Well-posedness of the problem of non-penetrating cracks in elastic bodies whose material moduli depend on the mean normal stress

The well-posedness of the problem of non-penetrating crack in an elastic body whose material moduli depends on the mean normal stress is studied. The type of models considered are based on a new implicit theory for the response of elastic bodies. Bodies defined by these implicit theories are more general than Cauchy elastic bodies. The problem is studied within the context of a variational inequality.