Author:

Abstract:

Modelling of elastic deformations in materials containing frictional cracks of known configuration is possible via modern finite element methods. However, it is necessary to define boundary conditions at crack faces considered as additional (internal) boundaries. The classical Coulomb friction law for flat contact surfaces does not provide explicitly the desired load-displacement relationship. Indeed, once the threshold condition is reached, the tangential displacement becomes undefined. Therefore we use another approach in which contact displacements are considered as arguments and not functions. This has been done for contact between rough surfaces. Surface relief engenders a partial slip regime (absent for flat faces) and makes it possible to express the tangential displacement as a sum of partial slip and total sliding components. The partial slip regime corresponds to the Hertz-Mindlin problem of contact between two spheres with friction, except that its solution should be extended for rough surface geometries and arbitrary loading histories. We build up this extension using the previously developed method of memory diagrams and finally obtain a semi-analytical load-displacement solution to the contact problem. The algorithm has been integrated into the COMSOL solid mechanics unit. We present several examples produced by our numerical code and also provide nonlinear analysis.