Some unexpected behaviour in shear for elasticity models of arterial tissue that only use the I1, I4, I6 invariants (original) (raw)
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It is shown that a widely used class of constitutive models for the mechanical response of elastic arteries, which includes the so-called HGO model, responds as if it were inextensible in simple tension in the zero limit of a non-dimensional ratio of material parameters. A significant auxetic response is predicted for an incompressible hyperelastic elastic sheet reinforced with inextensible cords. Thus, a significant lateral deformation of arterial specimens modelled by this class of materials should be observed in simple tension for small values of the non-dimensional parameter. However, such a response has not been observed experimentally. The analysis therefore suggests that predictions for this class of strongly anisotropic constitutive models for arteries should be treated with caution.
Mechanical Behavior of Human Arteries in Large Deformation Using Non-Linear Elasticity Theory
2016
ARTICLE INFORMATION ABSTRACT Original Research Paper Received 17 August 2015 Accepted 26 October 2015 Available Online 21 November 2015 Mechanical behavior of live cells and tissues is non-linear and their deformations are large. Using a suitable mechanical model that could predicts this behavior, is an important step in the prevention and treatment of various diseases and the production of artificial tissues. In this paper, using the non-linear elasticity theory and non-linear Mooney-Rivlin model, mechanical analysis of human arteries has been studied under internal pressure and axial tension. By using the experimental study of biaxial test, the elastic constants of the arteries are calculated. For modeling, the arteries are considered as long homogeneous and isotropic cylinders. Radial and circumferential stress distribution on the minimum and maximum blood pressure is calculated. Variation of artery radius due to internal pressure is calculated and compared with the reported expe...
Elastic Behavior of Porcine Coronary Artery Tissue Under Uniaxial and Equibiaxial Tension
Annals of Biomedical Engineering, 2000
The aim of this study was to characterize the nonlinear anisotropic elastic behavior of healthy porcine coronary arteries under uniaxial and equibiaxial tension. Porcine coronary tissue was chosen for its availability and similarity to human arterial tissue. A biaxial test device previously used to test human femoral arterial tissue samples (Prendergast, P. ) was further developed to test porcine coronary tissue specimens. The device applies an equal force to the four sides of a square specimen and therefore creates a biaxial stretch that demonstrates the anisotropy of arterial tissue. The nonlinear elastic behavior was marked in both uniaxial and biaxial tests. The tissue demonstrated higher stiffness in the circumferential direction in four out of eight cases subjected to biaxial tension. Even though anisotropy is demonstrated it is proposed that an isotropic hyperelastic model may adequately represent the properties of an artery, provided that an axial stretch is applied to the vessel to simulate the in vivo longitudinal tethering on the vessel. Isotropic hyperelastic models based on the Mooney-Rivlin constitutive equation were derived from the test data by averaging the longitudinal and circumferential equibiaxial data. Three different hyperelastic models were established to represent the test specimens that exhibited a high stiffness, an average stiffness, and a low stiffness response; these three models allow the analyst to account for the variability in the arterial tissue mechanical properties. These models, which take account of the nonlinear elastic behavior of coronary tissue, may be implemented in finite element models and used to carry out preclinical tests of intravascular devices. The errors associated with the hyperelastic models when fitting to both the uniaxial and equibiaxial data for the low stiffness, average stiffness, and high stiffness models were found to be 0.836, 5.206, and 2.980, respectively.
International Journal for Numerical Methods in Biomedical Engineering, 2015
The distribution of stresses in arterial walls under physiological loading conditions is considered; transmural stress distributions are a major driving factor for atherogenesis. The accurate prediction of transmural stresses requires the use of a model for the vessel wall that is able to capture the relevant features of the material behavior. An anisotropic hyperelastic and almost incompressible material model is considered, based on a polyconvex strain energy function. One of the main contributions of this paper is the use of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction (FSI), together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. Realistic predictions of transmural stress distributions require the simulation of the interaction between the blood flow and the vessel wall deformation. The fluid-structure interaction problem is solved using a monolithic approach, i.e., the nonlinear system is solved (after time and space discretization) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple-but nonsymmetric-curved geometry is proposed which is suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. To incorporate the prestretch of the arterial wall due to the blood pressure, a ramp phase is used to bring the setting to a physiological blood pressure of 80mmHg, followed by a simulation of one or several heartbeats. We propose this benchmark to replace, for problems in biomechanics, the simpler problem of a short and steep wave in a straight tube, which is often used as a first test problem in FSI. Based on the curved benchmark geometry, and corresponding physiologicallybased boundary conditions, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. As a result of the almost incompressibility, linear shape functions in the structure are not sufficient to provide good approximations of the arterial wall stresses. This holds although reasonably fine discretizations using linear finite elements seem to provide good approximations of the wall displacements. Instead, suitable results are obtained by considering at least piecewise quadratic shape functions for the deformations. In addition, based on a piecewise quadratic discretization of the displacements, a discretization using a three-field approach and element-by-element static condensation of two of the three fields is applied in order to avoid locking effects. The results obtained are similar
A strain energy function for arteries accounting for wall composition and structure
Journal of Biomechanics, 2004
Identification of a Strain Energy Function (SEF) is used when describing the complex mechanical properties of soft biological tissues such as the arterial wall. Classic SEFs, such as the one proposed by Chuong and Fung (J. Biomech. Eng. 105 , have been mostly phenomenological and neglect the particularities of the wall structure. A more structural model was proposed by Holzapfel et al. (J. Elasticity 61 (2000) 1-48.) when they included the characteristic angle at which the collagen fibers are helically wrapped, resulting in an excellent SEF for applications such as finite element modeling. We have expanded upon the idea of structural SEFs by including not only the wavy nature of the collagen but also the fraction of both elastin and collagen contained in the media, which can be determined by histology. The waviness of the collagen is assumed to be distributed log-logistically. In order to evaluate this novel SEF, we have used it to fit experimental data from inflation-extension tests performed on rat carotids. We have compared the results of the fit to the SEFs of Choung and Fung and Holzapfel et al. The novel SEF is found to behave similarly to that of Holzapfel et al., both succeed in describing the typical S-shaped pressure-radius curves with comparable quality of fit. The parameters of the novel SEF obtained from the fitting, bearing the physical meaning of the elastic modulus of collagen, the elastic modulus of elastin, the collagen waviness, and the collagen fiber angle, were compared to experimental data and discussed. r