An anisotropic hyperelastic model with an application to soft tissues

A better and flexible hyperelastic model is required to describe the anisotropic behavior of highly nonlinear elastic materials, especially in a compressive state. In this paper, a generalized hyperelastic model for anisotropic materials with large nonlinear elastic deformations is formulated and proposed. A strain energy function for the model is proposed and decomposed into an isotropic part and an anisotropic part which allows for a variety of combinations of isotropic and anisotropic functions. The model is formulated based on the framework of the invariant theory as well as polyconvexity and coercivity conditions. The proposed strain energy function includes the invariants important when materials are in a compressive state. In order to show the potential capability of the model, it is applied to predicting the highly nonlinear elastic and anisotropic behavior under incompressibility constraint of soft tissues subjected to different load patterns including compression. The numerical results show a good agreement compared with the experimental and previous numerical results.