Recent advances in the numerical modeling of constitutive relations

Abstract

This chapter presents an overview of the recent developments in the area of numerical and finite element modeling of nonlinear constitutive relations. The chapter discusses the elastic, hyperelastic, elastoplastic and anisotropic plastic material models. A simple and commonly used constitutive law for elastic materials under large deformations is expressed in the chapter. In large strain situation, the components of the constitutive tensor are normally functioning of the strain state turning the equations to be nonlinear. 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 model, emphasis is given to the practicality of proposed theories and its feasible and economical use in the finite element environment.