The contact patch test for linear contact pressure distributions in 2D frictionless contact

It is well known that the classical one-pass node-to-segment algorithms for the enforcement of contact constraints fail the contact patch test. The situation is particularly critical when using the penalty method. In a recent study, the authors proposed a modified one-pass node-to-segment algorithm able to pass the contact patch test also in conjunction with the penalty method. However, in a general situ- ation the pressure distribution transferred across a contact surface is non-uniform. Hence, even for a contact element which passes the contact patch test under a uni- form distribution of the contact pressures, the transfer of a non-uniform state of stress across the contact surface may give rise to disturbances related to the discret- ization. Such disturbances introduce local solution errors and ultimately affect the accuracy of the analysis. This paper, following on from the previous study, develops an enhanced node-to-segment formulation able to pass a modified version of the contact patch test whereby a linear distribution of pressures has to be transmitted across the contact surface.