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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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Details

Category:
Articles
Type:
artykuły w czasopismach
Published in:
Lobachevskii Journal of Mathematics no. 41, pages 1992 - 1998,
ISSN: 1995-0802
Language:
English
Publication year:
2020
Bibliographic description:
Eremeev V., Dell'Isola F.: Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity// Lobachevskii Journal of Mathematics -Vol. 41,iss. 10 (2020), s.1992-1998
DOI:
Digital Object Identifier (open in new tab) 10.1134/s1995080220100078
Verified by:
Gdańsk University of Technology

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