Classical Theories of Continuum Mechanics

Abstract

The balance relations of thermomechanics are general laws of nature: all substances and systems of material bodies are governed by them alike. However, the balance relations for mass, momentum, energy and entropy are not sufficient for determining the fields contained in them, a fact that was established in the final remarks on the subject of balance relations (Sect. 3. 6). Additional equations are therefore required for completing the balance relations and setting up initial-boundary-value problems, to permit the development of solutions. The supplementary equations needed describe the properties constituting the individual make-up of the materials and are hence termed constitutive equations. The physical significance of the constitutive equations is the circumstance that physical processes are not determined by the balance relations alone, but also by the individual material properties, which cause different substances to behave in an entirely different way, given the same external conditions. Accordingly, constitutive equations have to be distinguished from general laws of nature referring to kinematics and balance relations. They are mathematical models, intended to reflect the characteristic features of the actual material behaviour in an idealised form. Each time we match a set of specially selected constitutive equations to the balance relations, the outcome is a specific theory of continuum mechanics.