Gradient Elasticity Theories and Methods for Identifying Gradient Model Parameters

The development of new nano-structured materials contributes to the development of nonclassical, in particular, gradient theories of elasticity. The use of gradient elasticity theories is considered justified for micro- and nano-scales in various practical problems of materials science, mechanics of composite materials, etc. This paper is devoted to a review of research on gradient elasticity theories, concerning both the development of general theo-retical approaches and their application to solving various practical problems. The article an-alyzes works where static, dynamic, and thermal processes were studied within the frame-work of gradient theories of elasticity; examples of problems of using non-classical theories of elasticity for materials and structures with individual cracks, damage, phase transitions, etc. are considered. It should be noted that a special problem in such problems is the identifi-cation of parameters of nonclassical models, which is non-trivial in contrast to the classical theory of elasticity. In this regard, the article proposes an original method for identifying the parameter of the simplified gradient elasticity model by E. Aifantis based on the presented analytical solution to the problem of one-dimensional deformation of a heavy thin layer.