Crystal Elasticity Simulations of Polycrystalline Material Using Rank-One Approximation

This study focuses on investigating alternative computationally efficient techniques for numerically estimating the mesoscale (grain and sub-grain scales) stress and strain in volume elements within an elastic constitutive framework. The underlying principle here lies in developing approximations for the localization tensor that relates the stress and strain fields at the component level to the mesoscale, using low rank approximations. The study proposes two methods to build low rank approximations of localization tensor using different mathematical principles. Numerical results are presented to discuss the relative merits of low rank approximation vis-a-vis full scale simulations across various metals.