Energetic rate-independent systems

Abstract

To keep the connection with continuum mechanics, cf. also Section 1.3.2, we consider the basic state space split to two spaces Q=yxz 2.0.1, where the fast component y and the slow component z of the state q = (y, z) live. Whenever possible, however, we will write q instead of (y, z) to shorten the notation. The splitting is done such that the evolution of z in time involves dissipation, whereas that of y does not. The state space Q is equipped with a Hausdorff topology (Formula Presented), and we denote by (Formula Presented) and (Formula Presented) the corresponding convergence of sequences. Throughout, it will be sufficient to consider sequential closedness, compactness, and continuity. For notational convenience, we will not write this explicitly.