Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity

V. A. Eremeyev (1, 2) , F. Dell'Isola (3, 2)

1 Faculty of Civil and Environmental Engineering Gdańsk University of Technology Gdańsk Poland
2 Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod Russia
3 MEMOCS - International Research Center for the Mathematics & Mechanics of Complex Systems

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.

Mots clés: and phrases: strain-gradient elasticity; weak solution; existence; uniqueness; gra- dient incomplete strain-gradient elasticity

Domaines: Physique mathématique [math-ph]

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⟩