Second-order phase transition and universality of self-buckled elastic slender columns

References

• Deegan RD, Bakajin O, Dupont TF, et al. Capillary flow as the cause of ring stains from dried liquid drops. Nature. 1997;389:827–829. doi: 10.1038/39827
   Web of Science ®Google Scholar
• Lee A, Brun P-T, Marthelot J, et al. Fabrication of slender elastic shells by the coating of curved surfaces. Nature Commun. 2016;7:11155. doi: 10.1038/ncomms11155
   Web of Science ®Google Scholar
• Jawed MK, Dieleman P, Audoly B, et al. Untangling the mechanics and topology in the frictional response of long overhand elastic knots. Phys Rev Lett. 2015;115:118302. doi: 10.1103/PhysRevLett.115.118302
   Web of Science ®Google Scholar
• Miller JT, Lazarus A, Audoly B, et al. Shapes of a suspended curly hair. Phys Rev Lett. 2014;112:068103. doi: 10.1103/PhysRevLett.112.068103
   Web of Science ®Google Scholar
• Lazarus A, Miller JT, Reis PM. Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method. J Mech Phys Solids. 2013;61:1712. doi: 10.1016/j.jmps.2013.04.002
   Web of Science ®Google Scholar
• Akono A-T, Reis PM, Ulm F-J. Scratching as a fracture process: from butter to steel. Phys Rev Lett. 2011;106:204302. doi: 10.1103/PhysRevLett.106.204302
   Web of Science ®Google Scholar
• Vandeparre H, Pineirua M, Brau F, et al. Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains. Phys Rev Lett. 2011;106:224301. doi: 10.1103/PhysRevLett.106.224301
   Web of Science ®Google Scholar
• Reis PM, Hure J, Jung S, et al. Grabbing water. Soft Matter. 2010;6:5705. doi: 10.1039/c0sm00895h
   Web of Science ®Google Scholar
• Bîrsan M, Altenbach H, Sadowski T, et al. Deformation analysis of functionally graded beams by the direct approach. Composites: Part B. 2012;43:1315–1328. doi: 10.1016/j.compositesb.2011.09.003
   Web of Science ®Google Scholar
• Bîrsan M, Sadowski T, Marsavina L, et al. Mechanical behavior of sandwich composite beams made of foams and functionally graded materials. Int J Solids Struct. 2013;50:519–530. doi: 10.1016/j.ijsolstr.2012.10.011
   Web of Science ®Google Scholar
• Linul E, Marşavina L. Assesment of sandwich beams with rigid polyurethane foam core using failure-mode maps. Proc Romanian Acad Series A. 2015;16:522–530.
   Google Scholar
• Linul E, Valean C, Linul P-A. Compressive behavior of aluminum microfibers reinforced semi-rigid polyurethane foams. Polymers. 2018;10:1298. doi: 10.3390/polym10121298
   Web of Science ®Google Scholar
• Linul E, Marsavina L, Voiconi T, et al. Study of factors influencing the mechanical properties of polyurethane foams under dynamic compression. J Phys Conf Ser. 2013;451:012002. doi: 10.1088/1742-6596/451/1/012002
   Google Scholar
• Berto F, Razavi SMJ, Ayatollahi MR. Fatigue assessment of steel rollers using an energy based criterion. Procedia Struct Integr. 2017;3:93–101. doi: 10.1016/j.prostr.2017.04.013
   Google Scholar
• Berto F, Ayatollahi MR, Campagnolo A. Fracture tests under mixed mode I + III loading: an assessment based on the local energy. Int J Damage Mech. 2017;26:881–894. doi: 10.1177/1056789516628318
   Web of Science ®Google Scholar
• Zeyad AD. Viscoelastoplastic bodies under cyclic loading in thermal-radiation fields. J Taibah Univ Sci. 2017;11:605–612. doi: 10.1016/j.jtusci.2016.04.007
   Web of Science ®Google Scholar
• Greenhill A. Determination of the greatest height consistent with stability that a vertical pole or must can be made, and of the greatest height to which a tree of given proportion can grow. Proc Camb Philol Soc. 1881;4:65–73.
   Google Scholar
• Rotter JM, Sadowski AJ, Chen L. Nonlinear stability of thin elastic cylinders of different length under global bending. Int J Solids Struct. 2014;51:2826–2839. doi: 10.1016/j.ijsolstr.2014.04.002
   Web of Science ®Google Scholar
• Rotter JM, Sadowski AJ. Full plastic resistance of tubes under bending and axial force: exact treatment and approximations. Structures. 2017;10:30–38. doi: 10.1016/j.istruc.2016.11.004
   Web of Science ®Google Scholar
• Amalia N, Yuliza E, Margaretta DO, et al. A novel method for characterizing temperature-dependent elastic modulus and glass transition temperature by processing the images of bending cantilever slender beams at different temperatures. AIP Adv. 2018;8:115201. doi: 10.1063/1.5058689
   Web of Science ®Google Scholar
• Okomori K, Enomae T, Onabe F. Evaluation and control of coated paper stiffness. Proc Tappi Adv Coat Fundam Symp. 1999: 121–132.
   Google Scholar
• Ek G, Gellerstedt G, Henriksson G. Paper products physics and technology. Berlin: Walter de Gruyter; 2009.
   Google Scholar
• Landau LD, Lifshitz EM. Statistical physics. Volume 5. 3rd ed. Oxford: Butterworth-Heiemann; 1980.
   Google Scholar
• Pasini D, Mirjalili V. The optimized shape of a leaf petiole. Comparing Design Nat Sci Eng. 2006;87:35–45. doi: 10.2495/DN060041
   Google Scholar
• Ennos AR, Spatz H-C, Speck T. The functional morphology of the petioles of the banana. Musa Textilis. J Experiment Biol. 2000;51:2085–2093.
   Google Scholar
• Bobnar J, Susman K, Parsegian VA, et al. Euler strut: a mechanical analogy for dynamics in the vicinity of a critical point. Eur J Phys. 2011;32:1007. doi: 10.1088/0143-0807/32/4/014
   Web of Science ®Google Scholar
• Wolfram Mathematica. 2018. Calculated using the Wolfram Mathematica software (https://www.wolfram.com).
   Google Scholar