Surrogate-enhanced higher order eigenstrain-based reduced order homogenization for polycrystal plasticity

Reduced-order models (ROMs) are frequently employed within concurrent multiscale frameworks to enhance the efficiency of nonlinear simulations and to mitigate the substantial computational expense associated with direct nonlinear homogenization schemes. Among these, transformation field analysis (TFA)-based ROMs have gained particular prominence due to their reliance on linear elastic simulations for model construction and their characteristically low dimensionality. However, extensive studies have demonstrated that these models often exhibit an artificially stiff response when applied across a broad spectrum of materials. In the present study, a higher order eigenstrain homogenization scheme is presented to mitigate the overly stiff response predicted by these models. Another challenge with the incorporation of nonuniform or higher order basis within models based on TFA is the expensive integration of the constitutive response due to nonuniform fields. A novel approach to compute these integrals is established that reduces the number of integration parameters over complex three-dimensional domains without additional spatial constraints. It is demonstrated that the linear modes can soften the elasto-plastic response and that the proposed integration method achieves approximately an order-of-magnitude improvement in computational efficiency compared to brute-force integration over a background mesh.