Fiber-Matrix Interaction and Fiber Orientation in Simple Shearing of Fibrous Soft Tissues

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.