A variational method to wear with embedded roughness

A variational approach to contact mechanics with friction for the prediction of wear evolution under various indenters is proposed in this work. The contact problem is solved using the eMbedded Profile for Joint Roughness (MPJR) interface finite elements, here advanced to predict wear arising from the frictional contact problem between an indenter of any complex shape and an elastic body. The interface finite element formulation embeds the indenter shape, roughness, or any general deviation from planarity directly in the computation of the normal gap, updating the indenter geometry in time to account for the effect of wear through a microscopically postulated local Archard adhesive wear model. The formulation employs a regularized Coulomb law of friction to compute the tangential contact response, while a penalty approach is used to enforce the unilateral contact constraint. The methodology is exploited to get an insight into the complex relation between the macroscopically emergent global wear effects and the wear law at the microscale, which are intrinsically coupled through geometrical effects. To show the model predictive capability, the numerical examples consider three different indenter profiles with flat, cylindrical, and rough geometry.