Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

A two-dimensional problem in the Stroh formalism is derived for the continuum theory of thermoelectroelasticity with polarization gradients. Dissipative effects are accounted for, according to a constitutive model outlined in previous works. The eigenvector problem is studied in the frequency domain to obtain a representation of the solution in terms of two classes of modes corresponding to opposite signs of imaginary part of the eigenvalues. Impedance and admittance tensors are exploited to express the energy flux of the thermoelectroelastic transformed field across an interface S. The compatibility conditions at S are also derived. The eigenvector equations are then rewritten in the time domain to obtain two convolution-type integral equations for the Hilbert transforms of the real fields corresponding to each mode.