A coupled finite element-virtual element method for thermomechanical analysis of electronic packaging structures

TL;DR

The paper introduces a coupled FE-VE framework that partitions electronic packaging geometries into regular FEM regions and complex VE regions to efficiently handle multi-scale thermomechanical problems. By enforcing interface continuity via coincident nodal correspondence and using projection-based VE discretizations, it achieves accurate thermal and stress predictions with reduced meshing complexity. Validation across square plates, thick-walled cylinders, sintered silver interconnects, FC-BGA, and IGBT modules demonstrates consistent convergence and good agreement with reference solutions, while exhibiting favorable computational efficiency. This FE-VE approach provides a practical tool for reliability analysis of complex multi-material electronic packaging structures.

Abstract

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular geometries to maximize computational efficiency and VEM for complex shapes to enhance geometric flexibility. Interface compatibility is maintained through coincident nodal correspondence, ensuring solution continuity across domain boundaries while reducing meshing complexity and computational overhead. Validation through electronic packaging applications demonstrates reasonable agreement with reference solutions and acceptable convergence characteristics across varying mesh densities. The method effectively captures thermal distributions and stress concentrations in multi-material systems, establishing a practical computational framework for electronic packaging analysis involving complex geometries. Source codes are available at https://github.com/yanpeng-gong/FeVeCoupled-ElectronicPackaging.

Figures (32)

• Figure 1: Schematic of the thermoelastic coupling problem domain.
• Figure 2: Domain partitioning
• Figure 3: Interface mesh discretization
• Figure 5: Thermomechanical coupling analysis based on FE-VE coupled method.
• Figure 6: Geometric configuration and boundary conditions.