Equivalent histories, minimal state and initial value problem in viscoelasticity

The modelling of materials with memory is characterized by the process and the initial state. Because of the equivalence between histories, the state is identified with the response generated by the trivial process on the given initial strain. The process is the strain since the initial time. The occurrence of histories up to past infinity is then avoided. Within this setting, the inversion of the constitutive equation and a variational formulation are examined. Moreover a virtual-work type formulation provides a simpler weak form of the initial-value problem. Uniqueness of the solution to the initial-value problem is then established. Copyright \ua9 2004 John Wiley & Sons, Ltd