Itskov, Ehret, Mavrilas, 2006
This is a CellML version of the Polyconvex constitutive material law for Orthotropic, Incompressible materials, defining the relation between the nine independent strain components and the stress components. It is assumed that the strain components will be controlled externally by the application using this CellML model.
Please note that this CellML model has been implemented in such a manner that it could be used for peforming finite element model simulations on the CMISS software program developed at the Auckland Bioengineering Institute, The University of Auckland. For additional information on implementation of cellML files in CMISS, please refer to the following Link.
ABSTRACT: Polyconvexity of a strain-energy function is a very important mathematical condition, especially in the context of a boundary-value problem. In the present paper, we propose an exponential polyconvex anisotropic strain-energy function. It is given by a series with an arbitrary number of terms and associated material constants. Each term of this series a priori satisfies the condition of the energy- and stress-free natural state so that no additional restrictions have to be imposed. Due to the exponential form, the proposed hyperelastic model is suitable for soft biological tissues. Thus, a good agreement with experimental data on different types of tissues is achieved.
The original paper reference is cited below:
A Polyconvex anisotropic strain-energy function for soft collagenous tissues, M. Itskov, A.E. Ehret and D. Mavrilas, 2006. Biomechanics and Modeling in Mechanobiology, 5(1), 17-26. PubMed ID: 16362195