Three-dimensional plasticity with kinematic and isotropic hardening

This chapter provides an introduction to combined isotropic-kinematic hardening plasticity models in the three-dimensional small strain setting. The additive decomposition of the strain is introduced along with the concepts of plastic strain, equivalent tensile plastic strain, and back stress for three-dimensional problems. Plastic flow is discussed and defined, and a complete model of plasticity is formulated with Kuhn-Tucker loading/unloading conditions. The kinematic hardening model is based upon the Armstrong-Fredrick evolution law. Both rate-independent and rate-dependent (viscoplastic) models are discussed.

Three-dimensional plasticity with isotropic hardening

This chapter provides an introduction to isotropic hardening plasticity models in the three-dimensional small strain setting. The additive decomposition of the strain is introduced along with the concepts of plastic strain and equivalent tensile plastic strain for three-dimensional problems. Plastic flow is discussed and defined, and a complete model of plasticity is formulated with Kuhn-Tucker loading/unloading conditions. Both rate independent and rate dependent (viscoplastic) models are discussed with an emphasis on Mises-Hill type theories which utilizes a Prandtl-Reuss flow rule. A variety of important flow models are presented.

One-dimensional plasticity

This chapter provides an introduction to plasticity models in the one-dimensional setting. The phenomenology of plasticity is discussed together with concepts of isotropic and kinematic hardening. The additive decomposition of the strain is introduced along with the concepts of plastic strain and equivalent plastic strain. Plastic flow is discussed and defined, and complete models of plasticity are formulated with loading/unloading conditions. Both rate independent and rate dependent (viscoplastic) models are discussed. In addition, basic numerical methods for evaluating plasticity models are presented.

Natural convection of Casson fluid in a square enclosure

PurposeThe purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.Design/methodology/approachThe coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.FindingsResults highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.Originality/valueThe originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

Finite element implementation of viscoelastic and viscoplastic models

Purpose The purpose of this study is to present a finite element (FE) implementation of phenomenological three-dimensional viscoelastic and viscoplastic constitutive models for long term behaviour prediction of polymers. Design/methodology/approach The method is based on the small strain assumption but is extended to large deformation for materials in which the stress-strain relation is nonlinear and the concept of incompressibility is governing. An empirical approach is used for determining material parameters in the constitutive equations, based on measured material properties. The modelling process uses a spring and dash-pot and a power-law approximation function method for viscoelastic and viscoplastic nonlinear behaviour, respectively. The model improvement for long term behaviour prediction is done by modifying the material parameters in such a way that they account for the current test time. The determination of material properties is based on the non-separable type of relations for nonlinear materials in which the material properties change with stress coupled with time. Findings The proposed viscoelastic and viscoplastic models are implemented in a user material algorithm of the FE general-purpose program ABAQUS and the validity of the models is assessed by comparisons with experimental observations from tests on high-density polyethylene samples in one-dimensional tensile loading. Comparisons show that the proposed constitutive model can satisfactorily represent the time-dependent mechanical behaviour of polymers even for long term predictions. Originality/value The study provides a new approach in long term investigation of material behaviour using FE analysis.

Modeling Coupled Heat and Mass Transfer in Peristaltic Cylindrical Flow of Robertson-Stiff Fluid

The Robertson–Stiff fluid (RS) is a yield-pseudo-plastic model which has been used to describe the rheological properties of drilling fluids, cement slurries and bentonite suspensions. Experimentally, several rheological data showed that this model provides more consistently accurate descriptions of the rheology of such fluids than other viscoplastic models. This result motivates us to study theoretically the peristaltic transport for this shear-thinning model and for other viscoplastic models in the presence of heat and mass transfer in a cylindrical tube. For long wavelength and low Reynolds number approximations, an analytical solution is obtained. The results showed that the velocity and the temperature decrease with increasing the yield parameter and the power index while they increase with the increase in the occlusion parameter. We also observed an opposite behavior of the concentration versus these physical parameters. Moreover, all these parameters enhance the mechanical efficiency of pumping. In addition, the comparison shows that the velocity, temperature and the absolute value of concentration are greater for the proposed model than those of Herschel–Bulkley, Bingham and Casson models, respectively.