The authors consider antiplane shearing motions of an incompressible visco-plastic solid. The particular constitutive equation employed assumes that the stress tensor has an “elastic” component and a component which can exhibit hysteresis. The model exhibits both “kinematic” and “isotropic” hardening. Our results consist of a set of energy type estimates for the resulting system, L2 contractivi...

A simple constitutive model for the inelastic response of steel under monotonic and random cyclic loading conditions is developed within the framework of bounding surface plasticity. The particular feature that distinguishes this model from other similar ones is the ability of the bounding surface formulation to describe in a very simple way the initial “plateau” type of perfectly plastic respo...

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of Armstrong-Frederick type. Two implicit time-stepping methods are adopted for numerical integr...

In recent years, the studies on the enhancement of the prediction capability of the sheet metal forming simulations have increased remarkably. Among the used models in the finite element simulations, the yield criteria and hardening models have a great importance for the prediction of the formability and springback. The required model parameters are determined by using the several test results,...

The common engineering practice is the selection of certain physical factors such as geometry, loading, boundary conditions, and material properties. In reality these data are more or less uncertain. In many engineering problems this uncertainty should be taken into consideration. Fuzzy set theory allows to determine randomness model response to the external loading. Two methods extension princ...

Abstract In this paper a selected type of elasto-viscoplastic constitutive equations is considered. The viscoplastic model which was proposed by Marquis generalized allowing multiple terms describing the isotropic and kinematic hardening. Furthermore, presented formulation enables one to use an arbitrary equivalent plastic strain function describe hardening behavior. What more, backstress evolu...