Preamble

We refer to a material as elastic if it may be deformed by stress but recovers its original size and shape when released from the stress. In fact no material is perfectly elastic, even if subjected to indefinitely small stresses, but if recovery is almost complete (say >99%) and, subject only to inertial delay, effectively instantaneous, a material is regarded as elastic. Even for such a material we recognize that the slight departure from perfect elasticity has important consequences, which include the attenuation of seismic waves. At high shear stresses departure from ideal elasticity increases sharply. Each material has an approximate elastic limit or yield point, which is the magnitude of stress above which inelastic or permanent deformation starts to become significant. This is additional to the recoverable elastic response and may increase with time at constant stress. There is no sharp cut-off so that very prolonged stresses can cause continued very slow deformation or creep, especially at high temperatures, as in mantle convection.

Small elastic strains are normally proportional to stress (Hooke's law). Then the ratio of stress to strain is an elastic (‘stiffness’) modulus. Stress is force per unit area, measured in pascals (Pa ≡ Nm− 2), and strain is a fractional change in some dimension or dimensions, so that elastic moduli have the same units as stress, i.e. pascals. The theory of elasticity, as we normally consider it, deals only with very small strains, for which elastic moduli are effectively material constants.