PSI - Issue 80

Haolin Li et al. / Procedia Structural Integrity 80 (2026) 23–30 Author name / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 4. Deformed configurations under single-axis strain: (a) octet-truss metamaterial; (b) gyroid metamaterial; (c) spindoid metamaterial. The color represents the displacement distributions.

Fig. 5. Deformed configurations under random multi-axial strain: (a) octet-truss metamaterial; (b) gyroid metamaterial; (c) spindoid metamaterial. The color represents the displacement distributions.

4. Discussion

The results demonstrate that the proposed PINN method achieves accuracy comparable to that of FEM across both single-axis and multiple-axis strain cases. For all three metamaterial structures, the homogenised stresses predicted by PINN closely match those obtained from FEM, validating the correctness of the formulation and the implementation of the energy-based approach. In terms of e ffi ciency, the computing performance of PINN and FEM shows di ff erent behaviour depending on the structural volume fraction ( ϕ ). For the low-volume-fraction octet truss ( V f = 0 . 029), the computational times are comparable (PINN ≈ 8min; FEM ≈ 10 min). For the gyroid ( V f = 0 . 140), the gap widens (PINN ≈ 15min; FEM ≈ 47 min). For the high-volume-fraction spindoid ( V f = 0 . 307), the PINN method becomes significantly faster (PINN ≈ 23min; FEM ≈ 296 min). This di ff erence arises because FEM’s computational cost grows non-linearly with the number of mesh elements, whereas PINN exhibits only minor sensitivity to the increase in collocation points. Thee ff ectiveness of the proposed PINN model can be attributed to two key design choices. First, the adoption of an energy-based loss term enables faster convergence compared to the conventional strong-form PDE loss. Second, the