Wavelength selection in the twist buckling of pre-strained elastic ribbons
Year: 2024
Type: article
Abstract: A competition between short- and long-wavelength twist buckling instabilities has been reported in experiments on thin elastic ribbons having pre-strain concentrated in a rectangular region surrounding the axis. The wavelength of the twisting mode has been reported to either scale ( i ) as the width of the ribbon when the pre-strain is large (short-wavelength case) or ( ii ) as the length of the ribbon when the pre-strain is small (large-wavelength case). Existing one-dimensional rod or ribbon models can only account for large-wavelength buckling. We derive a novel one-dimensional model that accounts for short-wavelength buckling as well. It is derived from non-linear shell theory by dimension reduction and captures in an asymptotically correct way both the non-convex dependence of the strain energy on the twisting strain τ (which causes buckling) and its dependence on the strain gradient τ ′ . The competition between short- and long-wavelength buckling is shown to be governed by the sign of the incremental elastic modulus B 0 associated with the twist gradient τ ′ . The one-dimensional model reproduces the main features of equilibrium configurations generated in earlier work using 3D finite-element simulations. In passing, we introduce a novel truncation strategy applicable to higher-order dimension reduction that preserves the positiveness of the strain energy even when the gradient modulus is negative, B 0 < 0 .
Authors: Arun Kumar, Basile Audoly
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,100
OpenAlex ID: W4401525653