The geometric nature of plasticity laws
type: Item
instance of: scholarly article
title: The geometric nature of plasticity laws
zbMATH Open document ID: 0568.73034
DOI: 10.1016/0020-7225(85)90072-2
author: Nguyen Dang Hung
author: Géry de Saxcé
published in: International Journal of Engineering Science
publication date: 1985-01-01T00:00:00Z
review text: The classical constitutive equations of plasticity for small strains are rewritten in terms of differential geometry. The system state is defined as a point of a differentiable manifold. The state variables are the local coordinates of this point in a chart. The internal stresses are the components of a covariant vector of the cotangent bundle to internal state manifold and the elastic domain is a convex part of cotangent vector space. The plastic yield criteria, such as von Mises condition, define a Riemannian structure over the manifold. The metric element is identified with the internal dissipation element. Constitutive laws link the covariant derivatives of the thermodynamic stress with the state variable. Hardening modulus splits up in two parts, kinematic hardening and metric hardening. The last is defined by Christoffel connection coefficients. Applied to von Mises isotropic yield condition, the metric hardening is identified with isotropic hardening. Other more involved yield conditions are also considered. The Drucker's postulate requires the introduction of parallel transport of the internal stress covector.
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 3907883
zbMATH Keywords: non-differentiable yield criteria
zbMATH Keywords: metric tensor family
zbMATH Keywords: Riemann- Christoffel tensor
zbMATH Keywords: von Mises, Baltov-Sawczuk and Tresca models
zbMATH Keywords: small strains
zbMATH Keywords: system state
zbMATH Keywords: point of a differentiable manifold
zbMATH Keywords: state variables
zbMATH Keywords: internal stresses
zbMATH Keywords: components of a covariant vector
zbMATH Keywords: cotangent bundle
zbMATH Keywords: internal state manifold
zbMATH Keywords: elastic domain
zbMATH Keywords: convex part of cotangent vector space
zbMATH Keywords: metric element
zbMATH Keywords: internal dissipation element
zbMATH Keywords: covariant derivatives
zbMATH Keywords: kinematic hardening
zbMATH Keywords: metric hardening
zbMATH Keywords: Christoffel connection coefficients
zbMATH Keywords: von Mises isotropic yield condition
zbMATH Keywords: isotropic hardening
zbMATH Keywords: Drucker's postulate
zbMATH Keywords: parallel transport
zbMATH Keywords: internal stress covector
MaRDI profile type: Publication
full work available at URL: 0020-7225(85)90072-2
OpenAlex ID: W2124862770
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description: scientific article; zbMATH DE number 3907883