No mathematical theory can completely describe the complex world around us. Every theory is aimed at a certain class of phenomena, formulates their essential features, and disregards what is of minor importance. The theory meets its limits of applicability where a disregarded influence becomes important (Flugge, 1967).

Departures from linear viscous flow

Laboratory determinations of steady-state rock creep and field observations indicate that ductile rocks may not be well-approximated by homogeneous, isotropic, incompressible, and linear viscous fluids of uniform viscosity. In this chapter, we consider other constitutive relations that broaden the range in rock behavior described and provide a basis for understanding some of the differences arising. Because the linear Newtonian viscous fluid is the simplest material that undergoes large permanent deformation, the formulation and analysis of models using it and their application to interpret a set of field observations is always a useful first step (see Chapter 10). The results obtained establish a benchmark from which to understand differences in behavior associated with other constitutive relations. Whether the new model results in a large or subtle contrast in behavior relative to an already well-understood viscous model, we will achieve a better understanding of the reasons for the differences and a greater confidence in data interpretation.