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Folding in extreme materials and Eshelby forces in elastic rods

Davide Bigoni
University of Trento
Friday, May 10, 2019 - 14:30

When a ductile material is subject to severe strain, failure is preluded by the emergence of shear bands, which initially nucleate in a small area, but quickly extend rectilinearly and accumulate damage, until they degenerate into fractures. This is a known phenomenon which has attracted a strong research effort in the last 30 years. The same mathematical tools developed for the analysis of shear bands in ductile materials will be shown to lead to folding and faulting in constrained Cosserat materials, when these have a strong anisotropy, so that they are close to the elliptic boundary. In fact, folding is a process in which bending is localized at sharp edges separated by almost undeformed elements and folding in these materials can originate from ellipticity loss [1,2]. Shear banding is shown to inspire tensile buckling of an elastic rod and development of configurational, or 'Eshelby-like', forces in elastic structures, leading to the elastica arm scale and to models of snake locomotion [3] and self-restabilization [4].

[1] Gourgiotis, P.A. and Bigoni, D. (2017) The dynamics of folding instability in a constrained Cosserat medium. Phil. Tran. Royal Soc. A 375: 20160159; 
[2] Bigoni, D. and Gourgiotis, P.A. (2016) Folding and faulting of an elastic continuum. Proc. Royal Soc. A 472; 
[3] Dal Corso, F., Misseroni, D., Pugno, N.M., Movchan, A.B., Movchan, N.V. and Bigoni, D. (2017) Serpentine locomotion through elastic energy release. J. Royal Soc. Interface 14, 20170055; 
[4] Bosi, F., Misseroni, D., Dal Corso, F., Neukirch, S. and Bigoni, D. (2016) Asymptotic self-restabilization of a continuous elastic structure. Phys. Rev. E 94, 063005.

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