A visco-hyperelastic constitutive model of short- and long-term viscous effects on isotropic soft tissues

Abstract

Understanding and modeling the constitutive behavior of soft tissues represents an important challenge with significant relevance in medicine and biology. In this paper, we propose a new visco-hyperelastic model to describe the constitutive behavior of soft tissues as an isotropic and homogeneous material. The model is based on the nonlinear framework of continuum mechanics. A generalized Rivlin strain energy and a short-term viscous strain energy are used to describe the elastic part and time-dependence viscous part, respectively, while a long-term viscous function is derived through an integral framework of the applied stretch. To calibrate the material parameters, a set of self-designed uniaxial compression and relaxation tests are carried out on cylindrical samples of bovine liver. Moreover, the model is also validated against the experimental data of synthetic tissues reported by Khan et al. The good agreement between the predicted results and experimental data establishes the relevance of the proposed model. To investigate the model reliability, we have developed a “user-defined materials” subroutine to implement the constitutive behavior of the liver tissue in ABAQUS. By using the model, we simulate in vitro bovine liver behavior under compression and in relaxation and study the relative effects of the hyperelastic and viscous components on liver biomechanics.