Horgan Cornelius O, Murphy Jeremiah G
School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904, USA.
Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin 9, Ireland.
J Biomech. 2017 Nov 7;64:131-135. doi: 10.1016/j.jbiomech.2017.09.018. Epub 2017 Sep 27.
Fiber-reinforcement is a common feature of many soft biological tissues. Continuum mechanics modeling of the mechanical response of such tissues using transversely isotropic hyperelasticity is now well developed. The fundamental deformation of simple shear within this framework is examined here. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining a homogeneous deformation state in the bulk of the specimen. Here we consider the effect of anisotropy and fiber-orientation on the shear and normal stresses. It is shown that the confining traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy and on the angle of orientation of the fibers. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear so that one has the possibility of both a positive or negative Poynting effect. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. The general results obtained here are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fibrous biological soft tissues.
纤维增强是许多软生物组织的共同特征。利用横向各向同性超弹性对这类组织的力学响应进行连续介质力学建模现已得到充分发展。在此研究该框架内简单剪切的基本变形。众所周知，非线性弹性特有的法向应力效应在维持试样整体的均匀变形状态方面起着关键作用。这里我们考虑各向异性和纤维取向对剪应力和法向应力的影响。结果表明，为维持简单剪切而需施加在块体顶面和底面的围压牵引可能是压缩性的或拉伸性的，这取决于各向异性程度和纤维的取向角度。在没有这种外加牵引的情况下，无约束样品倾向于在垂直于剪切方向向外鼓出或向内收缩，从而可能产生正或负的泊松效应。利用其他作者获得的猪脑白质实验数据对结果进行了说明。这里得到的一般结果与开发用于确定纤维状生物软组织本构特性的精确剪切试验方案相关。
