Application of Reproducing Kernel Particle Method to Large Deformation Contact Analysis of Elastomers

Abstract

Abstract A meshless formulation based on the Reproducing Kernel Particle Method (RKPM) is applied to the large deformation and contact analysis of elastomeric components. In this approach, a kernel estimate that ensures the completeness requirement of a linear field is introduced to construct the global Reproducing Kernel shape functions of the displacements. The Galerkin approximation of the variational equation is formulated using the Reproducing Kernel shape functions, and the discretization can be performed without the need of a structured mesh. In this paper, a RKPM formulation for rubber materials including frictional contact conditions is presented. The contact constraint equations and essential boundary conditions are formulated in the nodal coordinate using a direct transformation method. The global Reproducing Kernel shape functions expressed in a material description are used in the total Lagrangian formulation of hyperelasticity. By the use of the smooth Reproducing Kernel shape functions, the method is effective in dealing with large deformation and contact conditions in elastomeric applications.