Dissipation Rate Functions, Pseudopotentials, Potentials and Yield Surfaces

Abstract

This chapter is about the role of the dissipation rate function---and other functions derived from it---in determining the constitutive behaviour of dissipative materials. It consists of a discussion of some general theory, followed by examples. We address the class of materials for which knowledge of the functional form of the dissipation rate function supplies the complete constitutive response, without recourse to further assumptions. A careful distinction is drawn between functions that are true potentials and those that are pseudopotentials (defined in the chapter), in order to clarify some aspects of terminology that the Author has elsewhere found confusing. In plasticity theory the intimate relationship between the dissipation rate function and the yield surface is explored. The chapter is illustrated by examples of simple one- and two-dimensional conceptual models, as well as full continuum models. Both rate independent (plastic) and rate-dependent (viscous, or viscoplastic) models are addressed.