This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Accurate modeling of solder joints in printed circuit boards (PCBs) under dynamic loads, such as shock and vibration, is critical for ensuring the reliability and durability of electronic devices. These components are highly susceptible to failure under dynamic loading conditions, making it essential to model their behavior with precision. Traditional modeling techniques often rely on simplified beam elements to improve computational speed or solid elements for more detailed analysis. However, these approaches have limitations in balancing efficiency and accuracy, especially when critical components like solder joints require detailed modeling. To address this challenge, this study introduces a two-scale co-simulation approach that optimizes both computational efficiency and accuracy in modeling complex systems, particularly in the context of solder joint behavior within PCBs. The core of the two-scale method is the division of the system into two models: a global model representing the overall assembly or structure and a local model focusing on detailed components, such as the solder joints. The global model is kept coarse to reduce computational costs, while the local model is refined to accurately capture the behavior of critical regions under dynamic loads. A key advantage of this method is the two-way communication between the global and local models, where detailed results from the local model are fed back into the global analysis at each time step. This allows the localized effects of the solder joints to influence the overall performance of the PCB, ensuring more accurate results compared to traditional single-scale models that ignore such localized interactions. In comparative tests, the two-scale co-simulation method demonstrated significant improvements in both accuracy and computational efficiency. Benchmarking results showed that the method achieved an error rate of only 10% compared to traditional modeling approaches. More importantly, it reduced computation time by up to 73% in the best case, highlighting the method'™s potential to provide highly accurate results while saving valuable computational resources. This efficiency is particularly crucial in dynamic simulations, where complex, time-consuming calculations can otherwise hinder the design and optimization process. The two-scale approach is highly versatile and can be applied to a wide range of engineering problems that require detailed modeling of localized phenomena. While this study focuses on solder joint modeling in PCBs, the method is equally effective for other critical components, such as complex material behaviors, intricate geometries, and structural elements in industries like aerospace, automotive, and electronics. The flexibility of the two-scale approach ensures both computational efficiency and accuracy, making it well-suited for a variety of analyses. By integrating the detailed local model results into the global analysis, this method improves the accuracy and efficiency of simulations across diverse engineering applications. In conclusion, this study presents a novel two-scale co-simulation method that balances computational efficiency and high-resolution detail, providing an effective solution for modeling solder joints under shock and vibration conditions. Its versatility makes it a valuable tool for engineers across multiple industries, ensuring more reliable and accurate simulations for modern technology.