Premium
A micro‐sphere‐based remodelling formulation for arterial tissue including residual stresses
Author(s) -
Waffenschmidt Tobias,
Menzel Andreas
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110057
Subject(s) - orthotropic material , residual stress , anisotropy , materials science , residual , constitutive equation , tensor (intrinsic definition) , biological system , mechanics , geometry , structural engineering , composite material , finite element method , mathematics , physics , engineering , optics , algorithm , biology
Abstract An essential property of soft biological tissues is the ability to adapt according to respective loading conditions, e.g. by means of fibre reorientation (remodelling). In particular with regard to arterial tissue, an externally unloaded state of the material is generally associated with residual stresses. In this contribution a three‐dimensional micro‐sphere‐based constitutive model for anisotropic soft biological tissue is presented, which includes fibre‐reorientation‐related remodelling as well as residual stress‐effects. As a key aspect of this contribution, time‐dependent remodelling effects are incorporated by introducing evolution equations for the integration directions of the micro‐sphere scheme, which thereby characterize the material's anisotropic properties. An appropriate remodelling approach for the orthotropic case is discussed, whereas the effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)