PSI - Issue 79

Marco Piacentini et al. / Procedia Structural Integrity 79 (2026) 394–403

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achieving the lowest validation loss was retained for testing. Random shu ffl ing of the training set was performed at each epoch. All models were implemented in MATLAB. Model performance was evaluated on the test set using MSE and the coe ffi cient of determination ( R 2 ) between predictions and targets, with each property rescaled to its physical magnitude.

3. Results and Discussion

3.1. Finite Element Analysis

Due to limitations of the structure generation method, 55 structures violated periodicity and were excluded from the FE analysis. 4 additional structures were excluded from further analysis due to the absence of an intersection between the 0 . 2%o ff set line and the simulated response. Hence, 0 . 59% of the structures was excluded in total. Structures generated with similar parameters exhibit comparable, clustered mechanical responses. Fig. 5 illustrates the identified yielding points, color-coded to visualize the relation with the generation parameters. Structures exhibiting the highest E and σ y correspond to configurations with large η and α , and θ = 0 ◦ (aligned with the compression axis). Reducing η —and thus ϕ —leads to a systematic decrease in both E and σ y . For structures with high α , shifting towards θ = 90 ◦ associates with a decrease in E and σ y and an increase in the yielding strain. These trends can also be observed directly in the scatter plot of E and σ y against the generation parameters, visible in Fig. 6. Fig. 6 additionally presents the scatter plot of ϕ against the generation parameters. As expected, ϕ is primarily governed by η , with a secondary dependence on α . This partially explains the observed trends, as ϕ is a key determinant of mechanical properties. We further analyze the dependency of E and σ y on ϕ in terms of n E and n σ y from the Gibson–Ashby scaling laws Gibson and Ashby (1997):

n E ,

n σ y

E = C E · ϕ

y = C σ y · ϕ

(2)

σ

where C E and C σ y are constants calibrated fitting the expressions for structure with α < 1 . 1. For α = 1 we observe scaling compatible with bending-dominated closed-cell lattices. As α increases, the dependency on ϕ becomes stronger for θ approaching 90 ◦ , while it decreases as θ approaches 0 ◦ , although the response remains far from stretching-dominated behavior ( n E = 1).

Fig. 5. Scatter plot of yielding points, color-coded based on the respective generation parameters.