Numerical analysis of evolution problems in nonlinear small strains elastoviscoplasticity
type: Item
instance of: scholarly article
title: Numerical analysis of evolution problems in nonlinear small strains elastoviscoplasticity
zbMATH Open document ID: 0674.73032
DOI: 10.1007/BF01406513
author: Michel Ravachol
author: Dominique Blanchard
author: P. Le Tallec
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133350
review text: This paper introduces the mathematical and numerical analysis of two- dimensional small strain viscoplasticity problems, written as an abstract evolution problem. The constitutive model is of Burger's type, which is general enough two include Maxwell, Kelvin and isotropic plasticity with four internal variables. The problem solution is obtained by finite elements in space, coupled with Euler's backward discretization in time and a preconditioned conjugate gradient algorithm for the resulting nonlinear equations. Three numerical examples are included to illustrate this interesting procedure.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 74C10
Mathematics Subject Classification ID: 74H99
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 4104482
zbMATH Keywords: Burger's type constitutive model
zbMATH Keywords: maximal monotone operator
zbMATH Keywords: convex optimisation
zbMATH Keywords: Maxwell
zbMATH Keywords: Kelvin
zbMATH Keywords: isotropic plasticity
zbMATH Keywords: four internal variables
zbMATH Keywords: finite elements in space
zbMATH Keywords: Euler's backward discretization in time
zbMATH Keywords: preconditioned conjugate gradient algorithm
zbMATH Keywords: nonlinear equations
reviewed by: J. C. F. Telles
MaRDI profile type: Publication
cites work: Nonlinear viscoelasticity with time-dependent coefficients
cites work: Numerical analysis of the equations of small strains quasistatic elastoviscoplasticity
cites work: Q3960030
cites work: Numerical Solution of Viscoplastic Flow Problems by Augmented Lagrangians
cites work: On numerically accurate finite element solutions in the fully plastic range
cites work: Q5186672
cites work: Integrals which are convex functionals
cites work: Evolution problems for a class of dissipative materials
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description: scientific article; zbMATH DE number 4104482