Unified Convolutional Neural Network Framework for Thermo-mechanical Modeling of Substrate with Multi-materials

In current advanced electronic packaging, the multi-scale characteristics of composite substrate structures pose significant challenges to thermo-mechanical simulations. The industry primarily adopts homogenization-based material equivalent methods to avoid fine mesh discretization of microstructures, thereby drastically reducing the scale of finite element analysis (FEA). To address the challenges in equivalent modeling of homogenized materials, this paper proposes a convolutional neural network (CNN)-based unified modeling approach for multi-material systems, enabling the characterization and computation of homogenized equivalent properties (HEPs). The proposed approach encodes unit layouts of the substrate into multi-channel images through pixelation and grayscale normalization, where pixel grayscale values map to the mechanical parameters of each matrix material in the composite substrate. Different image channels serve as encoding channels for distinct mechanical parameters and their anisotropic components. These multi-channel images, embedded with homogenized unit matrix material parameter information, are then input into the CNN, while the corresponding homogenized unit’s equivalent stiffness matrix parameters and coefficient of thermal expansion (CTE) are designated as outputs. This constructs a CNN-based surrogate model for equivalent mechanical parameter characterization. The method achieves encoding of multiple mechanical parameter information across different channels within a single pixel space, eliminating the need for separate surrogate models trained for each material system. Instead, a single unified model is realized for generalized representation of equivalent mechanical parameters across diverse material systems, enhancing the model’s versatility and usability.