The theory of media with defect fields and models of deformation of functional layers in isotropic materials

The model of deformation of functional interphase layers is developed using the theory of media with defect-dislocation fields and the Mindlin–Toupin gradient theories. Variational equations of the models of media with defect fields and gradient theories of elasticity are presented. The theorems on equivalence of the theory of media with defects and the Mindlin-Toupin theory of inhomogeneous medium, as well as between Mindlin–Toupin nonlocal models and classical models with variable properties are proven. The energy equivalence of variational models of defect media and media modeled within the gradient strain theory, on the one hand, and functional media with variable properties analyzed in the classical theory of elasticity, on the other hand, is established. As a result, deformation of media with defect fields and media with gradient localized interphase layers in the vicinity of the interface, special zones with changing boundary conditions, can be investigated as deformation of functional materials with variable properties that satisfy the classical theory of elasticity. © 2015 by Begell House, Inc.