Learning deep Implicit Fourier Neural Operators (IFNOs) with applications to heterogeneous material modeling

Constitutive modeling based on continuum mechanics theory has been a classical approach for the mechanical responses of materials. However, when constitutive laws are unknown or defects and/or high degrees heterogeneity present, these models may become inaccurate. In this work, we propose to use data-driven modeling, which directly utilizes high-fidelity simulation experimental measurements predict material's response without using conventional models. Specifically, material is modeled by learning implicit mappings between loading conditions and resultant displacement damage fields, with neural network serving as surrogate solution operator. To model complex due defects, develop novel deep operator architecture, coin Implicit Fourier Neural Operator (IFNO). IFNO, increment layers an integral capture long-range dependencies in feature space. As gets deeper, limit IFNO becomes fixed point equation that yields naturally mimics displacement/damage fields solving procedure problems. We demonstrate performance our proposed method number examples, including hyperelastic, anisotropic brittle application, further employ learn from digital image correlation (DIC) tracking measurements, show learned operators substantially outperform predicting fields.