An internal variable model for plastic remodeling in fibrous materials

Abstract

We propose a continuum model of fibrous materials that may undergo an internal reorganization, which turns out in a plastic change of the orientation of the fibers, if a threshold is achieved. We find that the remodeling may induce a rich material response. In a traction test, when the threshold condition is reached, we show that the most general transversely isotropic material may evolve in three different ways; in particular, the fibers asymptotically tend (regularly or with jumps): (A) to a given angle; (B) to align perpendicularly with respect to the load direction; (C) to align with the load direction if their initial angle is less than a given value, or perpendicularly, otherwise. We provide analytical solutions for the evolutive homogeneous problem and some numerical results for a non-homogeneous condition. The theory is very general and can find applications in several problems arising in material mechanics.