Coupled integral equations for microwave induced elastic wave in elastic media

The interaction of waves with materials could include multiple physics (multiphysics), depending on the properties of waves and materials. For microwave illumination on elastic media, the electromagnetic (EM) and mechanic processes exist simultaneously and are coupled together. To exactly describe the involved process with interaction of microwave and induced elastic wave, the coupled Maxwell's equations and elastic wave equations should be solved. Although such coupled equations have been derived earlier but they are in partial differential equation (PDE) form. The solutions for the equations are then only based on finite difference method (FDM) or finite element method (FEM) in addition to analytical approaches. In this work, we first derive coupled integral equations for governing the process from its PDE counterpart. The derivation is based on the Huygens' equivalence principle and extinction theorem by recognizing that the excitation of elastic wave is EM force and the induced elastic wave will be a new excitation source to affect the EM in return. The coupled integral equations is solved using Nystrm method in first time and some basic results from numerical examples for microwave illumination on piezoelectric materials are presented.