On pattern-switching phenomena in complex elastic structures
On pattern-switching phenomena in complex elastic structures
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复杂弹性结构中的模式切换现象
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Stephen Willshaw
中科院分区：
文献类型：
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作者：
Stephen Willshaw
我们调查全球模式切换的影响，在二维细胞固体中的空隙排列在一个正方形的晶格。这些结构的单轴压缩触发弹性不稳定性，在临界应变下引起空隙形状的倍周期转变。具体地，圆形空隙的正方形阵列形成相互正交的椭圆的图案，并且对于菱形空隙观察到类似的效果。不稳定性的发生是由空隙率和尺寸效应的实验样品中发现。我们建立了经验定律，这些定律描述了由正方形阵列的圆形孔洞组成的蜂窝结构的刚度、强度和稳定性。这些与离散模型预测的比较意味着低估了晶格的抗屈曲性，尽管尺寸效应是重复的。我们发现类似的模式切换效果的立方晶格，这是一个三维多孔立方体。该系统中的屈曲效应是在一个空隙平面中产生2D图案。在两相粒状晶体中，颗粒的正方形晶格的重新排列导致新的周期加倍的结构图案。如实验和数值模拟所示，这种切换可以通过中间相发生，这取决于颗粒的尺寸比。
We investigate global pattern-switching effects in 2D cellular solids in which the voids are arranged in a square lattice. Uniaxial compression of these structures triggers an elastic instability which brings about a period-doubling transformation of the void shapes at a critical strain. Specifically, a square array of circular voids forms a pattern of mutually orthogonal ellipses and a similar effect is observed for diamond-shaped voids. The onset of instability is governed by the void fraction and size-effects are found for the experimental samples. We establish empirical laws which characterise the stiffness, strength and stability of cellular structures comprising square arrays of circular voids. A comparison of these with predictions from a discrete model implies underestimation of the resistance of the lattice to buckling, although the size effects are replicated. We find similar pattern-switching effects in the cubic lattice, which is a three-dimensional porous cube. The effect of buckling in this system is to produce a 2D pattern in one plane of voids. In two-phase granular crystals, rearrangement of a square lattice of particles results in a new, period-doubled, structural pattern. This switch can occur via an intermediate phase depending on the size ratio of the particles as shown in experiments and numerical simulations.