugated structure (see Fig. 2). The temperature control system used in this test was the same as that of the uniaxial tensile test. Special jaws were used to tension the ring specimens. First, the jaws were set up in the testing machine by means of a ball joint attached to a 500 N loading cell. The initial distance between the jaw pins was adjusted to 17 mm. Then, the ring specimen was introduced between the pins and the assembly was finished with the filling of the test cell. Before each test, three loading–unloading cycles to 5% of the maximum rupture load were carried out. Then the test was performed at a loading cell speed of 0.03 mm/s, recording continually the force and the displacement. 2.2. Constitutive modelling The constitutive model analyzed in this work, which is an extension of that proposed by Planas et al. (2007), considers a deformable matrix reinforced by a dispersion of fibres. This model proposes a macroscopic approximation equivalent to the microscopic description of the reinforcing fibres, obtained by equating the mechanical deformation work of the fibres with the work of the effective continuum medium per unit volume in the reference configuration. Thus, the Second Piola–Kirchhoff stress tensor of the fibres S fibres is m f Θ sΘ X f f
S fibres ¼
Θ¼1
Fig. 1. General view of the analysed Dacron prosthesis.
where ff
Θ
λΘ f
ðN Θ N Θ Þ
is the volume fraction of the different m families of the fibres
ð1Þ
Θ, so that
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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Θ
Θ
Θ ¼ 1 f f ¼ 1, NΘ is the direction of the family of fibres Θ and sf is the nominal stress that relates the mechanical behaviour of the fibres Θ with the respective ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Θ stretching λf ¼ CN Θ N Θ . In addition, C ¼ F T F is the Cauchy–Green tensor, where F is the deformation gradient tensor with J ¼ detF. The Second Piola–Kirchhoff stress tensor of the composite material (fibres þ matrix) under the incompressibility hypothesis (J ¼1) is
S ¼ S fibres þ 2
∂W matrix ∂C
ð2Þ
where Wmatrix is the strain energy function of the hyperelastic material of the matrix. The constitutive elastic tensor that can be derive from Eq. (2) is 2 3 Θ m 2 X ∂sΘ ff 4 f sΘ 1 5ðN Θ N Θ N Θ N Θ Þ þ 4∂ W matrix ð3Þ C¼ 2 f Θ Θ Θ ∂C ∂C ∂ λf λf Θ ¼ 1 λf In this work the following definitions are adopted: Θ
Θ sΘ f ¼ s f ðλ f Þ ¼
3 X
Θ
K i ðλf 1Þi
ð4Þ Fig. 4. Experimental data of force versus stretch for the three directions analyzed.
i¼1
W matrix ¼ μðI1 3Þ=2
ð5Þ
where Ki are positive material parameters of the fibres, μ is the material parameter of the matrix and I1 is the first invariant of the Cauchy–Green tensor C. This constitutive model was implemented in an in-house finite element code extensively validated in many biomechanical applications (García-Herrera and Celentano, 2013).
3. Results 3.1. Uniaxial tensile test 3.1.1. Experimental measurements The average experimental force–stretching curves corresponding to the specimens oriented in the circumferential, longitudinal and bias directions are plotted in Fig. 4 (the vertical bars represent the standard deviation). Table 1 shows the rupture limits for the stretching, λrupt, and force, Frupt, according to the corresponding direction. It should be mentioned that there is not necessarily a relation between the values related to the longitudinal and bias specimens because, as already mentioned in Section 2.1, their sizes and shapes are different. 3.1.2. Fitting model parameters According to the model of Section 2.2, the constitutive equation characterises the material with a total of six positive constants: μ (matrix), K 1 , K 2 and K 3 (fibres), and the volumetric fractions fcirc and flong respectively associated with the circumferential and longitudinal PET fibres of the Dacron fabric. Due to the complex geometric distribution of the fibres present in this fabric, fcirc and flong can be considered in this constitutive model as stress weighting factors associated to both directions. In this context, these factors account for the braided character of the fibres and their frictional interaction since these effects are not explicitly addressed. Because of the corrugated geometry of the specimens, the generated stresses and strains do not present a homogeneous state and, therefore, the obtaining of the material parameters must be accomplished via numerical simulation of the tensile test considering a mesh according to the size of the specimens (see Figs. 2 and 3) with boundary conditions equivalent to the test making use of the problem's symmetries. As a basis for the calibration of the model, μ has been fitted by least squares of the test in the bias direction up to a sample stretch λ ¼ 1:30, because the response in this stretch range is due exclusively to the deformation caused by the stretching of the corrugate oriented at 45° and not to the direct tension of the fibres. Therefore, it is reasonable to expect up to this stretching that the response will represent completely the material's structure and rigidity. On the other hand, the constants K 1 , K 2 and K 3 of Eq. (4)
