Unified and accurate simulation for large elastic strain responses of rubberlike soft materials under multiple modes of loading

Abstract

A new and explicit form of the multi-axial elastic potential for elastic soft materials is constructed by means of two invariants of the Hencky strain. The new elasticity model with this form can bypass coupling complexities and uncertainties usually involved in parameter identification. Namely, exact closed-form solutions of decoupled nature are obtainable for stress responses under multiple benchmark modes. Unlike usual solutions with numerous coupled parameters, such new solutions are independent of one another and, as such, data sets for multiple benchmark modes can be separately matched with mutually independent single-variable functions. A comparative study is presented between a few well-known models and the new model. Results show that predictions from the former agree well with uniaxial and biaxial data, as known in the literature, but would be at variance with data for the constrained stress response in the plane-strain extension. In contrast, predictions from the new model agree accurately with all data sets. Furthermore, exact solutions for the Poynting effect of freely twisted elastic thin-walled tube are obtained from the new model.