This equation applies approximately for small perturbations of any system in stable equilibrium, as can be seen by a second order Taylor expansion of the energies involved.  
This equation applies approximately for small perturbations of any system in stable equilibrium, as can be seen by a second order Taylor expansion of the energies involved.  Cauchy expanded its anisotropic form to three dimensional bodies, making use of a compliance matrix and its inverse.  It asserts that locally, stress and strain have the same linear relationship as they would have in a perfect simple harmonic oscillator, but it breaks down beyond the elastic limit.  With a minus sign showing how the system tends to return to equilibrium, FTP what is this law commonly applied to springs that relates force to displacement?
This equation applies approximately for small perturbations of any system in stable equilibrium, as can be seen by a second order Taylor expansion of the energies involved.  
Hooke's Law