Exploring buckling and post-buckling behavior of incompressible hyperelastic beams through innovative experimental and computational approaches

References

• Akgöz, B., and Ö. Civalek. 2022. Buckling analysis of functionally graded tapered microbeams via rayleigh–ritz method. Mathematics 10 (23):4429. doi: 10.3390/math10234429
   Web of Science ®Google Scholar
• Amabili, M., P. Balasubramanian, I. D. Breslavsky, G. Ferrari, R. Garziera, and K. Riabova. 2016. Experimental and numerical study on vibrations and static deflection of a thin hyperelastic plate. Journal of Sound and Vibration 385:81–92. doi: 10.1016/j.jsv.2016.09.015.
   Web of Science ®Google Scholar
• Attard, M. M. 2003a. Finite strain––beam theory. International Journal of Solids and Structures 40 (17):4563–84. doi: 10.1016/S0020-7683(03)00216-6.
   Web of Science ®Google Scholar
• Attard, M. M. 2003b. Finite strain––isotropic hyperelasticity. International Journal of Solids and Structures 40 (17):4353–78. doi: 10.1016/S0020-7683(03)00217-8.
   Web of Science ®Google Scholar
• Attard, M. M., and G. W. Hunt. 2008a. Column buckling with shear deformations—a hyperelastic formulation. International Journal of Solids and Structures 45 (14-15):4322–39. doi: 10.1016/j.ijsolstr.2008.03.018.
   Web of Science ®Google Scholar
• Attard, M. M., and G. W. Hunt. 2008b. Sandwich column buckling–a hyperelastic formulation. International Journal of Solids and Structures 45 (21):5540–55. doi: 10.1016/j.ijsolstr.2008.05.022.
   Web of Science ®Google Scholar
• Azarniya, O., and G. H. Rahimi. 2022. Numerical and experimental analysis of free vibrations and static bending of a sandwich beam with a hyperelastic core. Mechanics Based Design of Structures and Machines:1–23. doi: 10.1080/15397734.2022.2121721.
   Web of Science ®Google Scholar
• Azarniya, O., G. Rahimi, and A. Forooghi. 2023. Large deformation analysis of a hyperplastic beam using experimental/fem/meshless collocation method. Waves in Random and Complex Media:1–20. doi: 10.1080/17455030.2023.2184645.
   Google Scholar
• Bai, J., T. Rabczuk, A. Gupta, L. Alzubaidi, and Y. Gu. 2023. A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics. Computational Mechanics 71 (3):543–62. doi: 10.1007/s00466-022-02252-0.
   Web of Science ®Google Scholar
• Cabello, M., J. Zurbitu, J. Renart, A. Turon, and F. Martínez. 2016. A non-linear hyperelastic foundation beam theory model for double cantilever beam tests with thick flexible adhesive. International Journal of Solids and Structures 80:19–27. doi: 10.1016/j.ijsolstr.2015.10.017.
   Web of Science ®Google Scholar
• Cai, K., D. Y. Gao, and Q. H. Qin. 2014. Post-buckling solutions of hyper-elastic beam by canonical dual finite element method. Mathematics and Mechanics of Solids 19 (6):659–71. doi: 10.1177/1081286513482483.
   Web of Science ®Google Scholar
• Chai, G. B., and C. W. Yap. 2008. Coupling effects in bending, buckling and free vibration of generally laminated composite beams. Composites Science and Technology 68 (7-8):1664–70. doi: 10.1016/j.compscitech.2008.02.014.
   Web of Science ®Google Scholar
• Chen, Y., and L. Jin. 2020. From continuous to snapping-back buckling: A post-buckling analysis for hyperelastic columns under axial compression. International Journal of Non-Linear Mechanics 125:103532. doi: 10.1016/j.ijnonlinmec.2020.103532.
   Web of Science ®Google Scholar
• Chen, Y., and L. Jin. 2021. Reusable energy‐absorbing architected materials harnessing snapping‐back buckling of wide hyperelastic columns. Advanced Functional Materials 31 (31):2102113. doi: 10.1002/adfm.202102113.
   Web of Science ®Google Scholar
• Civalek, Ö., S. Dastjerdi, and B. Akgöz. 2022a. Buckling and free vibrations of cnt-reinforced cross-ply laminated composite plates. Mechanics Based Design of Structures and Machines 50 (6):1914–31. doi: 10.1080/15397734.2020.1766494.
   Web of Science ®Google Scholar
• Civalek, Ö., B. Uzun, and M. Ö. Yaylı. 2022b. An effective analytical method for buckling solutions of a restrained fgm nonlocal beam. Computational and Applied Mathematics 41 (2):67. doi: 10.1007/s40314-022-01761-1.
