Material rate dependence and mesh-sensitivity in localization problems
type: Item
instance of: scholarly article
title: Material rate dependence and mesh-sensitivity in localization problems
zbMATH Open document ID: 0618.73054
DOI: 10.1016/0045-7825(88)90069-2
author: A. Needleman
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: The role of material rate dependence in setting the character of governing equations is illustrated in the context of a simple one- dimensional problem. For rate dependent solids, the incremental equilibrium equations for quasi-static problems remain elliptic and wave speeds for dynamic problems remain real, even in the presence of strain- softening. The pathological mesh sensitivity associated with numerical solutions of localization problems for rate-independent solids is eliminated. In effect, material rate dependence implicitly introduces a length scale into the governing equations, although the constitutive does not contain a parameter with the dimensions of length. Numerical results are presented that illustrate the localization behavior of slightly rate- dependent solids under both quasi-static and dynamic loading conditions.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
zbMATH DE Number: 4003639
zbMATH Keywords: material rate dependence
zbMATH Keywords: governing equations
zbMATH Keywords: one-dimensional problem
zbMATH Keywords: incremental equilibrium equations
zbMATH Keywords: dynamic problems
zbMATH Keywords: strain-softening
zbMATH Keywords: mesh sensitivity
zbMATH Keywords: length scale
zbMATH Keywords: localization behavior
zbMATH Keywords: no loss of ellipticity in quasi-static problems
zbMATH Keywords: wave speeds remain real
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90069-2
OpenAlex ID: W2065721961
cites work: Q3250235
cites work: Acceleration waves in solids
cites work: Q4144896
cites work: Flow localization in the plane strain tensile test
cites work: Finite element analysis of deformation of strain-softening materials
cites work: Influence of void nucleation on ductile shear fracture at a free surface
cites work: Rate sensitivity of plastic flow and implications for yield-surface vertices
cites work: A general theory of uniqueness and stability in elastic-plastic solids
cites work: A tangent modulus method for rate dependent solids
cites work: A finite element formulation for transient analysis of viscoplastic solids with application to stress wave propagation problems
cites work: A Pre´cis of Developments in Computational Methods for Transient Analysis
cites work: Numerical stability in quasi-static elasto/visco-plasticity
cites work: Q4070842
cites work: Q3701029
description: scientific article; zbMATH DE number 4003639