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 Jun;118:104410. doi: 10.1016/j.jmbbm.2021.104410. Epub 2021 Feb 25.
The response of fibrous soft tissues undergoing torsional deformations is a topic of considerable current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. A well-known context where such issues arise is in understanding the mechanical response of papillary muscles of the heart. Thus the classical torsion problem for solid or hollow cylinders composed of rubber-like materials has received renewed recent attention in the context of anisotropic materials. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible fiber-reinforced hyperelastic material. The focus of the work is on examining the effect of fiber-matrix interaction on the axial stress response with emphasis on the Poynting effect. The classic Poynting effect for isotropic rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely isotropic models considered here. For sufficiently small total angles of twist, well within the range of physiological response, a reverse-Poynting effect is shown to hold where the cylinder tends to shorten on twisting while for larger angles of twist, the usual positive Poynting effect occurs. It is shown that the influence of the fiber-matrix interaction is to enhance the reverse Poynting effect. The results are illustrated using experimental data of other authors for skeletal muscles and for brain white matter.
纤维软组织在扭转变形下的响应是当前相当关注的话题。这种变形在韧带中很常见，在心脏力学中也特别有趣。一个众所周知的出现这种问题的情况是，在理解心脏乳头肌的力学响应时。因此，在各向异性材料的背景下，经典的实心或空心圆柱体的扭转问题最近重新受到关注。在这里，我们考虑由各向异性不可压缩纤维增强超弹性材料组成的实心圆筒体的扭转。这项工作的重点是检查纤维-基体相互作用对轴向应力响应的影响，重点是研究庞廷效应。各向同性橡胶状材料的经典庞廷效应表明，扭转会导致圆柱体伸长，而对于这里考虑的各向异性模型，这种效应有很大的不同。对于扭转角度足够小，远在生理响应范围内，会出现一种反转庞廷效应，即扭转时圆柱体趋于缩短，而对于较大的扭转角度，通常会出现正的庞廷效应。结果表明，纤维-基体相互作用的影响是增强反转庞廷效应。使用其他作者关于骨骼肌肉和脑白质的实验数据来说明结果。
