Homogenization of fissured elastic solids in the presence of unilateral conditions and friction

摘要

The objective of this contribution is to find effective properties of hyperelastic bodies weakened by periodically distributed microfissures. Problems investigated are internal Signorini's problems with friction. Two such problems have been studied. The first problem is purely static and the friction law is of the deformational plasticity type. To find the overall properties an implicit variational inequality has been homogenized. The second problem concerns homogenization in the quasi-static case and the sliding rule of the flow law type. The variational formulation is obtained in the form of an implicit variational inequality coupled with a variational inequality. In both cases the macroscopic behaviour is elastic-plastic of nonstandard type.