ABSTRACT
Maxwell’s equations of electromagnetism cannot be proven in terms of a theoretical derivation from even more fundamental equations; they compose the brilliant design of a theory that must, of course, describe experimental observations without contradictions, and as such, they are axiomatically put on top in order to draw conclusions to be validated experimentally.47 In a similar sense, we put the governing equations of elastodynamics (3.1) and (3.2)— Newton-Cauchy’s equation and the deformation rate equation-axiomatically at the beginning, but we present physical arguments in the subsequent section because, different from Maxwell’s equations, they can be deduced from the physical laws of mechanics under the continuum hypothesis, the geometric linearization of small particle displacements, and the neglect of products of field quantities, that is to say, in a linear approximation.
