A Quadratic Contact Element Passing the Patch Test

For the two dimensional contact modeling, the standard node-to-segment quadratic contact elements are known to exhibit oscillations of the contact pressure. This situation is particularly critical when using the penalty method with a high penalty parameter because the amplitude of the oscillations increase with increasing penalty parameter. The aim of this article is to present a method for removing the oscillations of contact pressure observed while using quadratic contact element. For this purpose, the nodal forces at the slave and at the master nodes need to be evaluated appropriately. One possibility is to develop a suitable procedure for computing the nodal forces. In that sake, we selected the approach first proposed in [35] in an appropriate manner. After presenting the improved quadratic contact element, some numerical examples are illustrated in this paper to comparethe standard quadratic node-to-segment element with the proposed element. The examples show that the proposed element can strongly reduce the oscillating contact pressure for both plane and curved contact surfaces.