Parametric optimization of auxetic lattices using Grasshopper and Abaqus validation
DOI:
https://doi.org/10.46223/HCMCOUJS.acs.en.16.1.82.2026Tóm tắt
This study develops a parametric workflow for designing and optimizing auxetic-like cellular lattices in Rhino Grasshopper and Karamba3D, followed by nonlinear verification in ABAQUS. Since Karamba3D is limited to conventional linear-elastic material definitions, a Python routine was used to update the effective Young’s modulus of each lattice candidate from its geometry-based porosity through a porosity-modulus correlation. Honeycomb, diamond, and Voronoi lattices were parameterized and explored using the Galapagos evolutionary solver under geometric and manufacturability constraints, with tensile displacement under uniaxial loading as the optimization objective. Auxetic behaviour was evaluated through an effective Poisson’s ratio calculated from transverse and longitudinal gauge strains measured on the deformed configurations. The optimized cases maintained negative effective Poisson’s ratios of veff » -0.14 for the honeycomb lattice andveff » -0.9 for the diamond and Voronoi lattices. Selected designs were then transferred to ABAQUS for three-dimensional finite element verification using an Arruda-Boyce hyperelastic model calibrated to published tensile test data for hybrid PolyJet-printed Agilus30/VeroMagentaV specimens. The verification results indicate that lattice geometry plays the primary role in the observed response, with lower displacement and a more even stress distribution observed in the better-performing cases. Among the three lattice families, the Voronoi configurations showed the most consistent combination of low displacement, stable auxetic response, and comparatively uniform stress patterns.
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Aliha, M. R. M., Berto, F., Bahmani, A., & Gallo, P. (2017). Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Physical Mesomechanics, 20(2), 149-156. https://doi.org/10.1134/s1029959917020059
Arruda, E. M., & Boyce, M. C. (1993). A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids, 41(2), 389-412. https://doi.org/10.1016/0022-5096(93)90013-6
Attaran, M. (2017). The rise of 3-D printing: The advantages of additive manufacturing over traditional manufacturing. Business Horizons, 60(5), 677-688. https://doi.org/10.1016/j.bushor.2017.05.011
Cubukcuoglu, C., Ekici, B., Tasgetiren, M. F., & Sariyildiz, S. (2019). Optimus: Self-adaptive differential evolution with ensemble of mutation strategies for grasshopper algorithmic modeling. Algorithms, 12(7), Article 141. https://doi.org/10.3390/a12070141
Goldstein, R. V., Gorodtsov, V. A., & Lisovenko, D. S. (2015). Young’s modulus and Poisson’s ratio for seven-constant tetragonal crystals and nano/microtubes. Physical Mesomechanics, 18(3), 213-222. https://doi.org/10.1134/s1029959915030054
Goldstein, R. V., Gorodtsov, V. A., Lisovenko, D. S., & Volkov, M. A. (2014). Negative Poisson’s ratio for cubic crystals and nano/microtubes. Physical Mesomechanics, 17(2), 97-115. https://doi.org/10.1134/s1029959914020027
Jiang, Y., & Li, Y. (2016). 3D printed chiral cellular solids with amplified auxetic effects due to elevated internal rotation. Advanced Engineering Materials, 19(2), Article 1600609. https://doi.org/10.1002/adem.201600609
Jiang, Y., & Li, Y. (2018). 3D printed auxetic mechanical metamaterial with chiral cells and re-entrant cores. Scientific Reports, 8(1), Article 2397. https://doi.org/10.1038/s41598-018-20795-2
Kováčik, J. (1999). Correlation between Young’s modulus and porosity in porous materials. Journal of Materials Science Letters, 18(13), 1007-1010. https://doi.org/10.1023/a:1006669914946
Kováčik, J. (2006). Correlation between Poisson’s ratio and porosity in porous materials. Journal of Materials Science, 41(4), 1247-1249. https://doi.org/10.1007/s10853-005-4237-0
Linul, E., Serban, D. A., & Marsavina, L. (2018). Influence of cell topology on mode I fracture toughness of cellular structures. Physical Mesomechanics, 21(2), 178-186. https://doi.org/10.1134/s1029959918020121
Panin, V. E., & Egorushkin, V. E. (2009). Physical mesomechanics and nonequilibrium thermodynamics as a methodological basis for nanomaterials science. Physical Mesomechanics, 12(5-6), 204-220. https://doi.org/10.1016/j.physme.2009.12.002
Panin, V. E., Egorushkin, V. E., & Panin, A. V. (2013). Nonlinear wave processes in a deformable solid as a hierarchically organized system. Physical Mesomechanics, 15(3-4), 133-146. https://doi.org/10.1134/s1029959912020014
Panin, V. E., Panin, A. V., & Moiseenko, D. D. (2007). Physical mesomechanics of a deformed solid as a multilevel system. II. Chessboard-like mesoeffect of the interface in heterogeneous media in external fields. Physical Mesomechanics, 10(1-2), 5-14. https://doi.org/10.1016/j.physme.2007.06.001
Preisinger, C. (2013). Linking structure and parametric geometry. Architectural Design, 83(2), 110-113. https://doi.org/10.1002/ad.1564
Rajasekaran, S., & Pai, G. V. (2003). Neural networks, fuzzy logic and genetic algorithm: Synthesis and applications. PHI Learning.
Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: Theory and application. Advances in Engineering Software, 105, 30-47. https://doi.org/10.1016/j.advengsoft.2017.01.004
Tee, Y. L., Peng, C., Pille, P., Leary, M., & Tran, P. (2020). PolyJet 3D printing of composite materials: Experimental and modelling approach. JOM, 72(3), 1105-1117. https://doi.org/10.1007/s11837-020-04014-w
Varotsis, A. B. (2018). Introduction to SLS 3D printing. 3D Hubs. https://www.3dhubs.com/knowledge-base/introduction-sla-3d-printing
Warner, J. J., Gillies, A. R., Hwang, H. H., Zhang, H., Lieber, R. L., & Chen, S. (2017). 3D-printed biomaterials with regional auxetic properties. Journal of the Mechanical Behavior of Biomedical Materials, 76, 145-152. https://doi.org/10.1016/j.jmbbm.2017.05.016
Yang, W., Li, Z.-M., Shi, W., Xie, B.-H., & Yang, M.-B. (2004). Review on auxetic materials. Journal of Materials Science, 39(10), 3269-3279. https://doi.org/10.1023/B:JMSC.0000026928.93231.e0
Zenkour, A. M. (2020). Quasi-3D refined theory for functionally graded porous plates: Displacements and stresses. Physical Mesomechanics, 23(1), 39-53. https://doi.org/10.1134/s1029959920010051
Zheng, H., & Darweesh, B. (2019). Caterpillar: A gcode translator in grasshopper. 24th Annual Conference of the Association for Computer-Aided Architectural Design Research in Asia (CAADRIA 2019), Intelligent & Informed.
