Shape of an elastica under growth restricted by friction. (January 2019)

• Record Type: Journal Article
• Authors: Horváth, Marcell G.; Sipos, András A.; Várkonyi, Péter L.
• Is Part Of: International journal of solids and structures. Volume 156/157(2019)
• Page Start: 137
• Page End: 147
• Publication Date: 2019-01
• Subjects: Friction -- Buckling -- Elastica -- Growth; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2018.08.009
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: We investigate the quasi-static growth of elastic fibers in the presence of isotropic dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method for the determination of the critical length is developed. The post-critical behavior of the system is studied by using an appropriate numerical scheme based on variational methods. We find post-critical shapes for uniformly distributed as well as for concentrated growth and demonstrate convergence to a figure 8 shape for large lengths when self-crossing is allowed. Comparison with simple physical experiments yields reasonable accuracy of the theoretical predictions.