A new BEM for solving 2D and 3D elastoplastic problems without initial stresses/strains

Abstract

In this paper, new boundary-domain integral equations are derived for solving two- and three-dimensional elastoplastic problems. In the derived formulations, domain integrals associated with initial stresses (strains) are avoided to use, and material nonlinearities are implicitly embodied in the integrand kernels associated with the constitutive tensor. As a result, only displacements and tractions are explicitly involved in the ultimate integral equations which are easily solved by employing a mature efficient non-linear equation solver. When materials yield in response to applied forces, the constitutive tensor (slope of the stress–strain curve for a uniaxial stress state) becomes discontinuous between the elastic and plastic states, and the effect of this non-homogeneity of constitutive tensor is embodied by an additional interface integral appearing in the integral equations which include the differences of elastic and plastic constitutive tensors. The domain is discretized into internal cells to evaluate the resulted domain integrals. An incremental variable stiffness iterative algorithm is developed for solving the system of equations. Numerical examples are given to verify the correctness of the proposed BEM formulations.