PSI - Issue 79

Davide D’Andrea et al. / Procedia Structural Integrity 79 (2026) 283–290

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DBC is intended. Predictive model obtained by training Random Forest Algorithm with FEM results calculated on geometric configurations sampled by LHS demonstrated to be a useful tool for designers, who can derive from there valuable insight on SED without running simulations on a particular configuration. The optimal configuration, defined as the one exhibiting the lowest output, corresponding to the ratio between its SED and that of the no-dimple with a 90 degrees notch angle reference configuration, was identified using the Differential Evolution algorithm. The influence of each geometric parameter was quantified by computing the Spearman rank coefficients and by applying SHAP analysis to the Random Forest model. This integrated approach provided an in-depth understanding of the mechanical behaviour of DBC substrates and enabled the formulation of preliminary design guidelines, which can be further refined by comparison with experimental data. In the absence of such data, minimizing the SED level is an effective strategy for the design of these components. The optimal geometry identified by the model points towards the use of large notch opening angles and/or the introduction of dimples in the vicinity of the bi-material notch opening has to be contextualized on the particular application, since restrictive design constraints have to be considered. References Berto, F., 2015. A criterion based on the local strain energy density for the fracture assessment of cracked and V-notched components made of incompressible hyperelastic materials. Theoretical and Applied Fracture Mechanics 76, 17 – 26. https://doi.org/10.1016/j.tafmec.2014.12.008 Berto, F., Lazzarin, P., 2009. A review of the volume-based strain energy density approach applied to V-notches and welded structures. Theoretical and Applied Fracture Mechanics 52(3), 183 – 194. https://doi.org/10.1016/j.tafmec.2009.10.001 Diao, Y., Yan, L., Gao, K., 2022. A strategy assisted machine learning to process multi-objective optimization for improving mechanical properties of carbon steels. Journal of Materials Science & Technology 109, 86 – 93. https://doi.org/10.1016/j.jmst.2021.09.004 Gaiser, P., Klingler, M., Wilde, J., 2015. Fracture mechanical modeling for the stress analysis of DBC ceramics, 16th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2015. IEEE, pp. 1 – 6. https://doi.org/10.1109/eurosime.2015.7103115 Han, L., Liang, L., Chen, D., Zhao, Z., Luo, F., Kang, Y., 2020. Modeling and analysis of mesh pattern influences on DBC thermal cycling reliability. Microelectronics Reliability 110, 113645. https://doi.org/10.1016/j.microrel.2020.113645 Helton, J.C., Davis, F.J., 2003. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering & System Safety 81(1), 23 – 69. https://doi.org/10.1016/s0951-8320(03)00058-9 Kateb, M., Safarian, S., 2025. Machine learning-driven predictive modeling of mechanical properties in diverse steels. Machine Learning with Applications 20, 100634. https://doi.org/10.1016/j.mlwa.2025.100634 Klusák, J., Knésl, Z., 2010. Reliability assessment of a bi-material notch: Strain energy density factor approach. Theoretical and Applied Fracture Mechanics 53(2), 89 – 93. https://doi.org/10.1016/j.tafmec.2010.03.001 Mohamed, A.W., Sabry, H.Z., 2012. Constrained optimization based on modified differential evolution algorithm. Information Sciences 194, 171 – 208. https://doi.org/10.1016/j.ins.2012.01.008 Parmar, A., Katariya, R., Patel, V., 2019. A Review on Random Forest: An Ensemble Classifier, in: Lecture Notes on Data Engineering and Communications Technologies, vol. 26. Springer, Cham, pp. 758 – 763. https://doi.org/10.1007/978-3-030-03146-6_86 Pietranico, S., Pommier, S., Lefebvre, S., Pattofatto, S., 2009. Thermal fatigue and failure of electronic power device substrates. International Journal of Fatigue 31(11 – 12), 1911 – 1920. https://doi.org/10.1016/j.ijfatigue.2009.03.011 Xiao, C., Ye, J., Esteves, R.M., Rong, C., 2016. Using Spearman’s correlation coefficients for exploratory data analysis on b ig dataset. Concurrency and Computation: Practice and Experience 28(14), 3866 – 3878. https://doi.org/10.1002/cpe.3745 Xu, L., Wang, M., Zhou, Y., Qian, Z., Liu, S., 2016. An optimal structural design to improve the reliability of Al2O3 – DBC substrates under thermal cycling. Microelectronics Reliability 56, 101 – 108. https://doi.org/10.1016/j.microrel.2015.11.013 Zhang, C., Chen, C., Zhang, Y., Yan, Y., Kang, Y., 2022. A Stress-Relieved Method Based on Bottom Pattern Design Considering Thermal and Mechanical Behavior of DBC Substrate. IEEE Access 10, 125735 – 125743. https://doi.org/10.1109/access.2022.3225657