Extension of the viscoplasticity theory based on overstress (VBO) to capture non-standard rate dependence in solids
type: Item
instance of: scholarly article
title: Extension of the viscoplasticity theory based on overstress (VBO) to capture non-standard rate dependence in solids
zbMATH Open document ID: 1050.74011
DOI: 10.1016/S0749-6419(01)00011-0
author: Kwangsoo Ho
author: Erhard Krempl
published in: International Journal of Plasticity
publication date: 2002-09-08T00:00:00Z
review text: The authors proposed a new VBO model. The constitutive equations are rate-dependent, which means that no loading and unloading conditions are used in the evolution of state variables. Only isothermal processes are considered, and the constitutive functions inferred in the model are identified from uniaxial experimental data. The uniaxial constitutive equations are first introduced in section 2, while the extension to a three-dimensional tensor representation is given at the end of the paper. The internal tensorial variables involved in the model are the equilibrium stress deviator \({\mathbf g}\) and the kinematic stress \({\mathbf f,}\) which allows to model the Bauschinger effect. The scalar material functions which characterize the inelastic flow law are decreasing viscosity function, or increasing flow function, considered to be dependent on the intensity of the overstress and on the drag stress, that is kept constant in the model. The overstress is defined as the difference between the stress and the equilibrium stress. The growth law for equilibrium stress is linearly dependent on the rate of stress and on the rate of kinematic stress, respectively, with the coefficients involving a viscoplastic like term. A scalar shape function controls the transition between initial quasi-elastic behaviour and fully established inelastic flow, being dependent on the intensity of the overstress and bounded by the tangent modulus and Young modulus. The viscoplastic term characterizes the long term behaviour. The authors explain that the long term solution is thought to apply when the inelastic flow is fully established. Two dimensionless function \(\lambda\) and \(\beta\) are inferred in the viscoplastic term, modeling the unusual rate dependence. The augmentation function \(\beta\) is dependent on the accumulated inelastic strain, while \(\lambda\) is considered to be equal to 1. The evolution equation for \({\mathbf f}\) is expressed in Prager hardening form. Numerical simu…
reviewed by: Sanda Cleja-Ţigoiu
Mathematics Subject Classification ID: 74C10
zbMATH DE Number: 1797343
zbMATH Keywords: kinematic hardening
zbMATH Keywords: equilibrium stress
zbMATH Keywords: viscosity function
zbMATH Keywords: shape function
zbMATH Keywords: inelastic flow
MaRDI profile type: Publication
full work available at URL: s0749-6419(01)00011-0
OpenAlex ID: W2089740379
Wikidata QID: Q127571336
description: scientific article; zbMATH DE number 1797343