PSI - Issue 79

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

286

Symmetry condition with respect to Y-axis normal plane was applied to reduce computational effort, while all degrees of freedom have been constrained to account for the presence of the surrounding material not explicitly modelled in this case study. Figure 2-a illustrates the FEM model developed for this study. Green triangles indicate the fixed constraints, whereas red triangles denote the symmetry conditions. Figure 2-b provides a detailed view of the mapped mesh in the vicinity of the notch. The SED control area is highlighted with an orange circular sector, and the control radius is represented by an orange arrow and indicated as R c . Since these devices are subjected to thermal cyclic loads going from -40 °C to 150 °C (Gaiser et al., (2015)), maximum and minimum temperatures have been applied to all the nodes to simulate the holding phases highlighted in red in Figure 2-c.

Figure 2 . a) DBC’s FEM model; b) mesh’ detail in the vicinity of the notch tip; c) Temperature’s trend during thermal fatigue tests.

Results obtained from FEM simulations performed on the DBC layouts, sampled by LHS method, were analysed through ML algorithms. A Random Forest (RF) model, a non-parametric ensemble learning method based on the aggregation of multiple decision trees to improve predictive accuracy and control overfitting, was employed to build a predictive model of the data. To identify the optimal layout characteristics, Differential Evolution, a global population-based optimization algorithm capable of minimizing complex objective functions with multiple input variables (Mohamed and Sabry, (2012)), was employed. The influence of each input variable on the output was assessed using Spearman correlation and SHAP (SHapley Additive exPlanations) analysis. Spearman correlation is a non-parametric measure of statistical dependence between two variables, evaluating how well the relationship between them can be described by a monotonic function. This is quantified through the Spearman rank coefficient, which is computed by ranking the variables and then measuring the correlation between these ranks capturing monotonic relationships (Xiao et al., (2016)). 3. Results and Discussion Following Gaiser et al., (2015) ’s methodology, who aimed to prevent DBC’s delamination by minimizing SIF and J integral, the analysis was extended to identify the combination of parameters yielding the lowest ratio of Strain Energy Density (SED) to that of the reference configuration. The reference configuration corresponded to the case without dimples and with a 90° notch opening angle (SED nd,90° ) , which exhibited the highest SED in the control area, as expressed in equation (1). Output= SED LHSi SED nd,90° (1) The statistical relationships between different compositions and mechanical properties were examined by using Spearman correlation (Kateb and Safarian, (2025)). Spearman correlation matrix reported in Figure 3 shows that the notch opening angle 2 and the dimple radius r dimple are inversely correlated with the output, indicating that lower values of these parameters correspond to higher output, while the dimple position, regulated through Cu increase