Physics-informed neural network for multiscale mechanical behavior of microstructured composite materials as Cosserat continuum

The microstructural characteristics (e.g., joints and interfaces) and their scale effects can be crucial determinants of mechanical behavior in microstructured composites such as rocks, advanced materials, and construction structures. In recent years, the physics-informed neural network (PINN) has undergone rapid development for solving problems in computational solid mechanics. However, the application of PINN to modeling multi-scale mechanical be- havior in microstructured composites remains largely unexplored. One rea- son is probably that the existence of microstructure in materials is inher- ently ignored in the classical Cauchy continuum that has been extensively adopted as the foundational continuum theory in previous PINN studies for computational solid mechanics. In the current work, physical laws and equations of a non-local model, i.e., Cosserat (or micropolar) continuum, are employed to design the loss function of a fully connected artificial neural network, establishing a PINN architecture capable of capturing mechani- cal behavior in three hexagon-structured composites (termed regular, hour- glass, and skew) with distinct microstructural length scales. The results show that the PINN method can successfully model the mechanical behavior of the microstructured composites. A quantitative comparison with finite element method (FEM) solutions reveals excellent agreement, with relative errors in the predicted displacement fields maintained within the range of 10−4 ∼10−8, thereby validating the accuracy and reliability of the PINN for mechanical analysis. Further, the results also demonstrate the capability of the PINN for simulating the multiscale mechanical behavior of microstruc- tured composites by considering the Cosserat continuum. As the microstruc- ture’s scale increases, the Cosserat mechanical responses of composites show varying characteristics and more significant deviation from the results of the Cauchy continuum. This study demonstrates a potential application of PINN in the context of computational multiscale mechanics by the Cosserat contin- uum, providing an essential framework for accurately capturing the realistic mechanical behavior of microstructured materials.