Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids
type: Item
instance of: scholarly article
title: Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids
zbMATH Open document ID: 0731.73031
DOI: 10.1016/0045-7825(90)90131-5
author: Gustavo Weber
author: Lallit Anand
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1990-01-01T00:00:00Z
review text: Topic of this paper are constitutive equations for elastic-viscoplastic bodies and their numerical integration. In this field, much research is done all over the world, and a lot of controversy is still going on. The first part of the paper gives a summary and review of the assumptions used previously by the second author as a basis for his constitutive model [e.g.: the authors and \textit{A. M. Lush}, Int. J. Plast. 5, No.5, 521-549 (1989; Zbl 0695.73009); the second author, Mech., Res. Commen. 11, 345-352 (1984; Zbl 0567.73006); J. Mech. Phys. Solids 31, 105-122 (1983; Zbl 0507.73026)]. An essential feature not occurring in other approaches is the hyperelastic relation connecting stress and logarithmic elastic strain, a generalization of Hooke's law suitable for moderately large deformation. The authors point out and discuss differences between their and other researchers' work. In the main part of the paper, a new procedure for the time integration of the constitutive equations is reported. Finally, the excellent agreement of numerical and analytical solutions to several problems verifies the accuracy of the integration procedure. The paper constitutes an essential contribution to the prediction of the behavior of elastic-viscoplastic bodies under load.
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74C20
Mathematics Subject Classification ID: 74C10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4209697
zbMATH Keywords: multiplicative decomposition of deformation gradient
zbMATH Keywords: elastic
zbMATH Keywords: plastic part
zbMATH Keywords: hypoelastic equation for stress
zbMATH Keywords: linearlized principle of virtual work
zbMATH Keywords: consistent, closed-from elasto-viscoplastic tangent operator
zbMATH Keywords: Jacobian
zbMATH Keywords: global balance
zbMATH Keywords: linear momentum
zbMATH Keywords: implicit two-point, deformation driven finite element algorithms
zbMATH Keywords: program ABAQUS
zbMATH Keywords: elastic- viscoplastic bodies
zbMATH Keywords: numerical integration
zbMATH Keywords: hyperelastic relation connecting stress and logarithmic elastic strain
zbMATH Keywords: generalization of Hooke's law
zbMATH Keywords: time integration of the constitutive equations
reviewed by: U. Gamer
Wikidata QID: Q60147444
describes a project that uses: ABAQUS
MaRDI profile type: Publication
full work available at URL: 0045-7825(90)90131-5
OpenAlex ID: W1966882731
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description: scientific article; zbMATH DE number 4209697