Trilocally approximated strong-permittivity-fluctuation theory for nonlinear composite mediums

The strong-permittivity-fluctuation theory/SPFT) is well-established in the context of the homogenisation of linear composite materials. Unlike conventional homogenisation formalisms, the SPFT takes account of coherent interactions between scattering centres at sub-wavelength length scales. A weakly nonlinear second-order SPFT, applicable to electrostrictive composite materials, has recently been developed. We present here the corresponding third-order theory, namely the trilocally approximated SPFT. The issues of nonlinear SPFT convergence and the manifestation of nonlinearity enhancement are explored by means of a numerical example. The sensitivity of the nonlinear SPFT to the choice of covariance function is discussed.