Table 1 Rupture limits of the Dacron specimens. Limit
Circumferential
Longitudinal
Bias
λrupt Frupt (N)
1.836 70.080 37.250 7 4.484
2.390 7 0.067 28.853 7 2.566
1.592 7 0.050 7.755 7 1.669
have been fitted from the circumferential test, since the behaviour for this direction is directly related to the response of the Dacron fibres and involves a simpler geometry. Finally, the simultaneous consideration of the circumferential and longitudinal responses allows the refitting of Ki and the derivation of the fractions fcirc and flong in an iterative manner. Fig. 5 shows the numerical results of the force compared to the experimental measurements using the parameters of the final fitting. The responses were plotted up to the first section of the curve (inflection point), approximately λcirc C 1:08 and λlong C 1:50 for each direction. 3.2. Ring tensile test 3.2.1. Geometry and boundary conditions The 3D ring model considered in the numerical simulation consists of 1/8 of the tested geometry in order to make use of the symmetry planes of the problem. Fig. 6 shows schematically the boundary conditions used in the analysis. The geometric configuration has an inner radius of 12 mm and a width of 2 mm, equivalent to one wave (as shown in Fig. 2). The pin that stretches the ring is defined as a rigid surface with a diameter of 6.35 mm. The circumferential and axial dimensions of the pin have been selected in order to guarantee an adequate contact during the whole deformation process. For the numerical model the mesh considered six elements along the thickness, 40 elements for the wave in the longitudinal direction distributed with greater density in the supports toward the pin, and 110 elements for the 90° sector in the circumferential direction, where 40 elements were used to mesh the zone that would be in contact with the pin (approximately 25°), for a total of 26,400 hexahedral elements with 31,857 nodes. Since this simulation involves large displacements and deformations, it is necessary to use a contact mesh between the pin and the Dacron ring whose nodes do not spatially coincide. The contact surface of the ring has a total of 1600 quadrilateral elements with 1681 nodes (green dots in Fig. 6). For the pin, on the other hand, the mesh considers 40 elements for the 120° sector and 95 elements for the length defined as having a greater density in the ring support zones, with a total of 3800 quadrilateral elements with 3895 nodes (red dots in Fig. 6). It should be noted that the numerical analysis assumes frictionless contact conditions.
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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Fig. 5. Experimental measurements and numerical results of force versus stretch along the circumferential (90°) and longitudinal (0°) directions in the tensile test. Final fitted material parameters: μ¼ 60.596 kPa; K 1 ¼ 10:234 kPa; K 2 ¼ 1:852 10 3 kPa; K 3 ¼ 1:420 107 kPa; f circ ¼ 0:95; f long ¼ 0:05.
Fig. 6. Geometry and boundary conditions in the ring tensile test simulation. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
3.2.2. Numerical results and principal stress contours Fig. 7 shows the experimental and computed force versus displacement of the jaws curves up to 14 mm. Although not shown, the experimental data of the ring tensile test reach rupture values of displacement 35.271.3 mm and force 91.6717.5 N, giving a curve with the same shape as that of the circumferential tensile tests. The principal Cauchy stresses in the final deformed configuration are shown in Fig. 8, which includes symmetries for better visualization. The principal directions follow the contours of the deformed geometry, i.e., the first, second and third principal directions approximately are oriented along the circumferential, axial and thickness directions, respectively. It should be noted that the mesh used in the computations is the result of a previous convergence study of the numerical response to different discretisations.
4. Discussion The experimental force–stretching curves of Fig. 4 show the anisotropic behaviour manifested by the material. In general, the shape of the curves of the circumferential and longitudinal specimens shows a similar trend with two sections: an elastic portion
Fig. 7. Experimental measurements and numerical results of force versus displacement of the jaws for the ring tensile test.
