The New Math of Wrinkling Patterns | Quanta Magazine

Abstraction: Mathematical theory predicting wrinkling patterns in elastic thin sheets

Key points:

• Ian Tobasco (Univ. of Illinois Chicago) published a 2021 paper showing that wrinkling patterns in curved elastic sheets pressed flat can be predicted by the sign of Gaussian curvature — positive curvature yields one class of ordered/disordered domains, negative (saddle-shaped) curvature yields another.
• Wrinkling patterns are minimum-energy configurations; Tobasco's theory identifies the geometric invariants (Gaussian curvature) that select one pattern over another without needing to specify exact material parameters.
• A 2022 Nature Physics paper by Tobasco, Joey Paulsen (Syracuse), and Eleni Katifori (UPenn) unified mathematical theory, physical experiment, and simulation, showing patterns fall into neat families of isosceles triangles demarcating ordered and disordered domains.
• Results apply across multiple orders of magnitude of sheet thickness, not just mathematical idealizations of infinitely thin material.
• Prior work (Reis 2015, Vella 2017) described specific geometries; Tobasco's contribution is the first systematic general framework from elasticity theory.

Connections: Ian Tobasco · Gaussian Curvature · Elastic Materials · Wrinkling Patterns · Mathematical Physics

Source: https://www.quantamagazine.org/the-new-math-of-wrinkling-patterns-20220922/