Phase-Field-Based Machine Learning Surrogates for Multiscale Analysis of Heterogeneous Quasi-Brittle Materials
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Heterogeneous quasi-brittle materials, such as concrete, exhibit mechanical behavior that is strongly governed by their microstructure, which makes their computational representation a challenging task [1]. Multiscale approaches based on Representative Volume Elements (RVE), including computational homogenization and FE² schemes, represent the state of the art in the physical modeling of such materials[1]. However, these approaches entail high computational costs and rely on parameters that are difficult to obtain in practical engineering design contexts. In this scenario, machine learning models (ML) have emerged as a promising alternative to replace the conventional explicit RVE, offering a pathway to reduce computational cost and to make FE²-based multiscale methodologies more applicable to real engineering problems [4]. Accordingly, it remains an open question how to replace the explicit RVE with ML models that preserve physical consistency, generalization capability, and representativeness of material heterogeneities, while simultaneously reducing computational cost and dependence on difficult-to-obtain microstructural parameters. To address this gap, the proposed methodology is based on the generation of synthetic data from two-dimensional finite element analyses of RVEs modeled using phase-field constitutive models[2]. Different types of concrete are described through variations in aggregate volume fraction and gradation, as well as in the mechanical properties of the mortar and the interfacial transition zone (ITZ), while aggregates are assumed elastic. Multiple biaxial loading states are applied to each RVE, producing complete stress–strain trajectories used to train ML model, whose thermodynamic consistency is enforced through regularization terms incorporated into the loss functions[3]. As a result, a ML model is obtained that is capable of representing the effective mechanical behavior of different concretes and replacing the explicit RVE in FE² schemes. The proposed model preserves material representativeness in multiscale analyses while significantly reducing computational cost and relying on simpler, more accessible parameters, providing a practical and robust approach for engineering applications.
