Visco-hyperelastic constitutive modeling of strain rate sensitive soft materials

Abstract

A novel viscous dissipation potential is proposed for the visco-hyperelastic constitutive modeling of short-time memory responses of soft materials, which can capture both linear and nonlinear large deformation behaviors over a wide range of strain rates. The proposed potential is compatible with objectivity and continuum thermodynamics principles, consists of physically motivated model parameters, and adds the capability of modeling strain rate sensitivity in the small strain regime, which is currently not possible with available external state variable driven viscous dissipation potentials. By combining the proposed viscous dissipation potential with the Mooney-Rivlin strain energy density function, a visco-hyperelastic relation is formulated and fit to the rate-dependent tensile stress-strain data of human patellar tendon, which was previously modeled using an existing viscous dissipation potential. It is demonstrated that the proposed model offers improvements in fitting accuracy and prevents possible thermodynamic instabilities in quasi-static hyperelastic models from corrupting the dynamic response. In addition, the uncomplicated mathematical form of the model and the accompanying multi-step multi-start optimization procedure helps prevent numerical instabilities. Multi-deformation mode fitting of human brain gray matter under all three primary deformation modes (compression, tension and shear) is also considered using a visco-hyperelastic model based on the proposed potential and the semi-empirical Gent-Gent strain energy density function. It is shown that visco-hyperelastic models based on the proposed viscous dissipation potential capture all the essential features of the stress-strain data with unique optimal model parameters, giving reasonable accuracy in both single and multiple deformation mode cases. Further, it is demonstrated that the proposed model is stable and robust with respect to both the choice of the hyperelastic strain energy density and the availability of data from multiple deformation modes.