Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials
Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials
复制标题
DOI：
10.1098/rspa.2011.0281
复制
发表时间：
2011-12-08
影响因子：
3.5
通讯作者：
Goriely, Alain
中科院分区：
文献类型：
--
作者：
Mihai, L. Angela;Goriely, Alain
最近的实验的生物聚合物凝胶，从而观察到通常的（积极的）坡印亭效应的逆转的动机，我们调查的影响，所谓的“adscillation不平等”的行为的超弹性材料剪切。我们首先证明，对于均匀的各向同性材料受到纯剪切，所产生的变形包括一个三轴拉伸结合简单的剪切力的方向上的当且仅当Baker-Ericksen不等式成立。对于纯剪切变形的立方体，如果“剪切面分开”，则出现正坡印亭效应，而如果“剪切面靠拢”，则出现负坡印亭效应。类似地，在简单剪切变形下，如果“剪切面倾向于分开”，则获得正坡印廷效应，而如果“剪切面倾向于靠拢”，则出现负坡印廷效应。当坡印廷效应发生在简单剪切下时，可以合理地假设在纯剪切下也得到相同符号的坡印廷效应。由于观察到的负坡印亭效应在半柔性生物聚合物意味着（更强的）经验不等式可能不成立，我们得出结论，这些不等式必须不施加时，这样的材料进行描述。
Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called 'adscititious inequalities' on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker-Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the 'sheared faces spread apart', whereas the negative Poynting effect is obtained if the 'sheared faces draw together'. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the 'sheared faces tend to spread apart', whereas the negative Poynting effect occurs if the 'sheared faces tend to draw together'. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is obtained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described.