Can creasing patterns be predicted from a charge crystallization analogy?

Prior work has shown that a simple “shear lag” model may be useful as a description of microscopic creases that form in compressed hyperelastic materials, as this model maps to two-dimensional (2D) electrostatics and treats the nonlinearly deformed crease core analogously to a thermodynamically inconsequential vortex core [1]. Here, we extend the shear lag concept to study patterns of macroscopic creases formed under equibiaxial compression [2,3]. Collections of finite-length creases are represented as collections of charged line segments that have pairwise, 2D screened-Coulomb interactions with each other. Random structure searching combined with conjugate gradient relaxation is used to predict ground state crystal structures formed by these line charges as a function of density and screening length. We compare our findings to known equibiaxial creasing patterns, including a square lattice of I-shaped creases with perpendicular nearest neighbors, and a triangular lattice of oriented Y-shaped creases [3]. Given the similarity of these patterns with 2D auxetic patterns, our results may also yield new insights in the latter context.



[1] T. A. Engstrom & J. M. Schwarz, EPL 118, 56005 (2017).

[2] V. Trujillo, J. Kim, & R. C. Hayward, Soft Matter 4, 564 (2008).

[3] T. Tallinen, J. S. Biggins, & L. Mahadevan, PRL 110, 024302 (2013).