James Casey

On the Characterization of Strain-Hardening in Plasticity

Abstract : In the context of a purely mechanical, rate-type theory of elastic-plastic materials and utilizing a strain space formulation, this paper is concerned mainly with developments pertaining to strain-hardening behavior consisting of three distinct types of material response, namely hardening, softening and perfectly plastic behavior. It is shown that such strain-hardening behavior may be characterized by a rate-independent quotient of quantities occurring in the loading criteria of strain space and the corresponding loading conditions of stress space. With the use of special constitutive equations, the predictive capability of the results obtained are illustrated for strain-hardening response and saturation hardening in a uniaxial tension test.

A prescription for the identification of finite plastic strain

Abstract Although the concept of plastic strain is fundamental to the theory of plasticity, no satisfactory method has been previously given for its identification at arbitrary finite deformations. In the present paper, a procedure is described, by means of which plastic strain can be identified, both conceptually and experimentally. This, and other procedures or prescriptions, enable one to relate the concepts which appear in the rate-type constitutive theory to measurements of stress and strain. The procedure given for the identification of plastic strain also allows one to define a multiplicative decomposition of the deformation gradient which is free from the shortcomings of the one that has been usually employed during the past 20 years.

On elastic-thermo-plastic materials at finite deformations☆

Abstract With the use of rate-type constitutive equations in a strain-temperature space setting, a thermomechanical development of plasticity is presented in Lagrangian form. Particular attention is given to the construction of an entropy function, and constitutive results due to thermodynarnical considerations are discussed.

On the advantages of a geometrical viewpoint in the derivation of Lagrange's equations for a rigid continuum

By way of background, it may be remarked that for a body consisting of finitely many particles, several different derivations of Lagrange’s equations can be found in the dynamics literature.1 These include: derivations proceeding from Newton’s second law by an unenlightening manipulation of partial derivatives; those employing the principle of virtual work; and those appealing to variational principles.

Selective cocaine-related difficulties in emotional intelligence: relationship to stress and impulse control.

Emotional Intelligence (EI) comprises the ability to perceive, use, understand, and regulate emotions and may potentially contribute to variability in risk-related factors such as stress perception and impulse control in cocaine dependent individuals. The main objective of the current study is to better define EI in cocaine dependent individuals compared with healthy controls, using the Mayer, Salovey, and Caruso Emotional Intelligence Test (MSCEIT). Secondary analysis investigates the association between EI, IQ factors, perceived stress, and impulse control in both populations. Seventy-two abstinent treatment-seeking cocaine patients and 52 healthy controls were administered the MSCEIT as well as measures of IQ, perceived stress, and impulse control. Findings showed that cocaine dependent participants demonstrated highly selective EI difficulties compared with healthy controls, specifically with regard to higher-level emotional reasoning including the understanding, management, and regulation of emotion. These EI problems were associated with increased perceived stress and impulse control difficulties. IQ was significantly associated with all MSCEIT measures in the cocaine dependent participants, but not controls. Findings indicate that specific aspects of EI may be of clinical importance to cocaine dependent populations, impacting relapse-related factors such as stress dysregulation and impulse control. 

Geometrical derivation of Lagrange’s equations for a system of particles

A concise but general derivation of Lagrange’s equations is given for a system of finitely many particles subject to holonomic and nonholonomic constraints. Based directly on Newton’s second law, it takes advantage of an inertia‐based metric to obtain a geometrically transparent statement of Lagrange’s equations in configuration space. Illustrative examples are included.

Pressure dependency, strength-differential effect, and plastic volume expansion in metals

Abstract Within the framework of a purely mechanical rate-type theory of finitely deforming elastic-plastic materials, a special set of constitutive equations is introduced. These equations include a dependence both on mean normal stress and on plastic strain, and involve non-normality of plastic strain-rate. They accommodate both the strength-differential effect and plastic volume expansion. Values of the material coefficients in the constitutive equations are approximately determined with the help of published experimental data for AISI 4330 steel. The plastic strain-rate is shown to have a large non-normal component, resulting in a small plastic volume expansion. The theory is in reasonable agreement with experiment for plastic strains up to about 2% in magnitude. Further experiments are suggested so that the constitutive coefficients can be completely and accurately determined.

On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity

The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another.

On the Lagrangian description of vorticity

This paper exploits a Lagrangian form of the vorticity field that is based on a formula of Beltrami, the merits of which do not seem to have been fully appreciated. A number of new results are readily derived by using the Lagrangian description, and the classical vorticity theorems are also included. The results, being purely kinematical, apply to all deformable media (including viscous fluids) and may also be of value in computations.

Approximate kinematical relations in plasticity

Abstract Within the framework of finite plasticity, it is shown how a number of kinematical approximations can be systematically derived from the multiplicative decomposition of the deformation gradient. Particular attention is devoted to two types of approximate theories: (a) those in which elastic deformations are of a different order of magnitude than plastic deformations; and (b) those in which rotations are of a different order of magnitude than strains.