Coexistent phase mixtures in the anti-plane shear of an elastic tube
type: Item
instance of: scholarly article
title: Coexistent phase mixtures in the anti-plane shear of an elastic tube
zbMATH Open document ID: 0816.73075
DOI: 10.1007/BF00943502
author: Ying Zhang
author: Roger Fosdick
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1995-07-06T00:00:00Z
review text: The structure of the deformed configuration of an elastic tube, whose cross-section is a ring subjected to a prescribed axial displacement of its lateral boundaries, is considered. The material is assumed to have a non-convex stored energy function. Special case when there is no minimizer in the associated anti-plane shear minimalization problem, but the energy functional has an infimum, is treated. The main variational problem is reduced to a free boundary problem, in which the subdomain where the strict convexity of the stored energy function breaks down must be determined as a part of the solution. The characterization of the intermediate phase mixture region is one of the purposes of this work.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 610989
zbMATH Keywords: non-convex stored energy function
zbMATH Keywords: minimalization problem
zbMATH Keywords: energy functional
zbMATH Keywords: free boundary problem
reviewed by: Nicolae Sandru
MaRDI profile type: Publication
cites work: Discontinuous deformation gradients away from the tip of a crack in anti- plane shear
cites work: A nonconvex variational problem related to change of phase
cites work: Transverse deformations associated with rectilinear shear in elastic solids
cites work: Helical shear of an elastic, circular tube with a non-convex stored energy
cites work: Rectilinear steady flow of simple fluids
cites work: The torsion problem for a nonconvex stored energy function
cites work: COMBINED AXIAL AND TORSIONAL SHEAR OF A TUBE OF INCOMPRESSIBLE ISOTROPIC ELASTIC MATERIAL
cites work: Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure
cites work: Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid
full work available at URL: https://doi.org/10.1007/bf00943502
OpenAlex ID: W2160662610
description: scientific article; zbMATH DE number 610989