The balance laws for mass, momentum, and energy and the imbalance law for entropy represent fundamental principles of continuum thermomechanics and as such are presumed to hold for all bodies, whether they be solid, liquid, or gas. In contrast, the constitution of a class of bodies composed of a particular material is specified by constitutive equations. Such equations limit the class of “processes” that bodies comprised of a given material may undergo.
In the words of Truesdell & Noll (1965, §1). “The general physical laws in themselves do not suffice to determine the deformation or motion of a body subject to given loading. Before a determinate problem can be formulated, it is usually necessary to specify the material of which the body is made. In the program of continuum mechanics, such specification is stated by constitutive equations, which relate the stress tensor … to the motion. For example, the classical theory of elasticity rests upon the assumption that the stress tensor at a point depends linearly on the changes in length and mutual angle suffered by elements at that point …, while the classical theory of viscosity is based on the assumption that the stress tensor depends linearly on the instantaneous rates of change of length and mutual angle. These statements … are definitions of ideal materials. The former expresses in words the constitutive equation that defines a linearly and infinitesimally elastic material; the latter a linearly viscous fluid. […]
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