Shear rheology, commonly referred to simply as rheology, is the scientific study of the deformational response (strain and rate of strain) of a body to an applied force (stress), often called the stress–strain relation, expressed symbolically as f (S,E, E) = ∅. The response depends principally on the composition of the body, although the temperature and pressure can be important. (For example, the rheology of butter depends rather strongly on the temperature.) If the stress is independent of the rate of strain, the body is elastic and the symbolic relation simplifies to f (S,E) = ∅. Most elastic materials deform only slightly in response to an applied stress and the strain response to stress is adequately described by a linear relationship, obeying Hooke's law; this relationship is developed in § 6.1.

If the stress is independent of the strain, the body is fluid and the symbolic relation simplifies to f (S,E)=∅. If this relationship is linear, the fluid is said to be Newtonian. The two most commonly encountered fluids, liquid water and air, are Newtonian. However, for many geological materials the relation between stress and flow is nonlinear and the material is non-Newtonian. In general, there are two types of nonlinear rheology: shear thinning and shear thickening. A shear-thinning fluid deforms more readily as the shearing force is increased. Familiar examples of such material are latex paint and quicksand. On the other hand, a shear thickening fluid becomes more resistant to flow as the shearing stress is increased. Many geological materials, including ice (in glaciers), lavas and Earth's silicate mantle behave as shear-thinning fluids. This behavior is investigated in § 6.2.

The classification of materials as either elastic or fluid is simplistic, and somewhat misleading. For viscoelastic materials the stress depends on both strain and rate of strain. In reality a material may exhibit elastic, fluid or even more complex behavior depending on its thermodynamic state, the magnitude of the stresses applied and the time scale of interest. Most solid materials, as they are heated toward their melting point, develop more fluid-like behavior.1 Many materials (such as emulsions likemayonnaise and whipped cream) behave elastically when the applied stress is small, but change their rheological character to fluid-like or viscoelastic at higher stresses.