publications

2025

2025

1. JMPS

   Wavelength selection in the twist buckling of pre-strained elastic ribbons

   Arun Kumar, and Basile Audoly

   Journal of the Mechanics and Physics of Solids, 2025

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   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 B0 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, B0<0.

   @article{kumar2025PrestrainedRib,
     author = {Kumar, Arun and Audoly, Basile},
     title = {Wavelength selection in the twist buckling of pre-strained elastic ribbons},
     journal = {Journal of the Mechanics and Physics of Solids},
     volume = {196},
     pages = {106005},
     year = {2025},
     issn = {0022-5096},
     doi = {https://doi.org/10.1016/j.jmps.2024.106005},
     url = {https://www.sciencedirect.com/science/article/pii/S002250962400471X},
   }

2023

2023

1. PRSA

   Asymptotic derivation of a higher-order one-dimensional model for tape springs

   Arun Kumar, Basile Audoly, and Claire Lestringant

   Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023

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   We derive a one-dimensional model for tape springs. The derivation starts from nonlinear thin-shell theory and uses a dimension reduction technique that combines a centreline-based parametrization of the tape-spring midsurface with the assumption that the strain varies slowly along the length of the tape spring. The one-dimensional model is effectively a higher-order rod model: at leading order, the strain energy depends on the extensional, bending and twisting strains and is consistent with classical results from the literature; the two following orders are novel and capture the dependence of the strain energy on the strain gradients. The cross-sectional displacements are solved as part of the dimension reduction process, making the one-dimensional model asymptotically exact. We expect that the model will accurately and efficiently capture the deformations and instabilities in tape springs, including those involving highly localized deformations. This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.

   @article{kumar2023asymptotic,
     author = {Kumar, Arun and Audoly, Basile and Lestringant, Claire},
     title = {Asymptotic derivation of a higher-order one-dimensional model for tape springs},
     journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
     volume = {381},
     number = {2244},
     pages = {20220028},
     year = {2023},
     doi = {10.1098/rsta.2022.0028},
     url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2022.0028},
   }

2021

2021

1. PRSA

   More views of a one-sided surface: mechanical models and stereo vision techniques for Möbius strips

   Arun Kumar, Poornakanta Handral, Darshan Bhandari, and 1 more author

   Proceedings of the Royal Society A, 2021

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   Moebius strips are prototypical examples of ribbon-like structures. Inspecting their shapes and features provides useful insights into the rich mechanics of elastic ribbons. Despite their ubiquity and ease of construction, quantitative experimental measurements of the three-dimensional shapes of Moebius strips are surprisingly non-existent in the literature. We propose two novel stereo vision-based techniques to this end—a marker-based technique that determines a Lagrangian description for the construction of a Moebius strip, and a structured light illumination technique that furnishes an Eulerian description of its shape. Our measurements enable a critical evaluation of the predictive capabilities of mechanical theories proposed to model Möbius strips. We experimentally validate, seemingly for the first time, the developable strip and the Cosserat plate theories for predicting shapes of Möbius strips. Equally significantly, we confirm unambiguous deficiencies in modelling Möbius strips as Kirchhoff rods with slender cross-sections. The experimental techniques proposed and the Cosserat plate model promise to be useful tools for investigating a general class of problems in ribbon mechanics.

   @article{kumar2021more,
     author = {Kumar, Arun and Handral, Poornakanta and Bhandari, Darshan and Rangarajan, Ramsharan},
     journal = {Proceedings of the Royal Society A},
     number = {2250},
     pages = {20210076},
     publisher = {The Royal Society},
     title = {More views of a one-sided surface: mechanical models and stereo vision techniques for M{\"o}bius strips},
     volume = {477},
     year = {2021}
   }

2020

2020

1. JMPS

   An investigation of models for elastic ribbons: Simulations & experiments

   Arun Kumar, Poornakanta Handral, CS Darshan Bhandari, and 2 more authors

   Journal of the Mechanics and Physics of Solids, 2020

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   Understanding the feature-rich buckling-dominated behavior of thin elastic ribbons is ripe with opportunities for fundamental studies exploring the nexus between geometry and mechanics, and for conceiving of engineering applications that exploit geometric nonlinearity as a functioning principle. Predictive mechanical models play an instrumental role to this end. As a direct consequence of their physical appearance, ribbons are usually modeled either as one-dimensional rods having wide cross sections, or as narrow two-dimensional plates/shells. These models employ drastically different kinematic assumptions, which in turn play a decisive role in their predictive capabilities. Here, we critically examine three modeling approaches for elastic ribbons using detailed measurements of their complex three-dimensional deformations realized in quasistatic experiments with annulus-shaped ribbons. We find that simple and practically realizable ribbon deformations contradict assumptions underlying strain-displacement relationships in nonlinear rod and von Kármán plate models. These observations do not point at shortcomings of the theories themselves, but highlight fallacies in their application to modeling ribbon-like structures that are capable of undergoing large displacements and rotations. We identify and validate, seemingly for the first time, the 1-director Cosserat plate theory as a model for elastic ribbons over a useful range of loading conditions. In the process, we demonstrate annular ribbons to be prototypical systems for studying the mechanics of elastic ribbons. Annular ribbons exhibit a tunable degree of geometric nonlinearity in response to simple displacement and rotation boundary conditions— a feature that we exploit here for highlighting the consequences of kinematic assumptions underlying different ribbon models. We additionally provide experimental evidence for the existence of multiple stable equilibria, bifurcation phenomena correlated with the number of zero crossings in the mean curvature, and localization of energy, thus making annular ribbons interesting mechanical systems to study in their own right.

   @article{kumar2020investigation,
     author = {Kumar, Arun and Handral, Poornakanta and Bhandari, CS Darshan and Karmakar, Anindya and Rangarajan, Ramsharan},
     journal = {Journal of the Mechanics and Physics of Solids},
     pages = {104070},
     publisher = {Elsevier},
     title = {An investigation of models for elastic ribbons: Simulations \& experiments},
     volume = {143},
     year = {2020},
   }