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Comparison of strain-gradient theory of elasticity and the classical model of media with nonconstant properties


S.A. Lurie, Y.O. Solyaev, S.S. Tarasov, C. Pham

The paper presents the interpretation of the gradient theory of elasticity, as a theory of media with nonconstant properties. By the example solving the problem of extension of two-phase one-dimensional fragment it is shown the correspondence of solutions obtained in the framework of strain-gradient models and the theory of medium with variable modulus of elasticity. The model with variable properties is constructed by adding to the original two-phase fragment the third phase (interphase layer), in which the modulus of elasticity varies along the length by a linear law or sinusoidally. Analytic functions of displacement and strain defined in this fragment. For given characteristics of the structure non-classical scaling parametre of gradient model is found for the best fit the conditions of the displacement equals in the two models, or by equating the strain energy. It is shown that strain-gradient model can approximately describes the various options of media with variable modulus of elasticity, with different values of the gradient parameter of the model determines various options for the variability of properties.
June 24, 2020
May 29, 2020

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