On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains - Archive ouverte HAL Access content directly
Journal Articles Mathematics and Mechanics of Solids Year : 2021

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.
Fichier principal
Vignette du fichier
eremeyev2021weak.pdf (150.68 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03427363 , version 1 (13-11-2021)

Identifiers

  • HAL Id : hal-03427363 , version 1

Cite

Victor A Eremeyev, Francesco Dell'Isola. On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains. Mathematics and Mechanics of Solids, 2021. ⟨hal-03427363⟩
26 View
96 Download

Share

Gmail Facebook X LinkedIn More