Recent advances in the numerical modeling of constitutive relations

In this paper we present an overview of the recent developments in the area of numerical and finite element modeling of nonlinear constitutive relations. The paper discusses elastic, hyperelastic, elastoplastic and anisotropic plastic material models. In the hyperelastic model an emphasis is given to the method by which the incompressibility constraint is applied. A systematic and general procedure for the numerical treatment of hyperelastic model is presented. In the elastoplastic model both infinitesimal and large strain cases are discussed. Various concerns and implications in extending infinitesimal theories into large strain case are pointed out. In the anisotropic elastoplastic case, emphasis is given to the practicality of proposed theories and its feasible and economical use in the finite element environment.