This study introduces a mathematical framework that offers an efficient way to predict the local strain field in two-phase composites at the meso-scale. Traditional numerical methods like finite elements are time-consuming for such analyses. The focus of this study is on a mathematical framework that approximates a high-dimensional function using low-rank approximations, particularly the first order (rank-1) approximation. This approximation method provides precise predictions of the meso-scale strain field for two-phase composites under mechanical loading. To evaluate its predictive capabilities, the proposed framework is tested on different types of two-phase composites (random, bi-continuous, and elongated morphology) and varying mechanical properties of the constituent phases, comparing the results with finite element predictions. The calibration process plays a crucial role in this approach, utilizing data, and the influence of dataset size is evaluated by measuring accuracy using statistical metrics.
The performance of the proposed rank-1-based approach is compared to existing data-science techniques and demonstrates not only accurate predictions but also requires a significantly smaller dataset compared to deep learning approaches.