(detailed in Fig. 5) up to λ C 1:08 in the circumferential case and λ C 1:50 in the longitudinal direction, and another one that involves viscous and plastic effects until the rupture of the material. Comparatively, a great difference is seen between orientations, the circumferential response becoming about twice rigid as illustrated by the slopes in Fig. 5. These differences can be explained due to the different filaments that compose the threads and their number in the fabric according to each direction (King et al., 2013) and, in addition, to the longitudinal corrugation that displaces the curve due to its stretching. The stretchings and rupture forces given in Table 1 show the great resistance of the PET fibres that constitute the Dacron prosthesis and, considering the sizes of the test specimens, values around 74 MPa and 72 MPa for the Cauchy stress (σ ¼ F=A, where F is the axial force and A is the cross section at the rupture stage) are obtained for the circumferential and longitudinal directions, respectively. According to the results reported by García-Herrera et al. (2012) and García-Herrera and Celentano (2013) for the aortic tension in the circumferential direction, a rupture Cauchy stress of about 2 MPa is obtained, resulting in 35 times smaller than that of the Dacron. In this relation, the graft would exhibit a high stiffness for damping the pressure wave and it would eventually modify the functioning of the cardiovascular cycle (de Tullio et al., 2011; Vardoulis et al., 2011). However, in the longitudinal direction the flexibility induced by the corrugated wall in the prosthesis would contribute to smooth this phenomenon and also prevent the collapse caused by the motion due to the arterial pressure. As seen in Fig. 5, the constitutive model correlates adequately the response of the material up to the considered stretchings, describing the progressive rigidization and the anisotropic characteristic of the fabric. Although not shown, the maximum principal stresses have values of 5.96 MPa for the circumferential case and 12.03 MPa for the longitudinal case in the mean transversal plane of the simulated geometry, following the direction of the loaded fibres and producing a nonuniform distribution with a concentration of stress toward the inner radii of the corrugated prosthesis. Regarding the performance of the model, in general terms it can be said that it describes the orthogonal interaction between the fibres, making the activation of the anisotropy directions occur for tensile stretching (λ 4 1). The above is confirmed because the narrowing across the width does not exceed 1%, compared to 25% for the thickness and, consequently, that the volume changes restrict the deformation to favour it through the thickness due to the rigidity of the fibres themselves. Also, this effect is shown
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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one, i.e., when the sides of the ring in the deformed configuration are parallel. In this way, from the numerical results it is possible to validate the parameters of the constitutive model fitted by means of the uniaxial tensile tests, because a geometry representative of the prosthesis with boundary conditions identical to the experimental test is considered. The stress concentration that can be seen in Fig. 8a toward the edges of the ring, and similarly in the symmetry plane as well as in the free end, reaches a maximum value of 16.76 MPa near the perpendicular to the tensile direction (zone A in Fig. 8a) and in the symmetry in contact with the pin values of 19.01 MPa (zone B in Fig. 8a). The above shows the high stress levels that the Dacron can achieve without breaking. However, a large part of the central zone of the folds does not exceed 0.54 MPa, attributing the resistance to the tension only to the circumferential fibres of the inner radii of the corrugated (edges) and, therefore, the deformation does not propagate to the smooth zone tensioned by the pin. The stresses plotted in Fig. 8b and c exhibit a marked compression zone in the inner part of the ring, with a value of 1.11 MPa along the deformed width and of 1.39 MPa through the thickness. This effect can be explained by the sliding and tension of the ring over the pin. In spite of this, the surface obtained by the tension achieves a uniform and flat shape defined according to the geometry of the pin, and even then the simulation can be improved by increasing the number of contact elements, but the numerical gain would increase considerably the computing time. The shear stresses (not shown) achieve maximum values of 9.02 MPa and 1.21 MPa in the zone where the contact between the ring and the pin stops (zone C in Fig. 8a). This generates a complex deformation field, distorting the free edge of the ring and inducing instability in the material due to the low rigidity of the matrix. Finally, it should be pointed out that the mechanical characterisation of the Dacron with the proposed model is limited to a quasi static condition, since the material has a marked viscous dependence which, according to studies like those of Hasegawa and Azuma (1979) and Lee and Wilson (1986), can be assimilated to the response of the canine proximal aorta. Furthermore, the work of Etz et al. (2007) determined that the grafts tend to dilate their diameter a mean of 19% one and a half years after the replacement surgery.
5. Conclusions
Fig. 8. Contour fill of principal Cauchy stresses at the final deformed (MPa).
when the stress generated in the radii of the specimens is considered, because the elements in that part work at a lower load, with values of 0.97 kPa for the circumferential tension and 5.67 kPa for the longitudinal tension, depending on the maximum principal stress. However, it should be mentioned that the model, because of its formulation, does not consider the interaction due to friction between the fibres (rotation and sliding among themselves) but, due to the acting loads and boundary conditions under which the graft would be working, this effect may be neglected. In Fig. 7, it is seen that the simulation represents properly the mechanical response for the whole evaluated range, with the circumferential fibres becoming loaded when the stretching approaches
Experimental and numerical results aimed at characterising the anisotropic mechanical response of a woven Dacron graft have been presented. The experimental data of the uniaxial tensile tests have been used to determine the parameters of the proposed constitutive model by means of a mixed methodology that simultaneously accounts for the simulated responses for both the circumferential and longitudinal samples directions. Furthermore, the constitutive model has been validated in the simulation of the ring tensile test, showing a complex stress state and a high resistance of the Dacron fabric. In particular, the application of this methodology is an original contribution of this research. The capacities and limitations of this model have also been discussed. In general, the characterisation made in this work gives a reasonable description of the mechanical behaviour under a static condition, representing adequately the directions of the fibres and considering the corrugated geometry of the material. The limitations of this work should be tackled in future research relaxing restrictive assumptions in the constitutive modelling (for example, by incorporating the viscous response and the interaction bet ween fibres) and complementing the validation by means of tests
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i
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that mimics the loading physiological conditions (e.g., the pressurisation test).
