Discontinuous energy minimizers in nonlinear elastostatics: An example of J. Ball revisited
type: Item
instance of: scholarly article
title: Discontinuous energy minimizers in nonlinear elastostatics: An example of J. Ball revisited
zbMATH Open document ID: 0575.73021
DOI: 10.1007/BF00041067
author: P. Podio-Guidugli
author: Giorgio Vergara Caffarelli
author: Epifanio G. Virga
published in: Journal of Elasticity
publication date: 1986-01-01T00:00:00Z
review text: [Compare \textit{J. M. Ball}, Philos. Trans. R. Soc. London, A 306, 557-611 (1982; Zbl 0513.73020).] Simple direct methods of the calculus of variations, together with mild a priori restrictions of a constitutive nature, are exploited to show that a uniform radial displacement at the boundary fails to induce a homogeneous radial expansion of a compressible elastic ball when the boundary displacement reaches a critical value (of which an explicit lower bound is offered): rather, above the critical value, energy minimizers are radial deformations with a hole at the center, and are accompanied by a stress field with radial stress vanishing, and circumferential stress unbounded, at the surface of the hole.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 3919920
zbMATH Keywords: boundary value problem replaced by minimization problem
zbMATH Keywords: properties of irregular minimizers
zbMATH Keywords: existence of singular equilibrium solutions
zbMATH Keywords: everywhere smooth radial equilibrium solutions with finite energy
zbMATH Keywords: three space dimensions
zbMATH Keywords: two space dimensions
zbMATH Keywords: fracture by loss of smoothness
zbMATH Keywords: direct methods
zbMATH Keywords: a priori restrictions of a constitutive nature
zbMATH Keywords: uniform radial displacement at the boundary
zbMATH Keywords: fails to induce a homogeneous radial expansion
zbMATH Keywords: compressible elastic ball
zbMATH Keywords: boundary displacement reaches a critical value
zbMATH Keywords: explicit lower bound
zbMATH Keywords: above the critical value
zbMATH Keywords: energy minimizers are radial deformations
zbMATH Keywords: hole at the center
zbMATH Keywords: stress field
zbMATH Keywords: radial stress vanishing
zbMATH Keywords: circumferential stress unbounded
zbMATH Keywords: surface of the hole
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00041067
OpenAlex ID: W2068817652
description: scientific article; zbMATH DE number 3919920