PSI - Issue 80

Haolin Li et al. / Procedia Structural Integrity 80 (2026) 23–30

29

Author name / Structural Integrity Procedia 00 (2023) 000–000

7

network architecture enforces boundary conditions exactly, so the optimisation focuses solely on minimising strain energy. This eliminates the balance problem among multiple competing loss terms that often complicates standard PINN training. Beyond accuracy and speed, the PINN method provides additional advantages. It naturally supports parallel com puting, which is particularly useful in engineering applications. It also avoids the need for mesh generation, thereby simplifying preprocessing and improving scalability. Moreover, the framework can be readily extended to other prob lem classes, such as history-dependent material models, by leveraging transfer learning. In contrast, FEM computa tions must be restarted from scratch when problem settings are modified. Overall, these results suggest that the proposed PINN approach is not only a viable alternative to FEM but also o ff ers unique advantages in flexibility and scalability, making it a promising tool for future studies of complex meta material systems. This work has presented a physics-informed neural network framework designed for homogenisation of meta materials subject to large deformation. By embedding periodicity directly into the neural network architecture and adopting an energy-based loss, the method enforces boundary conditions exactly and avoids balancing multiple loss terms. Comparative studies with finite element analysis show that the proposed PINN achieves similar accuracy, while demonstrating faster performance in complex, high-volume-fraction structures such as spindoids. Additional benefits of the PINN approach include its meshfree formulation, ease of parallelisation, and adaptability to extended problem classes through transfer learning. Taken together, these results suggest that PINNs provide an e ff ective and versatile alternative to conventional solvers, opening new possibilities for computational mechanics and metamaterial design. 5. Conclusion

Data availability

Regarding the computational procedures see Li, H.. (2025). Data for “Physics-Informed Neural Networks for Multiscale Large Deformation Analysis of Metamaterials” (1.0.0). Zenodo. https: // doi.org / 10.5281 / zenodo.17232199

Acknowledgements

The authors acknowledge the supports by the project BAANG – ”Building Actions in Smart Aviation with Envi ronmental Gains” funded by the European Union Programme Horizon Europe under grant agreement no. 101079091.

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