Abstract
A sequential presentation of the theory of media by conserved dislocations as a variant of the theory of media with a microstructure (according to Mindlin’s definition) is given as well as a rather complete description of the particular variants of the theory, relevant from an applied point of view: Cosserat and Aero–Kuvshinskii media, porous media, media with “twinning”. The correctness of the formulation of models is determined by the use of a “kinematic” variational principle based on a formal description of the kinematics of media, the formulation of kinematic constraints for media of different complexity, and the construction of the corresponding potential energy of deformation using the Lagrange multiplier procedure. A system of defining relations is established and an agreed formulation of the boundary value problem is formulated. In this paper, much attention is paid to the analysis of the physical side of models of the media studied. The interpretation of all physical characteristics responsible for nonclassical effects is proposed, and a description of the spectrum of adhesive mechanical parameters is given. The generalized Aero-Kuvshinskii hypothesis about the proportionality of free and constrained distortions is proposed.
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This work was supported particular by the Russian Foundation for Basic Research project No. 15-01-03649 and 16-01-00623, 17-01-00837.
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Lurie, S.A., Belov, P.A., Rabinskiy, L.N. (2018). Model of Media with Conserved Dislocation. Special Cases: Cosserat Model, Aero-Kuvshinskii Media Model, Porous Media Model. In: dell'Isola, F., Eremeyev, V., Porubov, A. (eds) Advances in Mechanics of Microstructured Media and Structures. Advanced Structured Materials, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-73694-5_13
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