Rheology is the study of deformation and the flow of materials under the influence of an applied stress (Ranalli, 1995). Where temperature, pressure, and the magnitudes of the applied stresses are relatively low, rocks tend to break along discrete surfaces to form fractures and faults. Where these factors are relatively high rocks tend to deform by ductile flow. Measures of strain are used to quantify the deformation.

Stress (a) is defined as the force exerted per unit area of a surface, and is measured in Pascals (Pa). Any stress acting upon a surface can be expressed in terms of a normal stress perpendicular to the surface and two components of shear stress in the plane of the surface. The state of stress within a medium is conveniently specified by the magnitudes and directions of three principal stresses that act on three planes in the medium along which the shear stress is zero. The principal stresses are mutually orthogonal and are termed a2, and a3, referring to the maximum, intermediate and minimum principal stresses, respectively. In the geosci-ences, compressive stresses are expressed as positive and tensile stresses negative. The magnitude of the difference between the maximum and minimum principal stresses is called the differential stress. Deviatoric stress represents the departure of a stress field from symmetry. The value of the differential stress and the characteristics of deviatoric stress both influence the extent and type of distortion experienced by a body.

Strain (£) is defined as any change in the size or shape of a material. Strains are usually expressed as ratios that describe changes in the configuration of a solid, such as the change in the length of a line divided by its original length. Elastic materials follow Hooke's law where strain is proportional to stress and the strain is reversible until a critical stress, known as the elastic limit, is reached. This behavior typically occurs at low stress levels and high strain rates. Beyond the elastic limit, which is a function of temperature and pressure, rocks deform by either brittle fracturing or by ductile flow. The yield stress (or yield strength) is the value of the differential stress above the elastic limit at which deformation becomes permanent. Plastic materials display continuous, irreversible deformation without fracturing.

The length of time over which stress is applied also is important in the deformation of Earth materials (Park, 1983). Rock rheology in the short term (seconds or days) is different from that of the same material stressed over durations of months or years. This difference arises because rocks exhibit higher strength at high strain rates than at low strain rates. For example, when a block of pitch is struck with a hammer, that is, subjected to rapid "instantaneous" strain, it shatters. However, when left for a period of months, pitch deforms slowly by flowing. This slow long-term flow of materials under constant stress is known as creep. On time scales of thousands of years, information about the strength and rheology of the lithosphere mainly comes from observations of isostasy and lithospheric flexure (Section 2.11.4). On time scales of millions of years, Earth rheology generally is studied using a continuum mechanics approach, which describes the macroscopic relationships between stress and strain, and their time derivatives. Alternatively, the long-term rhe-ology of the Earth may be studied using a microphysi-cal approach, where the results oflaboratory experiments and observations of microstructures are used to constrain the behavior of rocks. Both of these latter approaches have generated very useful results (e.g. Sections 7.6.6, 8.6.2, 10.2.5).

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