An elastoplastic state of the continuously inhomogeneous medium with a cavity (Q1584110)

The author discusses a model of nonhomogeneous elastoplastic body and its application to the analysis of nonhomogeneous medium with a cavity. The elastoplastic state of the medium is determined for the case when the type of nonhomogeneity is given around the cavity. The estimates of displacements in the area of nonelastic strain are obtained in terms of generalization of two approaches. One approach is based on the associated law of plastic flow and the other incorporates the Khristianovich-Shemyakin hypotheses [see \textit{S.~A.~Khristianovich} and \textit{E.~I.~Shemyakin}, Izv. Akad. Nauk SSSR, Mekh. Tverdogo Tela 1967, No.~4, 86--97 (1967)].