Development of a Finite Element Contact Analysis Algorithm to Pass the Patch Test

Abstract

A finite element contact analysis algorithm has to pass the so-called patch test. In the conventional one-pass approach, the virtual work due to contact force is evaluated by concentrated contact force and corresponding virtual displacement. This means that the contact force at the contact surface between deformable bodies is not transmitted appropriately in the virtual work sense. This paper proposes a new algorithm based on the one-pass approach, which evaluates the virtual work due to contact force by integrating it on the contact surfaces. Furthermore, the nodal contact pressure in the master contact surface is transmitted from that in the slave contact surface by projecting the master node onto the slave element. In this way, the proposed algorithm is capable of correctly evaluating the equivalent nodal contact force and passing the contact patch test. Two numerical examples verify the effectiveness of the new algorithm.