Huang Rui, Im Se Hyuk
Department of Aerospace Engineering & Engineering Mechanics, University of Texas, Austin, TX 78712, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 2):026214. doi: 10.1103/PhysRevE.74.026214. Epub 2006 Aug 30.
A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a power-law scaling under uniaxial compression. More complicated dynamics is predicted under equibiaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a chaotic labyrinth pattern under equibiaxial stresses. Under stresses of the same magnitude, the two patterns have the same average wavelength, but different amplitudes. It is noted that the dynamics of wrinkling, while analogous to other phase ordering phenomena, is distinct and rich under the effects of stress and substrate elasticity.
软基底上的应力薄膜会形成复杂的皱纹图案。通过线性微扰分析可以很好地描述起皱的起始和初始生长，并且可以使用能量方法分析平衡皱纹。在此期间，皱纹图案会经历一个具有特殊动力学的粗化过程。通过适当的尺度变换和二维数值模拟，本文对从初始生长到粗化直至平衡的起皱动力学有了定量的理解。研究发现，在初始生长阶段，会选择一个与应力相关的波长，并且皱纹幅度随时间呈指数增长。在粗化过程中，皱纹波长和幅度都会增加，在单轴压缩下遵循幂律尺度变换。在等双轴应力下预测会有更复杂的动力学，它开始时粗化速率更快，然后渐近地趋近于单轴应力下的相同尺度变换。在平衡时，单轴应力下会得到平行条纹图案，等双轴应力下会得到混沌迷宫图案。在相同大小的应力下，这两种图案具有相同的平均波长，但幅度不同。需要注意的是，起皱动力学虽然与其他相序现象类似，但在应力和基底弹性的影响下是独特且丰富的。
