Computational aspects of a pseudo-elastic constitutive model for muscle properties in a soft-bodied arthropod

In this paper we discuss the computational implementation of a new constitutive model that describes the muscle properties in a soft-bodied arthropod. Qualitatively, the muscle tissues behave similar to particle-reinforced rubber and are capable of large non-linear elastic deformations, show a hysteretic behavior, and display stress softening during the first few cycles of repeated loading. Such behavior can be described by the framework of pseudo-elastic transversely isotropic hyperelasticity. The computational model assumes compressible overall response, and is based upon a multiplicative split of the deformation gradient tensor into volumetric and isochoric parts. Details regarding the implementation of the computational model in the context of an implicit finite element solution procedure are presented. In particular, an explicit expression is provided for the material tangent stiffness tensor. Results obtained utilizing the new implementation are also presented.