Deep Learning-Based Cross-scale Modeling of Mechanical Heterogeneity in Weibull Random-Field Materials

Abstract

Cross-scale mechanical characterization of heterogeneous rock-like materials remains an important challenge because their macroscopic responses are strongly affected by multiscale heterogeneity and non-uniform mechanical-property distributions. Directly resolving microscale heterogeneity in laboratory- or engineering-scale simulations is computationally expensive and inefficient. To address this issue, this study develops a deep learning-assisted multiscale framework based on Weibull random-field modeling for efficient cross-scale mechanical prediction under two-dimensional tensile loading. A Weibull random-field algorithm is first used to generate microscale heterogeneous samples, which are then converted into finite element models. The phase-field cohesive zone model (PF-CZM) is used to calculate tensile-strength responses and generate high-fidelity labels for supervised learning. An Attentive Gated Convolution Network (AGC-Net) is trained at the microscale to establish an implicit mapping between heterogeneous-field images and tensile strength. For larger-scale prediction, the framework adopts a decomposition–aggregation strategy: the laboratory-scale domain is partitioned into microscale units, AGC-Net rapidly predicts the local tensile strength of each unit, and these predicted values are integrated into the larger-scale numerical model. AGC-Net achieves an R2 of 0.789, an RMSE of 0.0344, and a MAPE of 1.46%, outperforming the tested CNN- and Transformer-based baselines. Additional RVE representativeness, transfer-learning, error-propagation, fracture-statistics, and computational-efficiency analyses support the consistency and efficiency of the framework. These results demonstrate that the proposed framework can efficiently propagate microscale strength variability into larger-scale fracture simulations, offering a practical surrogate-assisted strategy for cross-scale mechanical prediction.