A reproducing kernel smooth contact formulation for metal forming simulations

This paper presents a meshfree smooth contact formulation for application to metal forming problems. The continuum-based contact formulation requires \(\text {C}^{2}\) continuity in the approximation of contact surface geometry and displacement variables, which is difficult for the conventional \(\text {C}^{0}\) finite elements. In this work, we introduce a reproducing kernel approximation to achieve arbitrary degree of smoothness for contact surface representation and displacement field approximation. This approach allows the employment of continuum-based contact formulation, leading to a continuous contact force vector and a consistent tangent particularly advantageous in the Newton iteration of contact analysis. The proposed meshfree smooth contact formulation has been applied to the simulation of metal forming processes and is shown to improve the convergence significantly in comparison with the finite element-based \(\text {C}^{0}\) contact formulation.