Dictionary:Elastic constants, elastic moduli
Elasticity deals with deformations that vanish entirely upon removal of the stresses that cause them. For small deformations, Hooke's law holds and strain is proportional to stress. The passage of a low-amplitude seismic wave is an example.
The general 3x3x3x3 elasticity tensor relating stress and strain can be expressed as a 6x6 matrix, using Voigt notation (Figure H-7). In anisotropic media this matrix possesses up to 21 independent constants. In isotropic media, where properties are the same measured in any direction, these reduce to 2 independent constants. In polar anisotropic (transversely isotropic media), where properties are the same measured in two orthogonal directions but different in the third, these reduce to 5 independent constants (see also Thomsen parameters).
The "constants" are not really constant, since they vary with pressure and temperature, and with large stress, so they are more properly called elastic moduli (Figure E-6), or stiffnesses, to contrast them with compliances.