Deep Material Networks for Homogenization of Heterogeneous Piezoelectric Materials

  • Wei, Ting-Ju (National Taiwan University)
  • Chen, Chuin-Shan (National Taiwan University)

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Piezoelectric materials play a critical role in a wide range of engineering applications, including sensors, energy harvesters, and smart structures. In practical applications, these materials often exhibit pronounced microscale heterogeneity arising from complex phase distributions, material anisotropy, and nonlinear constitutive behavior of constituent phases. Accurate homogenization of piezoelectric representative volume elements (RVEs) is therefore essential for reliable multiscale analysis and design. In this study, Deep Material Networks (DMNs) are adapted as an efficient and physics-consistent surrogate framework for the homogenization of heterogeneous piezoelectric materials. Within the DMN architecture, the RVE is hierarchically decomposed into multiple subdomains to construct a reduced representation of the microstructure. Each subdomain is formulated to satisfy the fundamental averaging theorems and the Hill–Mandel condition for both mechanical and electrical fields. During offline training, the DMN is trained using datasets of linear elastic stiffness to learn this physically grounded reduced representation. During online prediction, the trained DMN parameters are analytically mapped to strain and electric field concentration tensors for the downscaling of macroscopic loading. Local constitutive laws with electromechanical coupling are then evaluated at the subdomain level, followed by homogenization to obtain the effective macroscopic response. Numerical results demonstrate that the trained DMN is capable of extrapolating to nonlinear electromechanical coupling responses while achieving substantial computational efficiency.