Space-Time Multiscale-Multiphysics Homogenization Methods for Heterogeneous Materials

We present a unified, homogenization framework for computational analysis of heterogeneous materials consisting of multiple length scales, multiple time scales and coupled-multiple physics. The research efforts also addresses the technological issues associated with modeling the morphological details of microstructures with randomly distributed inclusions. The Random Sequential Adsorption (RSA) algorithm is improved to accurately and effectively model the morphological details of materials with randomly distributed inclusions. The proposed algorithm is more robust; computational efficient and versatile in comparison to the existing methods. A temporal homogenization scheme is developed and integrated with the previously developed spatial homogenization theory for fatigue life analysis of heterogeneous materials. The unified space-time multiscale homogenization model is validated for fatigue life prediction of elevated temperature Ceramic Matrix Composites (CMCs). In the final phase of the research a mathematical model for coupled moisture diffusion-mechanical deformation is developed. This model is integrated with the spatial homogenization framework to analyze problems consisting of multiple length scales and coupled-multiple physics. The unified multiscale-multiphysics model is validated for evaluating the degradation of physical and mechanical properties of short glass fiber and carbon fiber filled thermoplastic material systems.