   Google Scholar
• Dai, H.-H., and F.-F. Wang. 2012. Analytical solutions for the post-buckling states of an incompressible hyperelastic layer. Analysis and Applications 10 (1):21–46. doi: 10.1142/S0219530512500029.
   Web of Science ®Google Scholar
• Dastjerdi, S., A. Alibakhshi, B. Akgöz, and Ö. Civalek. 2022. A novel nonlinear elasticity approach for analysis of nonlinear and hyperelastic structures. Engineering Analysis with Boundary Elements 143:219–36. doi: 10.1016/j.enganabound.2022.06.015.
   Web of Science ®Google Scholar
• Dey, S., T. Mukhopadhyay, S. Naskar, T. K. Dey, H. D. Chalak, and S. Adhikari. 2019. Probabilistic characterisation for dynamics and stability of laminated soft core sandwich plates. Journal of Sandwich Structures & Materials 21 (1):366–97. doi: 10.1177/1099636217694229.
   Web of Science ®Google Scholar
• Dey, S., S. Naskar, T. Mukhopadhyay, U. Gohs, A. Spickenheuer, L. Bittrich, S. Sriramula, S. Adhikari, and G. Heinrich. 2016. Uncertain natural frequency analysis of composite plates including effect of noise–a polynomial neural network approach. Composite Structures 143:130–42. doi: 10.1016/j.compstruct.2016.02.007.
   Web of Science ®Google Scholar
• Ebrahimi-Mamaghani, A., A. Forooghi, H. Sarparast, A. Alibeigloo, and M. Friswell. 2021. Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load. Applied Mathematical Modelling 90:131–50. doi: 10.1016/j.apm.2020.08.041.
   Web of Science ®Google Scholar
• Emam, S. A. 2009. A static and dynamic analysis of the postbuckling of geometrically imperfect composite beams. Composite Structures 90 (2):247–53. doi: 10.1016/j.compstruct.2009.03.020.
   Web of Science ®Google Scholar
• Emam, S. A., and A. H. Nayfeh. 2009. Postbuckling and free vibrations of composite beams. Composite Structures 88 (4):636–42. doi: 10.1016/j.compstruct.2008.06.006.
   Web of Science ®Google Scholar
• Flores, E. S., S. Adhikari, M. Friswell, and F. Scarpa. 2011. Hyperelastic axial buckling of single wall carbon nanotubes. Physica E: Low-Dimensional Systems and Nanostructures 44 (2):525–9. doi: 10.1016/j.physe.2011.10.006.
   Web of Science ®Google Scholar
• Forooghi, A., and A. Alibeigloo. 2022. Hygro-thermo-magnetically induced vibration of fg-cntrc small-scale plate incorporating nonlocality and strain gradient size dependency. Waves in Random and Complex Media:1–32. doi: 10.1080/17455030.2022.2037784
   Web of Science ®Google Scholar
• Forooghi, A., N. Fallahi, A. Alibeigloo, H. Forooghi, and S. Rezaey. 2022a. Static and thermal instability analysis of embedded functionally graded carbon nanotube-reinforced composite plates based on hsdt via gdqm and validated modeling by neural network. Mechanics Based Design of Structures and Machines:1–34. doi: 10.1080/15397734.2022.2094407.
   Web of Science ®Google Scholar
• Forooghi, A., S. Rezaey, S. M. Haghighi, and A. M. Zenkour. 2022b. Thermal instability analysis of nanoscale fg porous plates embedded on kerr foundation coupled with fluid flow. Engineering with Computers 38 (S4):2953–73. doi: 10.1007/s00366-021-01426-3.
   Google Scholar
• Giordano, A., L. Mao, and F.-P. Chiang. 2021. Full-field experimental analysis of a sandwich beam under bending and comparison with theories. Composite Structures 255:112965. doi: 10.1016/j.compstruct.2020.112965.
   Web of Science ®Google Scholar
• Guo, H., X. Zhuang and T. Rabczuk. 2019. A deep collocation method for the bending analysis of kirchhoff plate. Computers, Materials & Continua 59 (2):433–56.
   Google Scholar
• Hamzehei, R., J. Kadkhodapour, A. P. Anaraki, S. Rezaei, S. Dariushi, and A. M. Rezadoust. 2018. Octagonal auxetic metamaterials with hyperelastic properties for large compressive deformation. International Journal of Mechanical Sciences 145:96–105. doi: 10.1016/j.ijmecsci.2018.06.040.
