Proposing a new nonlinear hyperviscoelastic constitutive model to describe uniaxial compression behavior and dependence of stress-relaxation response on strain levels for isotropic tissue-equivalent material

Predicting the nonlinear response of biological tissues is challenging issue, due to strain rate- (short term) and time-dependent (long-term) nature of its response. While many of the tissue properties have already been extensively examined, some are left unnoticed, such as dependence of the stress-relaxation behavior on the strain levels. In this paper, a hyperviscoelastic constitutive model is derived within the integral form presented by Pipkin and Rogers model to remove this limitation. In the suggested model, the hyperelastic and short-term viscous parts are represented by the suitable strain energy function. The long-term viscous function includes the deformation history, which is expressed through a tensorial-relaxation function and has not been considered elsewhere. The constitutive model involves a number of material parameters. The values of those are identified from experimental data for Adiprene-L100 as a tissue-equivalent material. Parameters appearing in constitutive law are estimated by fitting the model with the experimental data. It is assumed that the tissue phantom is slightly compressible, isotropic and homogenous. The obtained results indicate that the presented model can describe the nonlinearity, strain rate- (short-term) and time-dependent (long-term) effects of materials. The validation of the model is investigated and shows very good agreement with the experimental data.