软固体圆柱体的扭转不稳定性
Torsion instability of soft solid cylinders
摘要：
已知将纯扭转施加到细长圆柱形杆上会引起扭转不稳定性，从初始扭结演变为纽结。在扭转平行板流变仪的双圆柱，几何约束强加零位移的轴的圆柱，防止发生这种扭转不稳定性。在这些实验条件下，在给定的临界角下，圆柱表面上出现褶皱。在这里，我们研究这一类弹性不稳定性-我们称之为扭转不稳定性-软圆柱体受到联合有限轴向拉伸和扭转，通过应用增量弹性形变叠加在有限应变的理论。我们制定的增量边界弹性问题的Stroh微分形式，并使用表面阻抗法建立一个强大的数值程序推导的边际稳定性曲线。我们提出了一种Mooney-Rivlin材料的结果，并研究了材料参数对弹性分叉的影响。
英文摘要：
The application of pure torsion to a long and thin cylindrical rod is known to provoke a twisting instability, evolving from an initial kink to a knot. In the torsional parallel-plate rheometry of stubby cylinders, the geometrical constraints impose zero displacement of the axis of the cylinder, preventing the occurrence of such twisting instability. Under these experimental conditions, wrinkles occur on the cylinder's surface at a given critical angle of torsion. Here we investigate this subclass of elastic instability--which we call torsion instability--of soft cylinders subject to a combined finite axial stretch and torsion, by applying the theory of incremental elastic deformation superimposed on finite strains. We formulate the incremental boundary elastic problem in the Stroh differential form, and use the surface impedance method to build a robust numerical procedure for deriving the marginal stability curves. We present the results for a Mooney-Rivlin material and study the influence of the material parameters on the elastic bifurcation.
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