On the utilization of the reproducing kernel particle method for the numerical simulation of plane strain rolling

This paper draws from fundamental research on the reproducing kernel particle method (RKPM) to the development of an innovative numerical approach for analyzing rolling under plane strain conditions. The approach is based on the flow formulation for slightly compressible rigid-plastic materials and a detailed description of the method and its numerical implementation is presented with the objective of making clear the fundamental differences to the well-established finite element method for slightly compressible rigid-plastic materials. Special emphasis is placed on the construction of shape functions and their derivatives, enforcement of the essential boundary conditions and treatment of frictional effects, along the contact interface between the workpiece and the roll. The effectiveness of the proposed approach is discussed by comparing theoretical predictions with experimental data found in the literature.