Foundations of Continuum Mechanics

Last week Mr. Noll presented a new, compact, and general theory of space-time structure for Euclidean continuum mechanics. In mathematical science organization can be effected at various levels. For example, we may construct the real numbers from the integers, or we may take axioms for the real numbers themselves as our starting point. Mr. Noll’s space-time structure furnishes a foundation for the theory of constitutive equations he formulated some years ago, but it does not change that theory or render it either more or less precise. Along with deepening the foundations, mathematical science strives also to broaden the structure. The great clarity gained from the abstract approach to constitutive equations for purely mechanical phenomena has made it possible to extend the structure of rational mechanics so as to include thermo-energetic effects in comparable generality. Thermostatics, now a century old, was never intended to apply to problems of deformation and motion; the linear “irreversible thermodynamics”, which rests on applying classical thermostatics to volume elements, has fallen so far behind recent views on mechanics as to put it quite out of the running, and the new thermodynamics, developed by Mr. Coleman, makes no use of its concepts or apparatus.