Reduced-order model for solder balls – Potential of projection-based approaches for representing viscoplastic behavior

Abstract

The increasing complexity of automotive and industrial electronic control units makes traditional finite element analysis impractical for comprehensive design optimization, particularly when addressing thermomechanical reliability. To tackle this issue, a novel approach is introduced that dramatically reduces computational effort while preserving accuracy. The key innovation lies in utilizing a modular system of reduced-order models, which provides a more efficient way to simulate and optimize complex systems. This paper presents projection-based techniques specifically designed to effectively capture the nonlinear material behavior of solder balls, a critical component in electronic assemblies. Employing the Discrete Empirical Interpolation Method enables the representation of all solder balls within an assembly using a single, generalized reduced-order model that captures the highly nonlinear, viscoplastic behavior. This approach reduces the number of elements, leading to significantly faster simulations. Despite the reduction in computational effort, the accuracy of the simulations is maintained, ensuring reliable predictions of the thermomechanical behavior of the solder balls under different loadings. The paper demonstrates the advantages of this method, showing that it can be applied to assemblies with multiple solder balls, offering substantial reductions in the number of elements without compromising accuracy. The results indicate that the proposed approach has great potential for the design process for electronic control units, allowing for more efficient thermomechanical design optimization. Further research will focus on extending the method to handle larger models and investigating its performance for more complex applications.