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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
Abstract
We provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of dilatation only. Such a model has many applications, e.g., to describe phenomena of interest in poroelasticity or in some situations where media with scalar microstructure are necessary. We present an extension of the previous results by Eremeyev et al. (2020 Z angew Math Phys 71(6): 1–16) to the case of domains with edges and when external line forces are applied. Let us note that the interest paid to Lipschitz polyhedra-type domains is at least twofold. First, it is known that geometrical singularity of the boundary may essentially influence singularity of solutions. On the other hand, the analysis of weak solutions in polyhedral domains is of great significance for design of optimal computations using a finite-element method and for the analysis of convergence of numerical solutions.
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Authors (2)
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Francesco dell'Isola Dr. hab. Prof
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- Accepted or Published Version
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- Copyright (2021 SAGE)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
MATHEMATICS AND MECHANICS OF SOLIDS
no. 27,
pages 433 - 445,
ISSN: 1081-2865 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Eremeev V., Dell'Isola F.: On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains// MATHEMATICS AND MECHANICS OF SOLIDS -Vol. 27,iss. 3 (2022), s.433-445
- DOI:
- Digital Object Identifier (open in new tab) 10.1177/10812865211025576
- Verified by:
- Gdańsk University of Technology
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