# Elasticity and Flexure

In the previous chapter we introduced the concepts of stress and strain. For many solids it is appropriate to relate stress to strain through the laws of elasticity. Elastic materials deform when a force is applied and return to their original shape when the force is removed. Almost all solid materials, including essentially all rocks at relatively low temperatures and pressures, behave elastically when the applied forces are not too large. In addition, the elastic strain of many rocks is linearly proportional to the applied stress. The equations of linear elasticity are greatly simplified if the material is isotropic, that is, if its elastic properties are independent of direction. Although some metamorphic rocks with strong foliations are not strictly isotropic, the isotropic approximation is usually satisfactory for the earth’s crust and mantle. At high stress levels, or at temperatures that are a significant fraction of the rock solidus, deviations from elastic behavior occur. At low temperatures and confining pressures, rocks are brittle solids, and large deviatoric stresses cause fracture. As rocks are buried more deeply in the earth, they are subjected to increasingly large confining pressures due to the increasing weight of the overburden. When the confining pressure on the rock approaches its brittle failure strength, it deforms plastically. Plastic deformation is a continuous, irreversible deformation without fracture. If the applied force causing plastic deformation is removed, some fraction of the deformation remains.

We consider plastic deformation in Section 7–11. As discussed in Chapter 1, hot mantle rocks behave as a fluid on geological time scales; that is, they continuously deform under an applied force. Given that rocks behave quite differently in response to applied forces, depending on conditions of temperature and ressure, it is important to determine what fraction of the rocks of the crust and upper mantle behave Structure formed immediately after rapidly pouring a very viscous fluid into a container. (b) Final shape of the fluid after a long time has elapsed. elastically on geological time scales. One of the fundamental postulates of plate tectonics is that the surface plates constituting the lithosphere do not deform significantly on geological time scales. Several observations directly confirm this postulate. We know that the transform faults connecting offset segments of the oceanic ridge system are responsible for the major linear fracture zones in the ocean. That these fracture zones remain linear and at constant separation is direct evidence that the oceanic lithosphere does not deform on a time scale of 108 years. Similar evidence comes from the linearity of the magnetic lineaments of the seafloor (see Section 1–8). There is yet other direct evidence of the elastic behavior of the lithosphere on geological time scales. Although erosion destroys mountain ranges on a time scale of 106 to 107 years, many geological structures in the continental crust have ages greater than 109 years. The very existence of these structures is evidence of the elastic behavior of the lithosphere. If the rocks of the crust behaved as a fluid on geological time scales, the gravitational body force would have erased these structures. As an example, pour a very viscous substance such as molasses onto the bottom of a flat pan. If the fluid issufficiently viscous and is poured quickly enough, a structure resembling a mountain forms (see Figure 3–1a). However, over time, the fluid will eventually cover the bottom of the pan to a uniform depth.

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