School of Engineering and Applied Science, University of Virginia, Charlottesville, VA, 22904, USA.
Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin, D09 W6Y4, Ireland.
J Mech Behav Biomed Mater. 2021 Dec;124:104782. doi: 10.1016/j.jmbbm.2021.104782. Epub 2021 Aug 17.
The response of fibrous soft tissues undergoing torsional deformations is a topic of current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. The problem of torsion superimposed on extension of incompressible hyperelastic solid circular cylinders is a classic problem of nonlinear elasticity that has been considered by many authors in the context of rubber elasticity particularly for isotropic materials. A striking feature of such problems is the instability that arises with sufficiently large twist where a kink and then a knot suddenly appears. An energy approach to examining this instability when the extension and twist are prescribed was described by Gent and Hua (2004) and illustrated there for a neo-Hookean isotropic elastic material. The theoretical results were compared with experimental observations on natural rubber rods. Murphy (2015) has shown that the approach of Gent and Hua (2004) for isotropic materials can be simplified when the rods are assumed to be thin and this theory was applied to transversely isotropic materials by Horgan and Murphy (2016). In contrast with the case for isotropic materials, it was shown there that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. Here we are concerned with the implications of this simplified thin rod instability theory for fiber-reinforced transversely isotropic materials that reflect fiber-matrix interaction. It is again shown that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. The results are illustrated for a specific strain-energy density function that models fiber-matrix interaction. It is shown that the critical twist at which kinking occurs decreases as a measure of fiber-matrix interaction is increased so that the fiber-matrix interaction has a destabilizing effect. The results are illustrated using experimental data of other authors for skeletal muscles and for porcine brain white matter tissue.
纤维软组织在扭转变形下的反应是当前研究的热点。这种变形在韧带和肌腱中很常见，在心脏力学中也特别重要。不可压缩超弹性圆柱的扭转与拉伸的组合问题是非线性弹性的经典问题，许多作者在橡胶弹性的背景下，特别是针对各向同性材料，对其进行了研究。这类问题的一个显著特点是，当扭转角足够大时会出现不稳定性，此时会突然出现扭结和结。Gent 和 Hua（2004）提出了一种能量法来研究这种不稳定性，该方法规定了拉伸和扭转的情况，并对各向同性neo-Hookean弹性材料进行了说明。Gent 和 Hua（2004）的理论结果与天然橡胶棒的实验观察进行了比较。Murphy（2015）表明，当杆假设为薄杆时，Gent 和 Hua（2004）的各向同性材料方法可以简化，并且 Horgan 和 Murphy（2016）将该理论应用于横向各向同性材料。与各向同性材料的情况不同，研究表明，即使没有拉伸，即纯扭转情况下，也会出现扭结不稳定性。在这里，我们关注的是这种简化的薄杆不稳定性理论对反映纤维-基体相互作用的纤维增强横向各向同性材料的影响。再次表明，即使没有拉伸，即纯扭转情况下，也会出现扭结不稳定性。结果用一种特定的应变能密度函数进行了说明，该函数模型化了纤维-基体的相互作用。结果表明，扭结发生的临界扭转角随着纤维-基体相互作用的增加而减小，因此纤维-基体相互作用具有不稳定性的影响。结果使用其他作者的实验数据进行了说明，包括骨骼肌肉和猪脑白质组织。
