The Minimum Free Energy for a Finite-Memory Material

Abstract

In this chapter, based on work reported in [74], we derive an expression for the minimum free energy corresponding to a relaxation function with the special property that its derivative is nonzero over only a finite interval of time. It will be seen that there are special features associated with the analytic behavior of the frequencyspace representation of such relaxation functions that render this a nontrivial extension, with unique features, of the general treatments presented in Chapters 6, 13. This property of finite memory is of interest in the first instance because finite and infinite memories are not necessarily experimentally distinguishable; also, the assumption of infinite memory can lead to paradoxical results for certain problems.