Fiber-reinforcement is a common feature of many soft biological tissues. The response of fibrous biotissues to applied shear is thus of considerable current interest. We consider here the fundamental deformation of simple shear within the framework of transversely isotropic incompressible hyperelastic materials for fiber-reinforced specimens with a single family of parallel fibers oriented at a general angle to the direction of shear. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining an homogeneous deformation state in the bulk of the specimen. Here we investigate the effects of fiber-matrix interaction on the shear and lateral normal stresses. The inclusion of fiber-matrix interaction stiffens the shear stress response. As regards the normal stress, it is shown that the confining normal 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, fiber-matrix interaction 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. It is shown that the fiber-matrix interaction enhances both the positive and negative Poynting effects. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. In particular, it is shown that, for sufficiently small angles of orientation, a transition amount of shear exists at which the normal stress changes character from tensile to compressive with increasing amount of shear. An increase in the degree of fiber-matrix interaction enlarges the range of orientation angles for which this transition can occur and decreases the transition amount of shear. These transition amounts of shear are well within the physiological strain regime. The 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。因此，纤维生物组织对施加的剪切的响应是当前相当大的兴趣。我们在此考虑横向各向同性不可压缩超弹性材料框架内简单剪切的基本变形，用于纤维增强试样，具有与剪切方向成一般角度取向的单一平行纤维族。众所周知，非线性弹性的法向应力效应特性对于保持试样整体的均匀变形状态起着至关重要的作用。在这里，我们研究了纤维-基体相互作用对剪切和横向法向应力的影响。纤维-基质相互作用的加入增强了剪切应力响应。至于正应力，结果表明，为了保持简单的剪切，需要施加到块的顶面和底面的限制法向牵引力可以是压缩的或拉伸的，这取决于各向异性的程度、纤维-基质相互作用和取向角度的纤维。在没有这种施加牵引力的情况下，无约束的样品往往会垂直于剪切方向向外凸出或向内收缩，因此有可能产生正或负的坡印廷效应。结果表明，纤维-基质相互作用增强了正负坡印廷效应。使用其他作者获得的猪脑白质实验数据说明了结果。特别是，它表明，对于足够小的取向角，存在剪切的 过渡量，在该过渡量处，法向应力随着剪切量的增加而从拉伸变为压缩。纤维-基质相互作用程度的增加扩大了可以发生这种转变的取向角范围并减少了剪切的转变量. 这些剪切的过渡量完全在生理应变范围内。此处获得的结果与用于确定纤维生物软组织的本构特性的准确剪切测试协议的开发有关。