   Web of Science ®Google Scholar
• Hamzehei, R., S. Rezaei, J. Kadkhodapour, A. P. Anaraki, and A. Mahmoudi. 2020. 2d triangular anti-trichiral structures and auxetic stents with symmetric shrinkage behavior and high energy absorption. Mechanics of Materials 142:103291. doi: 10.1016/j.mechmat.2019.103291.
   Web of Science ®Google Scholar
• Hosseini, S. M. H., H. Arvin, and Y. Kiani. 2022. On buckling and post-buckling of rotating clamped-clamped functionally graded beams in thermal environment. Mechanics Based Design of Structures and Machines 50 (8):2779–94. doi: 10.1080/15397734.2020.1784205.
   Web of Science ®Google Scholar
• Huang, J., N. Nguyen-Thanh, J. Gao, Z. Fan, and K. Zhou. 2022. Static, free vibration, and buckling analyses of laminated composite plates via an isogeometric meshfree collocation approach. Composite Structures 285:115011. doi: 10.1016/j.compstruct.2021.115011.
   Web of Science ®Google Scholar
• Khaniki, H. B., M. H. Ghayesh, R. Chin, and M. Amabili. 2021. Large amplitude vibrations of imperfect porous-hyperelastic beams via a modified strain energy. Journal of Sound and Vibration 513:116416. doi: 10.1016/j.jsv.2021.116416.
   Web of Science ®Google Scholar
• Khaniki, H. B., M. H. Ghayesh, R. Chin, and M. Amabili. 2022a. A review on the nonlinear dynamics of hyperelastic structures. Nonlinear Dynamics 110 (2):963–94. doi: 10.1007/s11071-022-07700-3.
   Web of Science ®Google Scholar
• Khaniki, H. B., M. H. Ghayesh, R. Chin, and L.-Q. Chen. 2022b. Experimental characteristics and coupled nonlinear forced vibrations of axially travelling hyperelastic beams. Thin-Walled Structures 170:108526. doi: 10.1016/j.tws.2021.108526.
   Web of Science ®Google Scholar
• Khaniki, H. B., M. H. Ghayesh, R. Chin, and S. Hussain. 2022c. Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories. Continuum Mechanics and Thermodynamics 34 (3):781–827. doi: 10.1007/s00161-022-01090-y.
   Web of Science ®Google Scholar
• Li, W., F. Sun, P. Wang, H. Fan, and D. Fang. 2016. A novel carbon fiber reinforced lattice truss sandwich cylinder: Fabrication and experiments. Composites Part A: Applied Science and Manufacturing 81:313–22. doi: 10.1016/j.compositesa.2015.11.034.
   Web of Science ®Google Scholar
• Liu, Y. 2018. Axial and circumferential buckling of a hyperelastic tube under restricted compression. International Journal of Non-Linear Mechanics 98:145–53. doi: 10.1016/j.ijnonlinmec.2017.10.016.
   Web of Science ®Google Scholar
• Liu, Y., and H.-H. Dai. 2014. Compression of a hyperelastic layer-substrate structure: Transitions between buckling and surface modes. International Journal of Engineering Science 80:74–89. doi: 10.1016/j.ijengsci.2014.02.020.
   Web of Science ®Google Scholar
• Mehta, S., G. Raju, and P. Saxena. 2022b. Wrinkling as a mechanical instability in growing annular hyperelastic plates. International Journal of Mechanical Sciences 229:107481. doi: 10.1016/j.ijmecsci.2022.107481.
   Web of Science ®Google Scholar
• Mukhopadhyay, T., S. Naskar, S. Chakraborty, P. Karsh, R. Choudhury, and S. Dey. 2021a. Stochastic oblique impact on composite laminates: A concise review and characterization of the essence of hybrid machine learning algorithms. Archives of Computational Methods in Engineering 28 (3):1731–60. doi: 10.1007/s11831-020-09438-w.
   Web of Science ®Google Scholar
• Mukhopadhyay, T., S. Naskar, S. Dey, Vaishali. 2023. On machine learning assisted data-driven bridging of FSDT and hozt for high-fidelity uncertainty quantification of laminated composite and sandwich plates. Composite Structures 304: 116276. doi: 10.1016/j.compstruct.2022.116276.
   Web of Science ®Google Scholar
• Mukhopadhyay, T., S. Naskar, K. Gupta, R. Kumar, S. Dey, and S. Adhikari. 2021b. Probing the stochastic dynamics of coronaviruses: Machine learning assisted deep computational insights with exploitable dimensions. Advanced Theory and Simulations 4 (7):2000291. doi: 10.1002/adts.202000291.
   Web of Science ®Google Scholar
• Naskar, S., T. Mukhopadhya, and S. Sriramula. 2020. A comparative assessment of ann and pnn model for low-frequency stochastic free vibration analysis of composite plates. In Handbook of probabilistic models, 527–47. Elsevier.
