Analysis of large plastic deformation by coupled EFG-NE method

The element-free Galerkin method (EFG) and the natural element method (NEM) are two well know methods in the computational mechanics and meshless methods. In this paper، a computational technique is presented based on coupling of EFG and NEM for large plastic deformation simulation in the tensile test and forward extrusion process. The coupling between EFG and NE is achieved by using the natural element shape functions as the weight functions for the element free Galerkin method. In this method، contrary to EFG method، the imposition of the essential boundary conditions is straight forward and shape functions fulfill the Kronecker delta property. The inspection cases are tensile test simulation in axi-symmetry state and forward extrusion simulation for circular shape components from round billets. In this method، the punch stroke value is divided to sub-steps whereas a new set of nodes become active at the end of each sub-step of deformation. Hollman-Ludwik law is selected to explain the material behavior after the yielding point. The validity of the proposed method is verified by comparing the results from EFG-NE simulation results with those obtained from finite element simulation (ANSYS result). It is concluded that the results obtained by EFG-NE method is in good agreement with those from FEM and therefore، the coupled EFG-NE method is capable to handle large plastic deformation simulation.