LCE: Variational Multiscale Methods to Embed Macromechanical Formulations with Fine Scale Physics

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Mathematical and computational methods will be developed to endow the macromechanical continuum formulation with the fine scale physics of micromechanical material models. Cases of interest are: (1) Micromechanical models that are typically applied at spatial scales of the order of a micron. (2) Theories which incorporate microscale kinematics, constitutive laws, forces and force balance coupled with macroscopic counterparts. The aim is to extend the applicability of fine scale micromechanics to macroscopic problems, which could then be analyzed with enhanced physical accuracy by the resulting multiscale model. The methods eliminate the need for computational grid refinement to the finest microscales, thereby ensuring efficiency, while preserving a tight coupling between coarse and fine scales.