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Journal Articles Lobachevskii Journal of Mathematics Year : 2020

Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity

Abstract

In this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first-and second-order. Such models appear as a result of homogenization of pantographic beam lattices and in some physical models. Using anisotropic Sobolev spaces we analyze the mathematical properties of weak solutions. Null-energy solutions are discussed.
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Dates and versions

hal-02915410 , version 1 (14-08-2020)

Identifiers

  • HAL Id : hal-02915410 , version 1

Cite

V. A. Eremeyev, F. Dell'Isola. Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity. Lobachevskii Journal of Mathematics, 2020, 41 (10), pp.191-197. ⟨hal-02915410⟩

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