A transversely isotropic visco-hyperelastic constitutive model for soft tissues
Sahil Kulkarni (Texas A&M University), Xin-Lin Gao (University of Texas at Dallas)
SES Medal Symposium in honor of D.J. Steigmann
Mon 10:45 - 12:15
MacMillan 115
A transversely isotropic visco-hyperelastic constitutive model is developed for soft tissues, which is suitable for arbitrary kinematics and high strain rates. In the first part of this paper, a constitutive model for quasi-static deformations of soft tissues is presented, in which a highly nonlinear and anisotropic soft tissue is simulated as a composite reinforced by collagen fibers. Motivated by recent experimental findings, the strain energy density function for soft tissues is additively decomposed into two parts: a neo-Hookean function for the base matrix, and a polyconvex polynomial function of four invariants for the collagen fibers. A comparison with available experimental data shows that this new model can well represent the mechanical behavior of soft tissues. In the second part, the strain energy density function is modified to account for both the quasi-static non-linear elastic behavior and the short-term memory effects, resulting in a visco-hyperelastic constitutive model. This model is tested for a wide range of loading rates from 0.01/s to 3000/s and for multiple loading scenarios. The least square method with upper/lower bound constraints is used to estimate parameters involved in the constitutive model. Explicit expressions for the elasticity and viscosity tensors are provided, which have been implemented in a finite element code to study blast induced traumatic brain injury.