Frictionless Signorini’s Contact Problem for Hyperelastic Materials with Interior Point Optimizer

This paper presents a method to solve the mechanical problems undergoing finite deformations and the contact problems without friction, between an hyperelastic body and an obstacle. The main idea is to formulate the contact problem into a constrained minimization one. The constraints are written in a simple form which makes the interior point method very useful to solve the problem. Finally, the FreeFEM and interior Point OPTimizer (IPOPT) software are used to compute and solve the contact problem. Our method is validated against several benchmarks and used on an industrial application example.