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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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Submitted on : Friday, August 14, 2020 - 1:45:00 PM
Last modification on : Monday, October 19, 2020 - 8:26:03 PM
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V. A. Eremeyev, F. Dell'Isola. Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity. Lobachevskii Journal of Mathematics, Pleiades Publishing, 2020, 41 (10), pp.191-197. ⟨hal-02915410⟩

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