Constitutive dual potentials in classical plasticity
type: Item
instance of: scholarly article
title: Constitutive dual potentials in classical plasticity
zbMATH Open document ID: 0598.73028
DOI: 10.1016/0022-5096(87)90025-1
published in: Journal of the Mechanics and Physics of Solids
publication date: 1987-01-01T00:00:00Z
review text: In several branches of solid mechanics the constitutive relations and their inverses are expressible as tensor gradients of Legendre potentials. Exceptionally the response of classical rigid/plastic materials has never been shown to admit dual potentials of any kind. This is remedied here when the yield surface is convex and the normality flow- rule applies. The sought-for potentials are nonlinear homogeneus functions of first degree: one governs the magnitude of Cauchy stress at yield and the other the magnitude of Eulerian strain-rate via a work- equivalence norm. The duality is not of Legendre type but reflects a correspondence based on polar reciprocity. The geometrical background is developed ab initio and the construction is illustrated by several examples.
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 3965541
zbMATH Keywords: constitutive dual potentials
zbMATH Keywords: yield surface is convex
zbMATH Keywords: normality flow- rule
zbMATH Keywords: nonlinear homogeneus functions of first degree
zbMATH Keywords: magnitude of Cauchy stress at yield
zbMATH Keywords: magnitude of Eulerian strain-rate
zbMATH Keywords: work-equivalence norm
author: Rodney Hill
MaRDI profile type: Publication
full work available at URL: 0022-5096(87)90025-1
OpenAlex ID: W2085541817
cites work: Some basic principles in the mechanics of solids without a natural time
cites work: Theoretical plasticity of textured aggregates
cites work: Extremal paths of plastic work and deformation
cites work: Elastic Potentials and the Structure of Inelastic Constitutive Laws
description: scientific article; zbMATH DE number 3965541