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Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling

Alastrue, V; Martinez, M A; Doblare, M and Menzel, Andreas LU (2009) In Journal of the Mechanics and Physics of Solids 57(1). p.178-203
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of the Mechanics and Physics of Solids
volume
57
issue
1
pages
178 - 203
publisher
Elsevier
external identifiers
  • wos:000262059300012
  • scopus:56949103255
ISSN
1873-4782
DOI
10.1016/j.jmps.2008.09.005
language
English
LU publication?
yes
id
7aba7a4c-c982-4255-a56e-8c5c8b71ab95 (old id 1515144)
date added to LUP
2009-12-10 10:24:03
date last changed
2017-12-10 04:08:29
@article{7aba7a4c-c982-4255-a56e-8c5c8b71ab95,
  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.},
  author       = {Alastrue, V and Martinez, M A and Doblare, M and Menzel, Andreas},
  issn         = {1873-4782},
  language     = {eng},
  number       = {1},
  pages        = {178--203},
  publisher    = {Elsevier},
  series       = {Journal of the Mechanics and Physics of Solids},
  title        = {Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling},
  url          = {http://dx.doi.org/10.1016/j.jmps.2008.09.005},
  volume       = {57},
  year         = {2009},
}