On the Continuum as an Assemblage of Homogeneous Elements or States

Summary

Some of the implications are explored of considering a continuum or a “point” in a material as an assemblage of simple models. A discussion is given of the need for and the distinction between a thermodynamics based upon a highly specialized or restricted model and one which is applicable to a wide class of material behavior. A thermodynamic statement developed on the basis of a model of material cannot be a valid general principle if it is not applicable to the combined response of two or more such models. Combinations of viscous models and combinations of elastic — perfectly plastic models are discussed in these terms. The significance of reversibility, or the ability to restore the initial state through mechanical deformation and moderate temperature changes alone, is related to dislocation concepts. Materials which work-harden with strain cycling are contrasted with those which work-soften and those which have been stabilized and do neither. The distinction between frictional and plastic behavior is discussed in thermodynamic terms along with the related questions of the degree of path independence in a space of controllable state variables and the order of the infinity of independent state variables.

The results in this paper were obtained in the course of research sponsored by the Office of Naval Research under Contract Nonr 562(20) with Brown University. Much of the approach described is complementary to that of Professor Meixner and that of Professor Kestin with whom I had so many valuable discussions.