Internal Variable Theory Research Articles

Simple thermodynamical model for rigid ferromagnets

A simple thermodynamic model for rigid ferromagnets with hysteresis phenomena is constructed on the basis of the second principle of thermodynamics and the time-evolution equation of the magnetization which is subjected to satisfying the former. Both Landau-Lifshitz and longitudinal relaxation effects are obtained for a nonlinear magnetic material in which the magnetization has not reached saturation and is subjected to the influence of temperature. The possibilities of extending the obtained results to the case of elastic ferromagnets and using the obtained equations in the description of fluid suspensions of magnetic particles are briefly explored. The approach in fact belongs in the thermodynamic theory of internal variables which therefore looks promising for the description of phase-transition phenomena.

On thermodynamics and intrinsically equilibrated materials

The existence and uniqueness of free energy functions is demonstrated for a class of materials broad enough to contain as special cases those of the theory of finite elasticity, the theory of hypo-elasticity, and the theory of internal state variables for which the path of evolution is invariant under rescalings of time.

Work Bounding Functions for Plastic Materials

The minimum work and maximum complementary work potentials for both time-independent and time-dependent plasticity are reconsidered from the viewpoint of internal variable theories. It is shown that the minimum work and maximum complementary work can be bounded in a simple and direct manner. The bounds provide the minimum work and maximum complementary work under certain limitations.

A note on the implications of thermodynamic stability in the internal variable theory of inelastic solids

Recently developed internal theories for inelastic solids are considered, and the consequences of thermodynamic stability requirements are explored. The results are expressed in a form which permits comparison with the stability postulates of Drucker and Ilyushin.

Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity

This paper is a study of the theoretical foundations of constitutive relations at finite strain for a class of solids exhibiting inelasticity as a consequence of specific structural rearrangements, on the microscale, of constituent elements of material. Metals deforming plastically through dislocation motion are of this class and form the primary application of the theory. The development is in terms of a general internal-variable thermodynamic formalism for description of the microstructural rearrangements, and it is shown how metal plasticity may be so characterized. The principal result is in the normality structure which is shown to arise in macroscopic constitutive laws when each of the local microstructural rearrangements proceeds at a rate governed by its associated thermodynamic force. This provides a theoretical framework for time-dependent inelastic behavior in terms of a “flow potential”, and reduces to statements on normality of strain increments to yield surfaces in the time-independent case. Conventional characterizations of the stress-state dependence of metallic slip are noted to be in accord with this concept of associated forces governing rates, so that the resulting normality structure may be considered directly applicable to metal plasticity.