# Deep material network for homogenization of piezoelectric composites

arXiv: https://arxiv.org/abs/2606.22566 · HTML: https://mlsanity.com/paper/2606.22566/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [Exploring the 3D architectures of deep material network in data-driven multiscale mechanics](https://mlsanity.com/paper/1901.04832/) (2019)
- [An FE-DMN method for the multiscale analysis of fiber reinforced plastic components](https://mlsanity.com/paper/2103.08253/) (2021)
- [LS-DYNA Machine Learning-based Multiscale Method for Nonlinear Modeling of Short Fiber-Reinforced Composites](https://mlsanity.com/paper/2301.02738/) (2023)
- [Micromechanics-Informed Parametric Deep Material Network for Physics Behavior Prediction of Heterogeneous Materials with a Varying Morphology](https://mlsanity.com/paper/2309.11814/) (2023)
- [An FE-DMN method for the multiscale analysis of thermomechanical composites](https://mlsanity.com/paper/2109.14403/) (2021)
- [Orientation-aware interaction-based deep material network in polycrystalline materials modeling](https://mlsanity.com/paper/2502.02457/) (2025)
- [Foundation Model for Composite Microstructures: Reconstruction, Stiffness, and Nonlinear Behavior Prediction](https://mlsanity.com/paper/2411.06565/) (2024)
- [Deep Material Network: Overview, applications and current directions](https://mlsanity.com/paper/2504.12159/) (2025)
- [Efficient Nonlinear Multiscale Prediction for Unseen Polycrystalline Textures via Self-Supervised Microstructure Pretraining](https://mlsanity.com/paper/2512.06770/) (2025)
- [Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins](https://mlsanity.com/paper/2512.18104/) (2025)

## Abstract (arXiv)

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 (LiNbO3) 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.