MOX Laboratory, Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133, Milano, Italy.
Centre National de la Recherche Scientifique (CNRS), Sorbonne Universités, UMR 7190, F-75005, Paris, France.
Nat Commun. 2018 Feb 5;9(1):496. doi: 10.1038/s41467-018-02979-6.
A soft solid subjected to a large compression develops sharp self-contacting folds at its free surface, known as creases. Creasing is physically different from structural elastic instabilities, like buckling or wrinkling. Indeed, it is a fully nonlinear material instability, similar to a phase-transformation. This work provides theoretical insights of the physics behind crease nucleation. Creasing is proved to occur after a global bifurcation allowing the co-existence of an outer deformation and an inner solution with localised self-contact at the free surface. The most fundamental result here is the analytic prediction of the nucleation threshold, in excellent agreement with experiments and numerical simulations. A matched asymptotic solution is given within the intermediate region between the two co-existing states. The self-contact acts like the point-wise disturbance in the Oseen's correction for the Stokes flow past a circle. Analytic expressions of the matching solution and its range of validity are also derived.
当一个柔软的固体受到很大的压缩时，在自由表面会形成尖锐的自接触褶皱，称为折痕。折痕在物理上与结构弹性失稳（如屈曲或起皱）不同。实际上，它是一种完全非线性的材料失稳，类似于相变。这项工作提供了折痕成核背后物理机制的理论见解。证明折痕是在全局分叉后发生的，分叉允许外变形和内解共存，而内解在自由表面上具有局部自接触。这里最基本的结果是成核阈值的解析预测，与实验和数值模拟非常吻合。在两种共存状态之间的中间区域给出了一个匹配的渐近解。自接触的作用类似于 Oseen 修正对过圆的斯托克斯流的点扰动。还推导了匹配解的解析表达式及其有效范围。
