A Linear Memory Model

Abstract

We now address the problem of finding explicit forms for the free energy of materials with constitutive relations given by linear memory functionals. Such materials are referred to in this work as linear memory materials. As we will see, the equilibrium (or alternatively, the instantaneous) contribution, which is to say the portion of the constitutive equation without memory effects, need not be linear. If the part of the constitutive equation without memory is also linear, we use the description a completely linear material. A linear viscoelastic material is understood to be completely linear, while a viscoelastic material with linear memory need not have this property.