Rigorous analogies between elastic and electromagnetic systems

By promoting the magnetic field variables from vectors to tensors, we have recast Maxwell's equations and the constitutive relations for an electromagnetic medium into a form that is identical with that of the basic equations for elastic waves. This approach establishes rigorous analogies between the basic equations of the two systems. Assuming that the electromagnetic energy, power and energy-power balance relations are known, we construct the corresponding relations for the elastic counterpart by using the established analogies and we find that the results are identical with those known in elastics. This illustrates that the translation of concepts and techniques from one area to the other can be effected in a simple and straight-forward manner.