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研究生： 羅万鈞
Lo, Wan-Chun
論文名稱： 旋性喀斯拉固體波松比之數值研究
NUMERICAL STUDY OF POISSON’S RATIO OF CHIRAL COSSERAT SOLIDS
指導教授： 王雲哲
Wang, Yun-Che
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 83
中文關鍵詞： 喀斯拉固體 、璇性喀斯拉固體 、普松比
外文關鍵詞： Cosserat solid, chiral Cosserat solid, Poisson’s ratio
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    • 本論文研究三維璇性喀斯拉圓柱固體在受單軸均勻軸力下的力學反應，一般純彈性材料和喀斯拉固體的普松比在-1與0.5之間，但璇性喀斯拉固體的普松比可以比-1小，或是比0.5大，本研究藉由探討璇性喀斯拉固體在軸力下的解析解，並以研究材料與幾何參數對普松比的影響。

    This thesis investigates the mechanical responses of three-dimensional chiral Cosserat solids under uniform tension. It is well-known that the Poisson’s ratio of the elastic or Cosserat solids is in the classical range of −1 < ν < 0.5, i.e. ν ∈ (−1, 0.5). However, the chiral Cosserat solids may exhibit a Poisson’s ratio beyond the classical range, i.e. ν < −1 or ν > 0.5, without violating strain energy density being positive definite. The analytical solutions of Cosserat and chiral Cosserat solids under simple tension are derived in this work. Parametric studies on the analytical solutions are performed to delineate the beyond-the-classical phenomenon on the Poisson’s ratio.

    CHINESE ABSTRACT i ABSTRACT ii ACKNOWLEDGMENTS iii LIST OF FIGURES vi NOMENCLATURE xv 1 Introduction 1 1.1 Goals and motivation 1 1.2 Literature review 1 1.3 Outline of this thesis 2 2 Theoretical considerations 3 2.1 Cosserat solids 3 2.2 Chiral Cosserat solids 14 3 Results and Discussion 22 3.1 Effects of C1 22 3.2 Effects of C2 30 3.3 Effects of C2 and C3 36 3.4 Effects of N on Poisson’s ratio 42 3.5 Effects of N on squeeze-twist coupling 46 3.6 Effects of N on bending and torsion rigidity 52 4 COMSOL simulation on Poisson’s ratio 56 4.1 Numerical model 56 4.2 Finite element implementation and boundary conditions 57 4.3 Numerical results 59 5 Conclusion and Future Work 65 5.1 Conclusion 65 5.2 Future work 65 LIST OF REFERENCES 66

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    [3] R.D. Gauthier and W.E. Jahsman. A quest for micropolar elastic constants. Journal ofApplied Mechanics, 42(2):369–374, 2024.
    [4] R.S. Lakes and R.L. Benedict. Noncentrosymmetry in micropolar elasticity. Int. J. Eng.Sci., 20(10):1161–1167, 1982.
    [5] R.S. Lakes, B. Huey, and K. Goyal. Extended poisson’s ratio range in chiral isotropic elasticmaterial. Physica Status Solidi (b), 259(12):2200336, 2022.
    [6] R.S. Lakes and B. Huey. Poisson’s ratio beyond the classically allowable range in chi-ral isotropic elastic materials: Effect of k and experiment. Physica Status Solidi (b),261(12):2300411, 2024.
    [7] P. Dai and R. Wang. Propagation characteristics of longitudinal-torsion coupled waves inphononic crystal rods of chiral materials. Archives of Mechanics, 75(5):543–558, 2023.
    [8] A. Kumar and S. Goyal. Plane dilatational and shear waves in a chiral porous thermoelasticmedium under strain gradient theory. International Journal of Numerical Methods for Heat& Fluid Flow, 34(12):4233–4256, 2024.
    [9] COMSOL. https://www.comsol.com. 2026.

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