Constitutive Equations

Abstract

This chapter contains a wide discussion about the constitutive axioms. These axioms constitute general rules that any material must satisfy in answering to external agents. The first two of them state that the answer of a material at a point depends, in a certain way, on past history of a neighborhood of that point. The third one is the objectivity principle stating that the response of materials does not depend on the rigid frame of reference adopted to observe their behavior. The fourth is the equipresence principle postulating that, a priori, the fundamental variables of the thermokinetic process influence all the fields describing the answer of the body. Finally, the last one, the dissipation principle, requires that materials, in reacting to the external agents, satisfy the second principle of thermodynamics in any process. In such a way, the entropy inequality becomes a restriction on the constitutive equations rather than a restriction on the processes. The effects of these principles on the constitutive equations are analyzed for thermoviscoelastic materials.