Homogenization of fissured elastic solids in the presence of unilateral conditions and friction
The aim of the paper is to obtain the overall behaviour of some cracked bodies. The effective solids should be without fissures and approximate the behaviour of the real fissured bodies. A homogenization method may by used for elastic solids with periodically distributed microfissures. Detailed bibliography on the subject is given by the author. The present contribution extends the previous results of the literature by considering a three-dimensional problem with nonrectilinear fissures and taking friction into account. It deals with a three-dimensional linear hyperelastic solid weakened by periodically distributed microfissures in the presence of the Signorini's conditions with friction. The size of the fissures is not supposed to be small in comparison with dimensions of the period. The friction conditions may be anisotropic and nonconvex. The friction laws are assumed in the subdifferential form. Two homogenization problems are investigated. The first problem is purely static with a friction law of deformational plasticity type. An implicit variational inequality posed on the periodic cracked domain has to be homogenized. The local problem has the same form but posed on the period. The displacement approach and the alternative stress approach are studied. The second homogenization problem is a quasi-static one. The subdifferential friction law is of the flow law type. This leads to additional difficulties, because the variational formulation is available in the form of an implicit variational inequality coupled with a variational inequality. In both cases, the macroscopic behaviour is elasto-plastic of nonstandard type with hardening and possibly softening.
friction law of deformational plasticity type
implicit variational inequality coupled with a variational inequality
scientific article; zbMATH DE number 4193205
scientific article