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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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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1002/zamm.202200474
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- Copyright (2023 Wiley-VCH GmbH)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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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
- DOI:
- Digital Object Identifier (open in new tab) 10.1002/zamm.202200474
- Sources of funding:
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- COST_FREE
- Verified by:
- Gdańsk University of Technology
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