From MMGWiki
In this effort, we are formulating efficient higher-order spectral representations for establishing precise correlations between the local mechanical response and the local details of microstructure. These correlations are expressed in the form of localization tensors. We have successfully computed elastic localization tensors for a range of composite and polycrystalline material systems. The spectral representations developed in this work are formulated in such a way as to effectively separate the microstructure morphology (i.e. structure) information from the fundamental material property information, facilitating independent search and optimization activities in the key design spaces. The spectral framework replaces complex integral relations for local stress and strain fields (derived from established composite theories) by 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. We have also formulated and demonstrated a viable approach to establishing the values of the second-order influence coefficients by calibration to the results of micromechanical finite element models.
