Dynamics of mechanically induced fiber reorientation in\ud the material reinforced by two families of fibers

The specific fiber alignment and its content in biological tissues are created and maintained by the cells, which respond to mechanical stimuli arising from properties of the surrounding material. This coupling between mechanical anisotropy and tissue remodeling can be modeled in the theory of nonlinear elasticity as a fiber-reinforced hyperelastic material where the remodeling is represented as the change in the fiber orientation and/or amount. Here, we study analytically a simple model of fiber reorientation in a rectangular elastic tissue reinforced by two symmetrically arranged families of fibers subject to constant external loads. In this model, the fiber direction tends to align with the maximum principal stretch. We characterize the global behaviour of the system for all material parameters and applied loads, and show that provided the fibers are tensile initially, the system converges to a stable equilibrium, which corresponds to either complete or intermediate fiber alignment