Physical Invariant Constitutive Equation for Soft Tissues

Principal axis formulations are regularly used in isotropic elasticity but they are not often used in dealing with anisotropic problems. In this paper, based on a principal axis technique, we develop a physical invariant constitutive equation for incompressible transversely isotropic solids, where it contains only a one variable (general) function. The corresponding strain energy function depends on four invariants that have immediate physical interpretation. These invariants are useful in facilitating an experiment to obtain a specific constitutive equation for a particular type of materials. The explicit appearance of the classical ground state constants in the constitutive equation simplifies the calculation for their admissible values. A specific constitutive model is proposed for soft tissues and the model fits reasonably well with existing experimental data; it is also able to accurately predict experiment data.