On locking materials
type: Item
instance of: scholarly article
title: On locking materials
zbMATH Open document ID: 0594.73037
DOI: 10.1007/BF00046725
published in: Acta Applicandae Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: Locking materials are hyperelastic materials for which the strain tensor is constrained to stay in some convex set. The strain energy density of these materials is convex. This paper is concerned with the boundary value problem of locking materials. The boundary value problem is formulated as a dual variational problem. The author gives the dual variational principles governing the equilibrium state of an elastic- locking material. Two minimum theorems of Prager are extended and inf-sup equality is proved by means of a penalty method. The locking limit analysis is presented and discussed. The upper and lower bound formulae for the safety factor are obtained by the simultaneous use of the two variational principles (statical and kinematical methods). The results of convex analysis are applied to get the mathematical proof of the duality relations and of the equality inf-sup. The appendices of the paper deal with the stress concentrations in a problem of torsion and with the limited compressibility. In limited compressibility, only volume changes are constrained. These materials lead to simpler mathematical problems. The existence of a stress solution which satisfies the boundary conditions is proved for the limited compressibility material.
Mathematics Subject Classification ID: 74R20
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74G70
zbMATH DE Number: 3956540
zbMATH Keywords: Locking materials
zbMATH Keywords: hyperelastic materials
zbMATH Keywords: dual variational problem
zbMATH Keywords: equilibrium state
zbMATH Keywords: minimum theorems of Prager
zbMATH Keywords: inf-sup equality
zbMATH Keywords: penalty method
zbMATH Keywords: upper and lower bound
zbMATH Keywords: safety factor
zbMATH Keywords: limited compressibility
zbMATH Keywords: stress solution
author: F. Demengel
author: Pierre Suquet
reviewed by: István Ecsedi
MaRDI profile type: Publication
cites work: Q5678486
cites work: Relaxation et existence pour le problème des matériaux à blocage
cites work: Q4053162
cites work: Q4767831
cites work: Q5549989
cites work: On Ideal Locking Materials
cites work: Convex Analysis
cites work: Q3917589
description: scientific article; zbMATH DE number 3956540