A Lagrangian-extended finite-element method in modeling large-plasticity deformations and contact problems

In this paper, a Lagrangian-extended finite-element (FE) method is presented in modeling large-plasticity deformations and contact problems. The technique is used to model arbitrary interfaces in two-dimensional (2D)/three-dimensional (3D) large deformations. The material interfaces are represented independent of the FE mesh and the process is accomplished by integrating enriched elements with a larger number of Gauss points, whose positions are fixed in the element. The large elasto-plastic deformation formulation is employed within the eXtended Finite-Element Method (X-FEM) framework to simulate the nonlinear behavior of materials. The interface between two bodies is modeled by using the X-FEM technique and applying modified level set and Heaviside enrichment functions. Finally, several numerical examples of arbitrary material interfaces are modeled to demonstrate the efficiency of the Lagrangian X-FEM technique in large deformation of plasticity and contact problems.