| 1. |
- Alastrue, V, et al.
(författare)
-
Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling
- 2009
-
Ingår i: Journal of the Mechanics and Physics of Solids. - : Elsevier BV. - 1873-4782 .- 0022-5096. ; 57:1, s. 178-203
-
Tidskriftsartikel (refereegranskat)abstract
- A fully three-dimensional anisotropic elastic model for vascular tissue modelling is here presented. The underlying strain energy density function is assumed to additively decouple into volumetric and deviatoric contributions. A straightforward isotropic neo-Hooke-type law is used to model the deviatoric response of the ground substance, whereas a micro-structurally or rather micro-sphere-based approach will be employed to model the contribution and distribution of fibres within the biological tissue of interest. Anisotropy was introduced by means of the use of von Mises orientation distribution functions. Two different micro-mechanical approaches -- a, say phenomenological, exponential ansatz and a worm-like-chain-based formulation -- are applied to the micro-fibres and illustratively compared. The passage from micro-structural contributions to the macroscopic response is obtained by a computational homogenisation scheme, namely numerical integration over the surface of the individual micro-spheres. The algorithmic treatment of this integration is discussed in detail for the anisotropic problem at hand, so that several cubatures of the micro-sphere are tested in order to optimise the accuracy at reasonable computational cost. Moreover, the introduced material parameters are identified from simple tension tests on human coronary arterial tissue for the two micro-mechanical models investigated. Both approaches are able to recapture the experimental data. Based on the identified sets of parameters, we first discuss a homogeneous deformation in simple shear to evaluate the models' response at the micro-structural level. Later on, an artery-like two-layered tube subjected to internal pressure is simulated by making use of a non-linear finite element setting. This enables to obtain the micro- and macroscopic responses in an inhomogeneous deformation problem, namely a blood-vessel-representative boundary value problem. The effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor which turns out to crucially affect the simulation results.
|
|
| 2. |
- Alastrue, V., et al.
(författare)
-
On the use of non-linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals. Application to the stress analysis in fibred soft tissues
- 2009
-
Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 79:4, s. 474-504
-
Tidskriftsartikel (refereegranskat)abstract
- Microsphere-based constitutive models are a helpful tool in the modelling of materials with a microstructure composed of contributing elements directionally arranged. This is the case, for instance, for fibred soft tissues. In these models, the macroscopic mechanical behaviour is obtained from the integration of the micro-structural contribution of each component (e.g. each fibre) over the surface of an underlying microsphere, which allows incorporating the mechanical features of the micro-constituents to the macroscopic response. The combination of this sort of models and the associated numerical techniques constitutes a powerful modelling tool for which an efficient integration scheme is required. In this regard, the unit sphere discretizations proposed by Bazant and Oh (ZAMM-J Appl Math Mech Z Angew Math Mech 1986; 66(1):37-49) have been used for the integration of the microscopic contributions in isotropic materials. Nevertheless, the inclusion of anisotropy has important implications with regard to the integration scheme, since very fine discretizations are needed to perform the integration accurately, causing the integration process to be very costly. In addition, the storage of internal variables at each integration direction of every integration point is required for constitutive models based on the use of internal variables at the micro-structural level, which renders this approach rather complex and memory demanding. In order to reduce the number of necessary integration directions, several non-linear transformations for the integration of rotationally symmetric functions over the Surface of the unit sphere are here presented. Their accuracy in the integration of the von Mises orientation distribution function is evaluated. Furthermore, a hyperelastic microsphere-based constitutive law for the modelling of soft biological tissues is used in order to check the accuracy and computational efficiency of the proposed transformations within a Finite Element context in inhomogeneous deformation problems. Simulation results show the suitability of the proposed methodology in order to accurately approximate the Value of the integrals within reasonable computational costs. Copyright (C) 2009 John Wiley & Sons, Ltd.
|
|
| 3. |
- Cacho, F., et al.
(författare)
-
A constitutive model for fibrous tissues considering collagen fiber crimp
- 2007
-
Ingår i: International Journal of Non-Linear Mechanics. - : Elsevier BV. - 0020-7462 .- 1878-5638. ; 42:2, s. 391-402
-
Tidskriftsartikel (refereegranskat)abstract
- A micromechanically based constitutive model for fibrous tissues is presented. The model considers the randomly crimped morphology of individual collagen fibers, a morphology typically seen in photomicrographs of tissue samples. It describes the relationship between the fiber endpoints and its arc-length in terms of a measurable quantity, which can be estimated from image data. The collective mechanical behavior of collagen fibers is presented in terms of an explicit expression for the strain-energy function, where a fiber-specific random variable is approximated by a Beta distribution. The model-related stress and elasticity tensors are provided. Two representative numerical examples are analyzed with the aim of demonstrating the peculiar mechanism of the constitutive model and quantifying the effect of parameter changes on the mechanical response. In particular, a fibrous tissue, assumed to be (nearly) incompressible, is subject to a uniaxial extension along the fiber direction, and, separately, to pure shear. It is shown that the fiber crimp model can reproduce several of the expected characteristics of fibrous tissues.
|
|
| 4. |
- Rodríguez, J. F., et al.
(författare)
-
Mechanical stresses in abdominal aortic aneurysm. Material anisotropy a parametric study
- 2007
-
Ingår i: Computational Plasticity - Fundamentals and Applications, COMPLAS IX. - 9788496736283 ; , s. 248-252
-
Konferensbidrag (refereegranskat)abstract
- Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress.
|
|
| 5. |
- Rodriguez, J. F., et al.
(författare)
-
Mechanical stresses in abdominal aortic aneurysms : Influence of diameter, asymmetry, and material anisotropy
- 2008
-
Ingår i: Journal of Biomechanical Engineering. - : ASME International. - 0148-0731 .- 1528-8951. ; 130:2
-
Tidskriftsartikel (refereegranskat)abstract
- Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The, results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.
|
|
