Lagrangian formulations of reproducing kernel particle method for large deformation analysis with reference to rubber-like material and elasto-plasticity with contact

The reproducing kernel particle method (RKPM) is applied to large deformation analysis of rubber-like material, elasto-plasticity, and contact constraint. The purpose is to explore RKPM as a potential approach to general large deformation analysis.; The total Lagrangian formulations for rubber-like material are developed. An accurate scheme to treat essential boundary conditions is proposed. The Newmark family of implicit time integration schemes is implemented, as well as the explicit time integration scheme based on a special diagonalization of a consistent mass matrix.; The updated Lagrangian formulation for large deformation elasto-plasticity is developed with both rate-based and hyperelastic-based formulations. A material kernel function is proposed within the updated Lagrangian formulations; this method substantially facilitates the RKPM implementation of the updated Lagrangian formulations.; A fully nonlinear frictional contact algorithm is developed with the penalty method and Coulomb law. The consistent tangent stiffness matrices are obtained, which leads to a robust contact algorithm which embodies the general contact conditions.; A set of numerical examples have been analyzed. Most of them are compared with the analytical or experimental results, or the reference results of the other numerical methods; they are used to systematically study the characteristics of RKPM, and to evaluate the performances of the proposed numerical schemes. Other numerical examples emphasize practical applications, including the analyses of engineering elastomers, and sheet metal forming processes.; It is observed that RKPM is effective in handling large deformations of structures, especially severe distortions. The incompressibility constraint can be treated effectively by RKPM. The adaptivity can be performed with less effort than FEM. The proposed direct treatment of essential boundary conditions is critical to the solution accuracy of large deformation problems. The hyperelastic-based elasto-plastic formulations are numerically superior to the rate-based ones. The contact algorithm performs very well for large frictional motion. RKPM has great practical potential in simulating large deformation of rubber components and metal forming processes.