Thermodynamics of Comtinua Considering Short-Renge Memory.

Abstract

In continuum mechanics, balance equations and constitutive equations are derived under the conditions of nonlocality and noninstantaneity. From the condition of nonlocality, Coleman's theorem is derived. In this paper, from the condition of noninstantaneity, another strong restriction is discussed whereby the 2nd-order strain rate cannot be introduced for the argument of the stress response function. This restriction is caused by the absence of terms of the 2nd-order strain rate in the dissipation function. In order to include these terms in the dissipation function, the 2nd law of thermodynamics should be modified. The author assumed that the increasing value in the entropy inequality is not an instantaneous value of entropy but is the average value in the short-range memory of entropy. With this assumption, the 2nd-order strain rate can be introduced in the argument of the stress response function.