Low-rank approximation of local strain in two-phase composites

Abstract

This study presents the development of a computationally efficient mathematical framework for predicting the meso-scale (local) strain field for two-phase composites under mechanical loading. The framework leverages low-rank approximations, specifically the first order (rank-1), to accurately estimate the complex meso-scale strain field, taking into account the underlying microstructure for two-phase composites. The predictive capability of the proposed framework is assessed across wide design space for two-phase composite microstructures and varying mechanical properties for the constituent phases with respect to predictions obtained from finite elements. An important step in this approach involves calibration using data, thus the effect of the size of the dataset is assessed by quantifying the accuracy using different statistical measures. The performance of the proposed method has been shown to be accurate and requires a significantly smaller dataset than existing deep learning techniques.