The Dynamics of Folding Instability in a Constrained Cosserat Medium

Gourgiotis, P.A.; Bigoni, D.

Abstract

Different from Cauchy elastic materials, generalized continua, and in particular constrained Cosserat materials, can be designed to possess extreme (near a failure of ellipticity) orthotropy properties and in this way to model folding in a three-dimensional solid. Following this approach, folding, which is a narrow zone of highly localized bending, spontaneously emerges as a deformation pattern occurring in a strongly anisotropic solid. How this peculiar pattern interacts with wave propagation in the time-harmonic domain is revealed through the derivation of an antiplane, infinite-body Green’s function, which opens the way to integral techniques for anisotropic constrained Cosserat continua. Viewed as a perturbing agent, the Green’s function shows that folding, emerging near a steadily pulsating source in the limit of failure of ellipticity, is transformed into a disturbance with wavefronts parallel to the folding itself. The results of the presented study introduce the possibility of exploiting constrained Cosserat solids for propagating waves in materials displaying origami patterns of deformation.

Citation

Gourgiotis, P., & Bigoni, D. (2017). The Dynamics of Folding Instability in a Constrained Cosserat Medium. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375(2093), Article 20160159. https://doi.org/10.1098/rsta.2016.0159

• Journal Article Type: Article
• Acceptance Date: Sep 8, 2016
• Online Publication Date: Apr 3, 2017
• Publication Date: May 13, 2017
• Deposit Date: Sep 22, 2016
• Publicly Available Date: May 1, 2017
• Journal: Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.
• Print ISSN: 1364-503X
• Electronic ISSN: 1471-2962
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 375
• Issue: 2093
• Article Number: 20160159
• DOI: https://doi.org/10.1098/rsta.2016.0159
• Public URL: https://durham-repository.worktribe.com/output/1397118