1 Mathematical Institute , University of Oxford , Oxford , UK.
2 Living Matter Laboratory , Stanford University , Stanford , CA , USA.
Philos Trans A Math Phys Eng Sci. 2019 May 6;377(2144):20180076. doi: 10.1098/rsta.2018.0076.
Wrinkling is a universal instability occurring in a wide variety of engineering and biological materials. It has been studied extensively for many different systems but a full description is still lacking. Here, we provide a systematic analysis of the wrinkling of a thin hyperelastic film over a substrate in plane strain using stream functions. For comparison, we assume that wrinkling is generated either by the isotropic growth of the film or by the lateral compression of the entire system. We perform an exhaustive linear analysis of the wrinkling problem for all stiffness ratios and under a variety of additional boundary and material effects. Namely, we consider the effect of added pressure, surface tension, an upper substrate and fibres. We obtain analytical estimates of the instability in the two asymptotic regimes of long and short wavelengths. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.
起皱是一种普遍存在于各种工程和生物材料中的不稳定性。它已经在许多不同的系统中被广泛研究，但仍然缺乏全面的描述。在这里，我们使用流函数系统地分析了平面应变下薄超弹性膜在基底上的起皱。为了进行比较，我们假设起皱是由膜的各向同性生长或整个系统的横向压缩引起的。我们对所有的刚度比以及各种附加的边界和材料效应进行了详尽的线性分析。具体来说，我们考虑了外加压力、表面张力、上基底和纤维的影响。我们得到了在长波和短波两种渐近情况下不稳定性的解析估计。本文是主题为“里夫林在连续介质力学和应用数学中的遗产”的一部分。
