SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 690-705, January 2020.
This work provides a mathematical understanding of the elastic fingering provoked by a large axial extension of a soft solid cylinder bonded between rigid plates. In this prototypical system model, a topological transition from a ground axis-symmetric meniscus is quasi-statically controlled by the applied displacement, which acts as the order parameter of a pitchfork bifurcation. Since the isotropic elastic energy becomes nonconvex under finite strains, geometric nonlinearity is of paramount importance for the loss of uniqueness of the solution of the boundary value problem. Nonetheless, physical nonlinearity in the elastic energy is found to exert an opposite stabilizing effect. It indeed penalizes the local stretching at the free boundary that would arise as a consequence of any change of its Gaussian curvature. The theoretical and numerical results are in agreement with recent experimental observations, showing that elastic fingering is strongly affected by the aspect ratio of the disc and can be even suppressed in soft materials with physical nonlinearity.

中文翻译：

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牵引中粘合软盘的弹性指法：几何和物理非线性的相互作用

SIAM应用数学杂志，第80卷，第2期，第690-705页，2020年1月。
这项工作提供了对弹性指法的数学理解，该弹性指法是由结合在刚性板之间的软实心圆柱体的较大轴向延伸引起的。在此原型系统模型中，由地面轴对称弯月面产生的拓扑过渡由所施加的位移准静态控制，该位移充当干草叉分叉的阶次参数。由于各向同性弹性能在有限应变下变得不凸，因此几何非线性对于边界值问题解唯一性的丧失至关重要。但是，发现弹性能中的物理非线性会产生相反的稳定作用。实际上，它惩罚了由于其高斯曲率的任何变化而导致的在自由边界处的局部拉伸。