Anisotropy in hypoelastic soft-tissue mechanics, I: Theory

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.