Differential Equations and Nonlinear Mechanics pp 285-291 | Cite as

# On the Modelling of Dissipative Processes

## Abstract

A basic premise in the classical theory of elasticity (see Truesdell and Noll [1]) is that the body has a unique “natural configuration” modulo rigid motion, the “natural configuration” being usually understood as the stress free state. Such a premise is not generally true for most if not all materials, there being numerous other “configurations” in which they can exist naturally. Not all such states may be accessed by a body in a specific process, but that is not to say that such natural configurations do not exist. For instance, a virgin specimen of metal (if such a specimen is possible for after all such a specimen is produced via a complicated manufacturing process), that is in a stress free state, could be subject to sufficiently small deformations by the application of sufficiently small loads, which on the removal of the loads could return to its original stress free state (or “natural configuration”). However, the same body when subjected to a sufficiently large homogenous deformation would not return to its original stress free configuration on the removal of the load, as it might have undergone “plastic” deformation. A piece of steel, for instance, can undergo classical slip, or twin, or undergo solid to solid phase change on the application of loads, or it could melt due to an increase in temperature. At the end of any one of these above mentioned processes, the piece of steel would be associated with a different natural configuration from its initial natural configuration. In order to model the response of materials undergoing such processes, it is imperative to explicitly take cognizance of the fact that different natural configurations are accessed during such processes.

## Keywords

Reference Configuration Constitutive Theory Inelastic Behavior Stress Free State Simple Material## Preview

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