A linearly conforming radial point interpolation method (LC-RPIM) for contact problems in metal forming analysis

The total Lagrangian formulation and implementation of a linearly conforming radial point interpolation method (LC-RPIM) is presented for the analysis of contact-impact problems with large deformations and for the simulation of metal forming processes. In present method, the displacement field function is approximated using RPIM shape functions possessing Kronecker delta function property, which facilitates easy the enforcement of essential boundary conditions. The gradient smoothing operations are performed to the displacement gradient and the deformation gradient over smoothing domains associated with field nodes, and an integration scheme is used based on conforming nodal integration techniques. The geometrical nonlinearities and material nonlinearities for the dynamic solution are treated by using the total Lagrangian description and an elastic-plastic constitutive law. A simple general contact searching algorithm is used to treat the contact interface in the metal forming analysis and an algorithm is presented for the contact force. A typical numerical example is given to evaluate the effectiveness of present method compared with the FEM.