Continuum Mechanics as an 1 effective Theory

The continuum mechanics of solids and fluids serves as fhe prototypical example of the strategy of turning a blind eye to some subset of the full set of microscopic degrees of freedom. From a continuum perspective, the deformation of the material is captured kinematically through the existence of displacement or velocity fields, while fhe forces exerted on one part of the continuum by the rest are described via a stress tensor field. For many problems of interest to the mechanical behavior of materials, it suffices to build a description purely in terms of deformation fields and their attendant forces. A review of the key elements of such theories is the subject of this chapter. However, we should also note that the purview of continuum models is wider than that described here, and includes generalizations to liquid crystals, magnetic materials, superconductors and a variety of other contexts. 

As noted above, one of the central advantages that comes with the use of continuum models is that they reduce the complexity of description of the material 

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