Anisotropic hyperelastic modeling for face-centered cubic and diamond cubic structures

Abstract

A new hyperelastic model for a crystal structure with face-centered cubic or diamond cubic system is proposed. The proposed model can be simply embedded into a nonlinear finite element analysis framework and does not require information of the crystal structure. The hyperelastic constitutive relation of the model is expressed as a polynomial-based strain energy density function. Nine strain invariants of the crystal structure are directly used as polynomial bases of the model. The hyperelastic material constants, which are the coefficients of the polynomials, are determined through a numerical simulation using the least square method. In the simulation, the Cauchy-Born rule and interatomic potentials are utilized to calculate reference data under various deformation conditions. As the fitting result, the hyperelastic material constants for silicon, germanium, and six transition metals (Ni, Pd, Pt, Cu, Ag, and Au) are provided. Furthermore, numerical examples are performed using the proposed hyperelastic model.