2026 Theses Doctoral

Multiphysics Digital Twins of Composites with the Inclusion-Based Boundary Element Method

Zhang, Jinming

Micromechanics-based multiphysics modeling of composites predicts the effective material properties using representative volume elements (RVEs), but it often neglects meso-scale phenomena and size effects as the microstructure and boundary are often not exactly considered under homogenization. A digital twin of a material specimen with a digitalized microstructure can capture cross-scale interactions in the composite system and provide comprehensive information for overall structural behavior and local material response while interacting with the physical specimen for verification and validation, but the computational costs can be overly high when high-fidelity simulation is required.

This dissertation addresses that gap by developing the inclusion-based boundary element method (iBEM) as a numerical framework for analyzing the meso-scale behavior of actual composites with multiphysics, which combines Eshelby’s equivalent inclusion method (EIM) with the boundary element method (BEM) to calculate field responses using volume integrals of eigenfields and boundary integrals of surface loads. It captures boundary and size effects while bridging macro-scale interactions and local-scale behaviors.

The iBEM is well suited for multi-scale/physical modeling of composites. Multiphysics homogenization through iBEM is a bottom-to-top method that describes the interaction between actual microstructures and overall multiphysical response in the experimental settings, then captures the effective material properties of the specimens. New coupling phenomena can be illustrated on computer from the digital twin, which leads to new constitutive laws of multiphysical properties. For example, when a particulate composite is under a harmonic excitation, the effective stiffness can appear to be negative and effective density can become anisotropic due to the Willis coupling effect. Digital twins with iBEM provide a powerful tool for material design, manufacture, and performance prediction and demonstration.

Building on this framework of iBEM, this dissertation explores how particle size and orientation affect the effective properties of ferromagnetic composites. In particular, the size effects of magnetic spheroidal particles are analyzed. Ferromagnetic composites are fabricated by aligning particles in a polymer matrix with magnetic fields and then curing the matrix to lock the alignment. The resulting microstructure has a major impact on magnetic and mechanical properties, which can be precisely predicted using iBEM. Using the Green’s function technique, iBEM evaluates local magnetic fields, validates predictions against finite element simulations, and derives size-dependent magnetic forces and moments. Direct laboratory experiments interact with the iBEM digital twins, which provide the effective material properties and microstructural evolution during material fabrication.

When particulate composites are subjected to temperature and mechanical loadings, iBEM can be used to investigate the thermoelastic behavior, such as size effects arising from interactions between macro-scale specimens and meso-scale particles, especially as the specimen--particle size ratio (SPR) varies. The SPR plays a critical role in achieving convergent material properties. The iBEM algorithm can simulate a large number of particles for both local field and effective properties. Results show that thermal bending requires a larger SPR for convergence than uniform pure bending, highlighting shortcomings in traditional micromechanical models and the importance of cross-scale approaches for accurate predictions.

In addition, iBEM is used to examine how embedded particles affect the dynamic behavior and effective properties of viscoelastic composites under harmonic vibration, with particular focus on energy dissipation and natural-frequency changes. Digital twins with actual microstructures agree well with benchmark solutions and further reveal localized heat generation due to strain-energy loss. These local hotspots contribute to material softening and failure. The method can be used for digital twins of composite materials and structure under vibrational environment and temperature cycling, such as energetic composites, building materials, and solar panels.

To solve the inverse problem of defect detection, iBEM is combined with machine learning (ML) to identify and characterize 3D spherical inclusions in visco-elastodynamic structures. ML has been increasingly used for defect detection in nondestructive testing (NDT) and nondestructive evaluation (NDE). While a major bottleneck in ML is the need for large datasets, iBEM addresses this limitation of sample generation and trains an ML framework with a gradient-boosted-tree (GBT) classifier and class-specific deep neural networks (DNNs). The GBT classifier first determines the inclusion class under synthetic noise. Once the inclusion class is known, the ambiguity is reduced; then a class-specific DNN can predict the inclusion location and size. In this way, iBEM is applied to support near-real-time inference for structural health monitoring with minimal sensor deployment.

In conclusion, iBEM offers a reliable and efficient platform of multiphysics digital twins to simulate the cross-scale behavior of composite materials, predict the effective material properties, and optimize material design. The case studies on magnetic, thermal and viscoelastodynamic behaviors of particulate composites demonstrate the high-fidelity performance with low computational costs, which can be extended to other applications with multiphysical requirements. This study provides a solid foundation for developing advanced materials, especially for applications requiring dynamic stability, accurate property estimation, and structural strength.