3D adaptive RKPM method for contact problems with elastic–plastic dynamic large deformation

The adaptive procedure of reproducing kernel particle method (RKPM) for 3D contact problems with elastic–plastic dynamic large deformation is presented. In this study, a modified cell energy error (MCEE) estimate model is constructed to capture the high gradients of stresses behavior in large deformation. Refinement particles with a new proper refinement function are inserted into the high error distribution regions. A domain decomposition method is proposed to determine the support domain size for nodes. A collocation formulation is used in the discretization of the boundary integral of the contact constraint equations formulated by a penalty method. By the use of a particle-to-segment contact algorithm, the contact constraints are imposed directly on the new added contact nodes, consequently the contact forces and their associated stiffness matrices are formulated at the nodal coordinate. For verification of the simulation results, a general benchmark test is applied to justify the accuracy and efficiency of the adaptive RKPM method. Several numerical examples are provided to illustrate the effectiveness and robustness of the suggested approach.