<P> For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor; the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called the generalized Hooke's law . Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for the possibility of large rotations, large distortions, and intrinsic or induced anisotropy . </P> <P> For more general situations, any of a number of stress measures can be used, and it generally desired (but not required) that the elastic stress--strain relation be phrased in terms of a finite strain measure that is work conjugate to the selected stress measure, i.e., the time integral of the inner product of the stress measure with the rate of the strain measure should be equal to the change in internal energy for any adiabatic process that remains below the elastic limit . </P> <P> As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain . This relationship is known as Hooke's law . A geometry - dependent version of the idea was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", a linear relationship commonly referred to as Hooke's law . This law can be stated as a relationship between tensile force F and corresponding extension displacement x, </P> <Dl> <Dd> F = k x, (\ displaystyle F = kx,) </Dd> </Dl>

Who discovered the law of elastic properties of matter