Strain rate-dependent viscohyperelastic constitutive modeling of bovine liver tissue

The mechanical response of most soft tissue is considered to be viscohyperelastic, making the development of accurate constitutive models a challenging task. In this article, we present a constitutive model for bovine liver tissue that utilizes a viscous dissipation potential, and use it to model the response of bovine liver tissue at strain rates ranging from 0.001 to 0.04 s(-1). On the material modeling front of this study, the free energy is assumed to depend on the right Cauchy-Green deformation tensor, whereas a separate rate-dependent viscous potential is posited to characterize viscoelasticity. This viscous dissipation component is a function of the time rate of change of the right Cauchy-Green deformation tensor. On the experimental front, no-slip uniaxial compression experiments are conducted on bovine liver tissue at various strain rates. A numerical correction approach is used to account for the no-slip edge conditions, and the constitutive model is fit to the resulting corrected stress-strain data. The complete derivation of the material model, its implementation in the finite element software package ABAQUS, and a validation study are presented in this article. The results show that bovine liver tissue exhibits a strong strain-rate dependence even at the low strain rates considered here and that the proposed constitutive model is able to accurately describe this response.