Deep material network for homogenization of piezoelectric composites

Piezoelectric composites are widely used in sensors, actuators, transducers, and energy-harvesting devices because their effective electromechanical performance can be tailored by combining constituent phases and microstructural architecture. However, conventional computational homogenization based on direct numerical simulation (DNS) is computationally expensive, particularly for multiscale simulations and material design tasks that require repeated homogenization analyses. To address this limitation, this work proposes a piezoelectric deep material network (PDMN) to efficiently homogenize two-phase piezoelectric composites. The proposed framework embeds the governing electromechanical homogenization relations directly into the network architecture, yielding a physics-informed, semi-analytical surrogate that explicitly captures the two-way coupling between the mechanical and electrical fields across constituent phases. The network is trained offline on linear electroelastic datasets and, through a fully coupled Newton--Raphson solution with a consistent electromechanical tangent, subsequently used for efficient online prediction under broader constitutive settings, including nonlinear electroelasticity and history-dependent responses. The framework is validated on two-phase composites of polyvinylidene fluoride (PVDF) and lithium niobate (LiNbO$_3$) with reversed phase arrangements under nonlinear electroelastic loading, and on a viscoelastic--piezoelectric composite exhibiting coupled stress relaxation. Numerical examples show that the proposed PDMN achieves high predictive accuracy while reducing the computational cost by more than three orders of magnitude compared with DNS. The proposed framework, therefore, provides an efficient and reliable surrogate for the multiscale analysis and design of piezoelectric composites.

Orientation-aware interaction-based deep material network in polycrystalline materials modeling

Multiscale simulations are indispensable for connecting microstructural features to the macroscopic behavior of polycrystalline materials, but their high computational demands limit their practicality. Deep material networks (DMNs) have been proposed as efficient surrogate models, yet they fall short of capturing texture evolution. To address this limitation, we propose the orientation-aware interaction-based deep material network (ODMN), which incorporates an orientation-aware mechanism and an interaction mechanism grounded in the Hill-Mandel principle. The orientation-aware mechanism learns the crystallographic textures, while the interaction mechanism captures stress-equilibrium directions among representative volume element (RVE) subregions, offering insight into internal microstructural mechanics. Notably, ODMN requires only linear elastic data for training yet generalizes effectively to complex nonlinear and anisotropic responses. Our results show that ODMN accurately predicts both mechanical responses and texture evolution under complex plastic deformation, thus expanding the applicability of DMNs to polycrystalline materials. By balancing computational efficiency with predictive fidelity, ODMN provides a robust framework for multiscale simulations of polycrystalline materials.

Foundation Model for Composite Materials and Microstructural Analysis

The rapid advancement of machine learning has unlocked numerous opportunities for materials science, particularly in accelerating the design and analysis of materials. However, a significant challenge lies in the scarcity and high cost of obtaining high-quality materials datasets. In other fields, such as natural language processing, foundation models pre-trained on large datasets have achieved exceptional success in transfer learning, effectively leveraging latent features to achieve high performance on tasks with limited data. Despite this progress, the concept of foundation models remains underexplored in materials science. Here, we present a foundation model specifically designed for composite materials. Our model is pre-trained on a dataset of short-fiber composites to learn robust latent features. During transfer learning, the MMAE accurately predicts homogenized stiffness, with an R2 score reaching as high as 0.959 and consistently exceeding 0.91, even when trained on limited data. These findings validate the feasibility and effectiveness of foundation models in composite materials. We anticipate extending this approach to more complex three-dimensional composite materials, polycrystalline materials, and beyond. Moreover, this framework enables high-accuracy predictions even when experimental data are scarce, paving the way for more efficient and cost-effective materials design and analysis.