   Google Scholar
• Novoselac, S., T. Ergić, and P. Baličević. 2012. Linear and nonlinear buckling and post buckling analysis of a bar with the influence of imperfections. Tehnicki Vjesnik/Technical Gazette 19 (3):695–701.
   Web of Science ®Google Scholar
• Peres, M., and R. Bono. 2011. Modal testing and shaker excitation: Setup considerations and guidelines. SAE Technical Paper 2011-01-1652. doi: 10.4271/2011-01–1652.
   Google Scholar
• Selvan T, M., S. Sharma, S. Naskar, S. Mondal, M. Kaushal, and T. Mondal. 2022. Printable carbon nanotube-liquid elastomer-based multifunctional adhesive sensors for monitoring physiological parameters. ACS Applied Materials & Interfaces 14 (40):45921–33. doi: 10.1021/acsami.2c13927.
   PubMedGoogle Scholar
• Sharma, A., T. Mukhopadhyay, S. M. Rangappa, S. Siengchin, and V. Kushvaha. 2022. Advances in computational intelligence of polymer composite materials: Machine learning assisted modeling, analysis and design. Archives of Computational Methods in Engineering 29 (5):3341–85. doi: 10.1007/s11831-021-09700-9.
   Web of Science ®Google Scholar
• Sharma, S., M. Selvan, S. Naskar, S. Mondal, P. Adhya, T. Mukhopadhyay, and T. Mondal. 2022. Printable graphene-sustainable elastomer-based cross talk free sensor for point of care diagnostics. ACS Applied Materials & Interfaces 14 (51):57265–80. doi: 10.1021/acsami.2c17805.
   PubMed Web of Science ®Google Scholar
• Shojaeifard, M., K. Wang, and M. Baghani. 2022. Large deformation of hyperelastic thick-walled vessels under combined extension-torsion-pressure: Analytical solution and fem. Mechanics Based Design of Structures and Machines 50 (12):4139–56. doi: 10.1080/15397734.2020.1826963.
   Web of Science ®Google Scholar
• Tabatabaei, S. S., and A. Fattahi. 2022. A finite element method for modal analysis of fgm plates. Mechanics Based Design of Structures and Machines 50 (4):1111–22. doi: 10.1080/15397734.2020.1744004.
   Web of Science ®Google Scholar
• Vahidi Bidhendi, M., G. H. Rahimi, M. S. Gazor, and A. R. Zangoei. 2022. Experimental and numerical investigation of debonding in the composite sandwich structures with a foam-composite core under tpsb test. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44 (12):604. doi: 10.1007/s40430-022-03907-y.
   Web of Science ®Google Scholar
• Wang, S., J. Wang, H. Lu, and W. Zhao. 2021. A novel combined model for wind speed prediction–combination of linear model, shallow neural networks, and deep learning approaches. Energy 234:121275. doi: 10.1016/j.energy.2021.121275.
   Web of Science ®Google Scholar
• Wang, Y., and W. Zhu. 2021a. Nonlinear transverse vibration of a hyperelastic beam under harmonic axial loading in the subcritical buckling regime. Applied Mathematical Modelling 94:597–618. doi: 10.1016/j.apm.2021.01.030.
   Web of Science ®Google Scholar
• Wang, Y., and W. Zhu. 2021b. Nonlinear transverse vibration of a hyperelastic beam under harmonically varying axial loading. Journal of Computational and Nonlinear Dynamics 16 (3):031006. doi: 10.1115/1.4049562.
   PubMed Web of Science ®Google Scholar
• Wang, Y., and W. Zhu. 2022. Supercritical nonlinear transverse vibration of a hyperelastic beam under harmonic axial loading. Communications in Nonlinear Science and Numerical Simulation 112:106536. doi: 10.1016/j.cnsns.2022.106536.
   Web of Science ®Google Scholar
• Zangoei, A. R., G. H. Rahimi, M. S. Gazor, M. Vahidibidhendi, and O. Azarniya. 2023. Experimental and numerical study of delamination phenomenon in sandwich structures with hybrid corrugated core in the mode ii of crack growth. Journal of Composite Materials 57 (6):1199–210. doi: 10.1177/00219983221150429.
   Web of Science ®Google Scholar
• Zolfagharian, A., M. Bodaghi, R. Hamzehei, L. Parr, M. Fard, and B. F. Rolfe. 2022. 3D-printed programmable mechanical metamaterials for vibration isolation and buckling control. Sustainability 14 (11):6831. doi: 10.3390/su14116831.
   Web of Science ®Google Scholar