Study on the generalized Prandtl-Reuss constitutive equation and the corotational rates of stress tensor
type: Item
instance of: scholarly article
title: Study on the generalized Prandtl-Reuss constitutive equation and the corotational rates of stress tensor
zbMATH Open document ID: 0924.73070
DOI: 10.1007/BF02457748
author: Lizhou Pan
author: Fubao He
author: Li-Jun Shen
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1999-11-10T00:00:00Z
review text: Two shortcommings of the Prandtl-Reuss constitutive equations of nonlinear elastic-plastic materials are pointed out: 1) the lack of a rational justification for using the additive decomposition of the total deformation rate into the elastic and plastic parts in deriving this law, and 2) the difficulty to explain the phenomenon of the simple shear stress oscillation, difficulty which seems to be due to an inadequate choosing of objective rates of the stress tensor. The authors use the material corotational rate of the stress tensor to derive a generalized Prandtl-Reuss constitutive equation governing the behaviour of a nonlinear elastic material which seems to clarify the simple shear oscillation phenomenon. In obtaining this constitutive equation, the authors do not use the above mentioned additive decomposition of the deformation rate. The contents of the paper: 1. Introduction; 2. Generalized Prandtl-Reuss equations based on material corotational rates; 3. Analysis of the cause of the simple shear stress oscillation; 4. Generalized Prandtl-Reuss equations based on a modified relative corotational rates; 4.1. Prandtl-Reuss equations of kinematic hardening materials, 4.2. Prandtl-Reuss equations of von Mises-type isotropic hardening materials; 5. Numerical calculation of a simple shear deformation; 6. Conclusions.
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74C20
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 1292960
zbMATH Keywords: additive decomposition of total deformation rate
zbMATH Keywords: nonlinear elastic-plastic materials
zbMATH Keywords: simple shear stress oscillation
zbMATH Keywords: modified relative corotational rates
zbMATH Keywords: kinematic hardening materials
zbMATH Keywords: von Mises-type isotropic hardening materials
zbMATH Keywords: simple shear deformation
reviewed by: Gheorghe Gr. Ciobanu
MaRDI profile type: Publication
cites work: Elastic-Plastic Deformation at Finite Strains
cites work: Corotational rates in constitutive modeling of elastic-plastic deformation
cites work: Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity
cites work: Corotational Rates for Kinematic Hardening at Large Plastic Deformations
cites work: On the analysis of rotation and stress rate in deforming bodies
cites work: A discussion of material rotation and stress rate
cites work: A critical review of the state of finite plasticity
cites work: Effect of kinematic hardening on localized necking in biaxially stretched sheets
cites work: Finite elasto-plastic analysis of torsion problems using different spin tensors
cites work: Rotations, stress rates and strain measures in homogeneous deformation processes
full work available at URL: https://doi.org/10.1007/bf02457748
OpenAlex ID: W1989054654
description: scientific article; zbMATH DE number 1292960