Irreversible Transition in Continuum Mechanics

Summary

There is hardly any branch of science or technology in which we do not come across transition into irreversible processes. Elasticity, plasticity, visto-elasticity, creep, boundary layers, shocks and oscillations are well-known examples. For elastic-plastic deformation, the ideal model is to assume some type of yield condition. For creep, a number of creep strain laws have to be taken. For boundary layers, the pressure from the irrotational flow has to be used in the layer. In shocks a number of jump conditions are utilized.

Irreversibility, and hence, non-linearity, is involved in all such problems; but generally they are linearized with the result that discontinuities, singular surfaces (non-differential regions) have to be introduced over which two successive states of a medium are matched together with the help of some empirical laws. Analytically this involves complex constitutive equations.

It is shown that irreversible transition may be identified with the asymptotic solutions at the transition points of the field equations of the system. Combined with the concept of a generalized measure, which provides for the intrinsic non-linearity in a condensed form, the use of semi-empirical laws is eliminated and a number of new and interesting results are obtained.