Spectral representation of higher-order localization relationships for elastic behavior of polycrystalline cubic materials

A computationally efficient higher-order spectral framework has been formulated for the calculation of the elastic localization tensors for polycrystalline material systems using the generalized spherical harmonics as the Fourier basis. This new approach offers tremendous potential for rapid analysis of the elastic performance of a very large set of microstructures in any selected polycrystalline material system. The spectral framework transforms the complex integral relations for local stress and strain fields (derived from established generalized composite theories) into relatively simple algebraic expressions involving polynomials of structure parameters and morphology-independent influence coefficients. These coefficients need to be established only once for a given material system. In this paper, we formulate and demonstrate a viable approach to establishing the values of the second-order influence coefficients for cubic polycrystals by calibration to the results of micromechanical finite element models.