Asymptotic analysis and design of linear elastic shell lattice metamaterials
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915357309009920 |
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| author | Zhang, Di Liu, Ligang |
| author_facet | Zhang, Di Liu, Ligang |
| contents | We present an asymptotic analysis of shell lattice metamaterials based on Ciarlet's shell theory, introducing a new metric--asymptotic directional stiffness (ADS)--to quantify how the geometry of the middle surface governs the effective stiffness. We prove a convergence theorem that rigorously characterizes ADS and establishes its upper bound, along with necessary and sufficient condition for achieving it. As a key result, our theory provides the first rigorous explanation for the high bulk modulus observed in Triply Periodic Minimal Surfaces (TPMS)-based shell lattices. To optimize ADS on general periodic surfaces, we propose a triangular-mesh-based discretization and shape optimization framework. Numerical experiments validate the theoretical findings and demonstrate the effectiveness of the optimization under various design objectives. Our implementation is available at https://github.com/lavenklau/minisurf. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic analysis and design of linear elastic shell lattice metamaterials Zhang, Di Liu, Ligang Analysis of PDEs Numerical Analysis We present an asymptotic analysis of shell lattice metamaterials based on Ciarlet's shell theory, introducing a new metric--asymptotic directional stiffness (ADS)--to quantify how the geometry of the middle surface governs the effective stiffness. We prove a convergence theorem that rigorously characterizes ADS and establishes its upper bound, along with necessary and sufficient condition for achieving it. As a key result, our theory provides the first rigorous explanation for the high bulk modulus observed in Triply Periodic Minimal Surfaces (TPMS)-based shell lattices. To optimize ADS on general periodic surfaces, we propose a triangular-mesh-based discretization and shape optimization framework. Numerical experiments validate the theoretical findings and demonstrate the effectiveness of the optimization under various design objectives. Our implementation is available at https://github.com/lavenklau/minisurf. |
| title | Asymptotic analysis and design of linear elastic shell lattice metamaterials |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2506.18910 |