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I will present a new set of geometrically-exact equilibrium equations for the deformation of thin inextensible strips of finite width.
I will present a new set of geometrically-exact equilibrium equations for the deformation of thin inextensible strips of finite width. The equations are ODES and are the Euler-Lagrange equations for a geometrical variational problem reduced to the strip's centreline. The equations are used to solve the long-standing problem of finding the characteristic shape of a material Möbius strip. Solutions for increasing width-to-length ratio show the formation of creases bounding nearly flat triangular regions, a feature also familiar from fabric draping and paper crumpling. This suggests that our approach could give new insight into energy localisation phenomena in unstretchable elastic sheets, which for instance could help to predict points of onset of tearing.
The reduction technique for deriving equilibrium equations can be generalised to intrinsically curved sheets (shells). In the second part of the talk I will apply this to study the force-extension behaviour of helical ribbons. Unlike previous rod models our strip model predicts hysteresis behaviour for low-pitch ribbons of arbitrary material properties.
Associated with it is a first-order transition between two different helical states, a phenomenon observed in experiments with cholesterol ribbons. Numerical solutions reveal a new non-uniform uncoiling scenario in which a ribbon of very low pitch shears under tension and successively releases a sequence of almost planar loops.
- Speaker
- Dr Gert Van der Heijden, Department of Civil Engineering, UCL
- Venue
- FN, G011