Strain Space Formulation Research Articles

Closure to “Discussion of ‘On the Nonequivalence of the Stress Space and Strain Space Formulations of Plasticity Theory’” (1984, ASME J. Appl. Mech., 51, p. 448)

Closure to “Discussion of ‘On the Nonequivalence of the Stress Space and Strain Space Formulations of Plasticity Theory’” (1984, ASME J. Appl. Mech., 51, p. 448)

On the Nonequivalence of the Stress Space and Strain Space Formulations of Plasticity Theory

Yoder and Iwan [7] have recently claimed that the stress space and strain space formulations of plasticity are equivalent. This conflicts with the results of Casey and Naghdi [6]. The main objective of the present paper is to demonstrate, with the use of fairly general constitutive equations of the type employed in [7], that the stress space and strain space formulations of plasticity theory are not equivalent. It is also shown that if the loading criteria of strain space are adopted as primary, then the main features of [7] may be obtained by specializing the results of [6].

Small deformations superposed on large deformations of an elastic-plastic material

In the context of a purely mechanical rate-type theory of plasticity, and utilizing a strain space formulation, an infinitesimal theory is developed for motions superposed on any given motion of an elastic-plastic material. The given motion may involve all forms of elastic-plastic deformation, including both loading and unloading, and in addition, the loading conditions are allowed to change due to the superposed motion. The infinitesimal theory is properly invariant under arbitrary finite superposed rigid motions.

On the Formulation of Strain-Space Plasticity With Multiple Loading Surfaces

An alternative formulation of plasticity is discussed in which strain rather than stress serves as the independent variable. The relationship of the formulation to traditional plasticity is examined for cases of both single and multiple loading surfaces. Conditions are given under which the stress and strain-space formulations are equivalent.

On the Characterization of Strain-Hardening in Plasticity

In the context of a purely mechanical, rate-type theory of elastic-plastic materials and utilizing a strain space formulation introduced in [1], 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.

Elasto-plastic coupling within a thermodynamic strain space formulation of plasticity

Elasto-plastic coupling is studied within a general thermodynamic train space formulation of rate-independent plasticity by means of plastic internal variables. The strain space formulation offers a unified approach in treating both stable and unstable material behavior simultaneously. The conditions on elasto-plastic coupling are imposed by the second law of thermodynamics and the consistency equation in the strain space formulation, and are expressed by two inequalities. This is further illustrated by specific examples where explicit necessary and sufficient conditions on the elastic moduli and their change with plastic deformation are derived for the two inequalities to be satisfied.

Il'iushin's postulate and resulting thermodynamic conditions on elasto-plastic coupling

Il'iushin's postulate is restated within a general thermodynamic strain space formulation of rate independent plasticity by means of plastic internal variables. This yields a general expression in terms of appropriate thermodynamic potentials. A combination of a thermodynamic condition, derived from the general development, with the results of Il'iushin's postulate, furnishes explicit conditions on elasto-plastic coupling. A specific example is presented, with the plastic work being the only plastic internal variable. Necessary and sufficient consitbns on the elastic moduli and their change with plastic deformation are derived, for the thermodynamic condition to be satisfied.