Derivation of Novel Isotropic Metamaterials at the Hashin Shtrikman Stiffness Limit Enabled by Physics Informed Neural Networks
Abstract
Current methods of deriving ultrastiff isotropic metamaterials require heuristics or topology optimization, which are highly inefficient and limited by human input. To circumvent this, Physics Informed Neural Networks are applied to analytical equations to systematically solve for plate orientations in closed cell lattices. Following a standardized procedure, the plate orientations were modelled and assembled into geometries resembling quasi random foams for validation via finite element simulations. Closed cell 6-plate geometries were also additively manufactured using LAPIS and experimentally characterized. The results indicate that a minimum of 6 plates is required to constitute an ultrastiff isotropic lattice, 7 plates would return the established plate Cubic Octet structure while 8 to 10 plate geometries did not show significant differences in properties. Despite the introduction of some plate bending due to sub-optimal plate placement strategy, relative stiffness of the PINNs lattices adheres closely to the Hashin Shtrikman upper bound, 90 percent of Hashin Shtrikman upper bound at a relative density of 0.4, and the lattices maintain near isotropic behaviour, achieving a Zener ratio of 0.95 at a relative density of 0.1. Benchmarking results show that specific stiffness of PINNs lattices is higher than the majority of isotropic architectures reported in the literature.
Related
- A physics-informed peripheral hemodynamic digital twin for personalized estimation of arterial stiffness
- A Framework Integrating the Dynamic Stiffness Matrix with Physics-Informed Neural Networks for Solving Eigenvalue Problems and Analysing Dynamic Response
- Bandgaps at high frequency from highly oscillatory metamaterials
- Learning Topology-Aware Representations for Mechanics-Relevant TPMS Metamaterials
- A surrogate-assisted generative framework for on-demand inverse design of phononic metamaterials
BibTeX
@misc{singh2026derivation,
title = {{Derivation of Novel Isotropic Metamaterials at the Hashin Shtrikman Stiffness Limit Enabled by Physics Informed Neural Networks}},
author = {Manish Kumar Singh and Dominic Kang Jueh Lim and Anson Wen Han Cheong and Adams Wai Kin Kong and Chang Quan Lai},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02622},
eprint = {2611.02622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02622},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Derivation of Novel Isotropic Metamaterials at the Hashin Shtrikman Stiffness Limit Enabled by Physics Informed Neural Networks
AU - Manish Kumar Singh
AU - Dominic Kang Jueh Lim
AU - Anson Wen Han Cheong
AU - Adams Wai Kin Kong
AU - Chang Quan Lai
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02622
UR - https://arxiv.org/abs/2611.02622
AB - Current methods of deriving ultrastiff isotropic metamaterials require heuristics or topology optimization, which are highly inefficient and limited by human input. To circumvent this, Physics Informed Neural Networks are applied to analytical equations to systematically solve for plate orientations in closed cell lattices. Following a standardized procedure, the plate orientations were modelled and assembled into geometries resembling quasi random foams for validation via finite element simulations. Closed cell 6-plate geometries were also additively manufactured using LAPIS and experimentally characterized. The results indicate that a minimum of 6 plates is required to constitute an ultrastiff isotropic lattice, 7 plates would return the established plate Cubic Octet structure while 8 to 10 plate geometries did not show significant differences in properties. Despite the introduction of some plate bending due to sub-optimal plate placement strategy, relative stiffness of the PINNs lattices adheres closely to the Hashin Shtrikman upper bound, 90 percent of Hashin Shtrikman upper bound at a relative density of 0.4, and the lattices maintain near isotropic behaviour, achieving a Zener ratio of 0.95 at a relative density of 0.1. Benchmarking results show that specific stiffness of PINNs lattices is higher than the majority of isotropic architectures reported in the literature.
ER -