A comparative study of hyperelastic and hypoelastic material models with constant elastic moduli for large deformation problems

Many finite element programs including commercial codes for large deformation analysis employ incremental formulations of rate-type constitutive equations which are based on hyperelastic or hypoelastic material models with constant elastic moduli. In this paper, a comparative study is carried out for hyperelastic and hypoelastic material models with constant elastic moduli of a face-centered cubic single crystal of copper. A strain energy function from the inter-atomic potential for single-crystal copper is also considered for the hyperelastic material model to obtain physically based elastic deformations. Numerical results show that constant elastic moduli of hypoelastic material models can cause considerable errors in stress and strain increments when the changes in volume and cross-sectional area of a material are not negligible.