arXiv subjects

Anshuman S. Pal

Publications and source records attributed to Anshuman S. Pal.

3 recordsLinked to original sources

arXiv2024

Faceted wrinkling by contracting a curved boundary

Single-mode deformations of two-dimensional materials, such as the Miura-ori zig-zag fold, are important to the design of deployable structures because of their robustness; these usually require careful pre-patterning of the material. Here we show that inward contraction of a curved boundary produces a fine wrinkle pattern with a novel structure that suggests similar single-mode characteristics, but with minimal pre-patterning. Using finite-element representation of the contraction of a thin circular annular sheet, we show that these sheets wrinkle into a structure well approximated by an isometric structure composed of conical sectors and flat, triangular facets. Isometry favours the restriction of such deformations to a robust low-bending energy channel that avoids stretching. This class of buckling offers a novel way to manipulate sheet morphology via boundary forces.

cond-mat.soft↗

arXiv2023

Hysteretic wavelength selection in isometric, unsupported radial wrinkling

In [Pal et al., arXiv:2206.03552], the authors discuss how an unsupported flat annulus contracted at its inner boundary by a factor $Δ$, buckles into a radial wrinkling pattern that is fully isometric and tension-free. What selects the wavelength in such a pure-bending configuration, in the absence of any competing sources of work? In this paper, with the support of numerical simulations, we argue that competition between stretching and bending energies at local, mesoscopic scales leads to the selection of a wavelength scale $λ^*$ sensitive to both the width $w$ and thickness $t$ of the sheet: $λ^* \sim w^{2/3} t^{1/3} Δ^{-1/6}$. This scale $λ^*$ corresponds to an arrest criterion for wrinkle coarsening starting from any wavelength $λ\lesssim λ^*$, which can be interpreted in terms of both size and energetic barriers to further coarsening. However, the sheet can support coarser wavelengths: $λ\gtrsim λ^*$, since there is no penalty to their existence. Since this wavelength selection mechanism depends on the value of $λ$ itself, it is hysteretic.

cond-mat.soft↗

arXiv2019

A unified geometric framework for axisymmetric thin sheet buckling

Thin sheets that are forced at their boundaries develop a variety of shapes aimed at minimising elastic energy by curving spontaneously in ways that break the symmetry of the sheet and the forcing. Characterising such buckling generally requires detailed analysis. Here, we follow a complementary approach, applicable to axisymmetric systems. It aims to predict the qualitative nature of any buckling using only the simple axisymmetric geometry of the initial system. We view an axisymmetric deformation according to the displacement it imposes on the radial lines making up the sheet. Thus, e.g., in-plane tensile loads on a disk-shaped annulus move radial lines along their length. Any compressional strain present in this deformed state then implies symmetry-breaking buckling out of the original plane. Using only these radial motions, we account for the buckling predicted by more detailed analysis: axial wrinkling confined to the inner part of the annulus. A second type of imposed deformation on radial lines is motion normal to the sheet. Considering the strains induced by rotating these lines through some common angle $α$, one may similarly account for both the buckling of d-cones and that of curved creases. Our framework thus unifies three previously unconnected buckled shapes.

cond-mat.soft↗