Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition

TY - JOUR

T1 - Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition

AU - Gomez, Michael

AU - Reis, Pedro M.

AU - Audoly, Basile

PY - 2023/12

Y1 - 2023/12

N2 - We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure–volume–temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.

AB - We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure–volume–temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.

KW - Elastic ribbon

KW - Pre-stress

KW - Torsional buckling

KW - Phase separation

KW - Dimension reduction

U2 - 10.1016/j.jmps.2023.105420

DO - 10.1016/j.jmps.2023.105420

M3 - Article

SN - 0022-5096

VL - 181

JO - JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

JF - JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

ER -