Fiber orientation effects in simple shearing of fibrous soft tissues

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.