| Abstract: | The kinematics of shearing deformation in fiber reinforced materials can lead to fibers that (a) first shorten, (b) then return to their original length, and (c) then elongate. In a hyperelastic constitutive treatment this can cause the shear stress to be a nonmonotone function of the amount of shear if the fibers are sufficiently more stiff than the matrix. Here, we explore how this effects the emergence and development of kink surfaces in the context of a variety of boundary value problems. Kink surfaces are surfaces across which the deformation gradient is discontinuous. For fiber reinforced materials such surfaces generate an abrupt change in the fiber orientation (a kink). We characterize the appearance of kink surfaces in terms of three general mechanisms: fade-in, pair creation, and boundary emission. Each has a counterpart for kink surface disappearance. These mechanisms are highly sensitive both to changes in the original fiber orientation field, including spatial variation in this field, and to changes in the nature of the applied boundary conditions. A variety of examples are presented. |
