各向同性压缩薄板的热屈曲
Thermalized buckling of isotropically compressed thin sheets
摘要：
弹性薄板的屈曲是一种典型的力学失稳现象，它发生在很宽的尺度范围内。在像石墨烯这样的原子级薄膜的极限情况下，热波动可以极大地改变这种机械不稳定性。我们在这里调查的边界条件，非线性力学和热波动的微妙的相互作用，在控制屈曲的各向同性压缩下的限制薄板。我们确定了两个不等价的力学系综的基础上的边界在恒定应变（等距）或在恒定应力（isotensional）conditions.Nothingly，在等距系综，边界条件诱导一种新的长程非线性相互作用之间的局部倾斜的表面在遥远的点。这种相互作用与自发产生的热张力相结合，导致重整化群描述的两个不同的普适性类的热化屈曲，实现费舍尔重整化临界指数的机械变体。我们制定了一个完整的缩放理论的屈曲作为一个不寻常的相变与尺寸依赖的临界点，并讨论了实验结果的机械操纵的纳米材料。
英文摘要：
The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical instabilities. We investigate here the delicate interplay of boundary conditions, nonlinear mechanics and thermal fluctuations in controlling buckling of confined thin sheets under isotropic compression. We identify two inequivalent mechanical ensembles based on the boundaries at constant strain (isometric) or at constant stress (isotensional) conditions.Remarkably, in the isometric ensemble, boundary conditions induce a novel long-ranged nonlinear interaction between the local tilt of the surface at distant points. This interaction combined with a spontaneously generated thermal tension leads to a renormalization group description of two distinct universality classes for thermalized buckling, realizing a mechanical variant of Fisher-renormalized critical exponents. We formulate a complete scaling theory of buckling as an unusual phase transition with a size dependent critical point, and discuss experimental ramifications for the mechanical manipulation of ultrathin nanomaterials.
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