Neural Operator Representation of Granular Micromechanics-based Failure Envelope
For researchers in computational mechanics and materials science, this provides a data-driven surrogate that accelerates the prediction and inverse design of failure envelopes for porous materials, though it is an incremental application of existing neural operator methods to a specific domain.
This work develops a differentiable neural operator (DeepONet) to learn the mapping from microstructure configurations to failure envelopes for granular materials, enabling efficient forward prediction and inverse identification without costly micromechanical simulations. The method incorporates physics-informed training to enforce convexity and uses active learning to reduce simulation costs, achieving accurate predictions with fewer high-fidelity simulations.
Micromechanics-based granular models are widely used to predict the failure behavior of porous and particulate materials, including concrete, soils, foams, and biological tissues. Although these models offer considerable flexibility through microstructural parametrization and statistical representation, their mapping to macroscopic responses, particularly failure envelopes, is implicit and requires costly nonlinear, non-smooth simulations, where each failure point is obtained by following a loading trajectory. This limitation is further amplified in inverse settings, where one seeks microstructure configurations that reproduce a target failure response. In this work, we propose a differentiable neural operator that learns the mapping from microstructure configurations to failure envelopes, enabling efficient forward prediction and inverse identification without repeated micromechanical simulations. To ensure mechanical admissibility, we incorporate a physics-informed training strategy that enforces convexity of the predicted envelopes, consistent with Drucker's postulate, thereby eliminating potential non-physical artifacts. We also compare finite difference and automatic differentiation for evaluating the proposed regularization, and find that finite difference provides a favorable practical trade-off in the present DeepONet-based setting. The operator is trained on failure envelopes represented as irregular point clouds, allowing learning from data sampled at heterogeneous resolutions. To further reduce computational cost, we introduce an active learning strategy that adaptively queries the micromechanical model in regions of high epistemic uncertainty. This leads to efficient exploration of the parameter space with fewer high-fidelity simulations. The versatility and performance of the method are demonstrated and benchmarked through several numerical examples.