Anisotropy in hypoelastic soft-tissue mechanics, I: Theory

Abstract

A hypoelastic constitutive theory is derived with an eye towards modeling the passive response of soft anisotropic biological tissues. Anisotropy is handled through a material tensor whose construction is independent of the constitutive formulation. Anisotropy tensors are provided for tissues that have a single dominant fiber family with an elliptic fiber projection onto the transverse plane, and their limiting cases. The tissue is comprised of two constituents: a matrix phase and a fiber phase. The theory is derived in the polar configuration, for ease of handling the derivatives, and then mapped into the commonly used Eulerian configuration. Kirchhoff stress and its conjugate strain-rate are the state variables.