Conflict of interest The authors have no conflicting interests regarding this paper.
Acknowledgements The supports provided by the DICYT Project no. 051415GH of the Universidad de Santiago de Chile (USACH) and the FONDECYT project number 1151119 of the Chilean Council for Research and Technology (CONICYT) are gratefully acknowledged.
References AbuRahman, A.F., DeLuca, J.A., 1995. Multiple nonanastomotic aneurysms in an external velour ringed Dacron femoropopliteal vascular prosthesis. Ann. Vasc. Surg. 9 (5), 493–496. Berger, K., Sauvage, L.R., 1981. Late fiber deterioration in Dacron arterial grafts. Ann. Surg. 193 (4), 477–491. De Paulis, R., Scaffa, R., Maselli, D., Salica, A., Bellisario, A., Welter, L., 2008. A third generation of ascending aorta Dacron graft: preliminary experience. Ann. Thorac. Surg. 85 (1), 305–309. De Tullio, M.D., Afferrante, L., Demelio, G., Pascazio, G., Verzicco, R., 2011. Fluid– structure interaction of deformable aortic prostheses with a bileaflet mechanical valve. J. Biomech. 44, 1684–1690.
Etz, C.D., Homann, T., Silovitz, D., Bodian, C.A., Luhuer, M., Di Luozzo, G., Konstadinos, A.P., Griepp, R.B., 2007. Vascular graft replacement of the ascending and descending aorta: do Dacron grafts grow?. Ann. Thorac. Surg. 84 (4), 1206–1213. García-Herrera, G.M., Celentano, D.J., Cruchaga, M.A., Rojo, F.J., Atienza, J.M., Guinea, G.V., Goicolea, J.M., 2012. Mechanical characterisation of the human thoracic descending aorta: experiments and modelling. Comput. Methods Biomech. Biomed. Eng. 15 (2), 185–193. García-Herrera, G.M., Celentano, D.J., 2013. Modelling and numerical simulation of the human aortic arch under in vivo conditions. Biomech. Model. Mechanobiol. 12 (6), 1143–1154. Hajjaji, R., Ben Abdessalem, S., Ganghofferb, J.F., 2012. The influence of textile vascular prosthetis crimping on graft longitudinal elasticity and flexibilily. J. Mech. Behav. Biomed. Mater. 16, 73–80. Hasegawa, M., Azuma, T., 1979. Mechanical properties of synthetic arterial grafts. J. Biomech. 12 (7), 509–517. King, M.W., Chung, S., 2013. Medical fibers and biotextiles. In: Ratner, B., Hoffman, A., Schoen, J., Lemons, J. (Eds.), Biomaterials Science: An Introduction to Materials in Medicine, thrid edition. Academic Press, pp. 301–320. Lee, J.M., Wilson, G.J., 1986. Anisotropic tensile viscoelastic properties of vascular graft material tested at low strain rates. Biomaterials 7 (6), 423–431. Planas, J., Guinea, G.V., Elices, M., 2007. Constitutive model for fiber-reinforced materials with deformable matrices. Phys. Rev. E 76 (4), 041903–041909. Tremblay, D., Zigras, T., Cartier, R., Leduc, L., Butany, J., Mongrain, R., Leask, R.L., 2009. A comparison of mechanical properties of materials used in aortic arch reconstruction. Ann. Thorac. Surg. 88 (5), 1484–1491. Vardoulis, O., Coppens, E., Martin, B., Reymon, P., Tozzi, P., Stergiopulos, N., 2011. Impact of aortic grafts on arterial pressure: a computational fluid dynamics study. Eur. J. Vasc. Endovasc. Surg. 42 (5), 704–710. Zilla, P., Bezuidenhout, D., Human, P., 2007. Prosthetic vascular grafts: wrong model, wrong questions and no healing. Biomaterials 28 (34), 5009–5027.
Please cite this article as: Bustos, C.A., et al., Mechanical characterisation of Dacron graft: Experiments and numerical simulation. Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.014i