Deep material network for homogenization of piezoelectric composites

2026-06-21

AI Summary

This work addresses the high computational cost of direct numerical homogenization for piezoelectric composites, which hinders its practical use in multiscale simulations and material design requiring frequent evaluations. To overcome this limitation, the authors propose a Piezoelectric Deep Material Network (PDMN)—a physics-informed, semi-analytical surrogate model that explicitly embeds bidirectional electro-mechanical coupling into its architecture for the first time. The framework enables efficient online prediction of nonlinear and history-dependent responses by integrating a fully coupled Newton–Raphson solver, a consistent electro-mechanical tangent operator, and a two-stage offline–online training strategy. Validated on PVDF/LiNbO₃ and viscoelastic–piezoelectric composites, the method achieves high-fidelity predictions with computational costs reduced by over three orders of magnitude compared to conventional approaches.

Abstract

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.

Problem

• computational homogenization
• piezoelectric composites
• direct numerical simulation
• multiscale simulation
• material design

Innovation

• deep material network
• piezoelectric composites
• computational homogenization
• physics-informed surrogate
• electromechanical coupling