On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli

Victor Eremeev

doi:10.1002/zamm.202200474

On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli

Abstract

Within the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order elastic moduli and two inequalities for the Lamé moduli. The conditions are less restrictive than those followed from the positive definiteness of the deformation energy.

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Author (1)

Victor Eremeev prof. dr hab.
- Faculty of Civil and Environmental Engineering
- Gdańsk University of Technology

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Publication version: Accepted or Published Version
DOI:: Digital Object Identifier (open in new tab) 10.1002/zamm.202200474
License: Copyright (2023 Wiley-VCH GmbH)

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Keywords

STRAIN GRADIENT ELASTICITY, ELASTIC MODULI, ELLIPTICITY, SOLVABILITY

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Category:

Articles

Type:

artykuły w czasopismach

Published in:

ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik no. 103, pages 1 - 11,
ISSN: 0044-2267

Language:

English

Publication year:

2023

Bibliographic description:

Eremeev V.: On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli// ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik -Vol. 103,iss. 6 (2023), s.1-11

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