Version of the Linear Elasticity Theory with a Structural Parameter
A. F. Revuzhenko
Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630091 Russia
Keywords: теория упругости, структура, гладкость поля смещений, дисперсия, elasticity theory, texture, smoothness of the displacement field, dispersion
Abstract
It is shown that, in the planar case, the system of constitutive equations of the linear elasticity theory should contain five independent equations. n the classical theory, only three equations are formulated, while the other two are contained in implicit form in the postulate of diffeomorphism, which the assumption of smoothness of the displacement field. A closed elasticity model is constructed without the assumption of diffeomorphism, and it contains a structural parameter having a dimension of length. It is shown that, in a static version, macrodeformations depend on stresses and the second derivatives of stresses by the coordinates, while there is dispersion of longitudinal and transverse waves in the dynamics.
DOI: 10.1134/S0021894416050060
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