On ellipticity of static equations of strain gradient elasticity and infinitesimal stability

Authors

  • Victor А. Eremeyev University of Cagliari, 2, via Marengo, Cagliari, 09123, Italy

DOI:

https://doi.org/10.21638/spbu01.2023.109

Abstract

Within the framework of strain gradient elasticity under finite deformations we formulate the strong ellipticity conditions of equilibrium equations. Within the model a strain energy density is a function of the first and second deformation gradients. Ellipticity involves certain constraints on the tangent elastic moduli. It is also closely related to infinitesimal stability which is defined as the positive definiteness of the second variation of the potential energy functional. Here we consider the first boundary-value problem, that is with Dirichlettype boundary conditions. For one-dimensional deformations we determine necessary and sufficient conditions of infinitesimal instability. The latter constitute two inequalities for elastic moduli.

Keywords:

strain gradient elasticity, strong ellipticity, infinitesimal stability

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Published

2023-03-03

How to Cite

Eremeyev V. А. (2023). On ellipticity of static equations of strain gradient elasticity and infinitesimal stability. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(1), 99–108. https://doi.org/10.21638/spbu01.2023.109

Issue

Vol. 10 No. 1 (2023)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.