A transversely isotropic visco-hyperelastic constitutive model is provided for soft tissues, which
accounts for large deformations, high strain rates, and short-term memory effects. In the first part, a constitutive model for quasi-static deformations of soft tissues is presented, in which a soft tissue is simulated as a transversely isotropic hyperelastic material composed of a matrix and reinforcing fibers. The strain energy density function for the soft tissue is additively decomposed into two terms: a
neo-Hookean function for the base matrix, and a polyconvex polynomial function of four invariants
for the fibers. A comparison with existing experimental data for porcine brain tissues and bovine
pericardium shows that this new model can well represent the quasi-static mechanical behavior of
soft tissues. In the second part, a viscous potential is proposed to describe the rate-dependent
short-term memory effects, resulting in a visco-hyperelastic constitutive model. This model is
tested for a range of strain rates from 0.1 /s to 90 /s and for multiple loading scenarios based on
available experimental data for porcine and human brain tissues. The model can be applied to other
soft tissues by using different values of material and fitting parameters.U.S. Arm