Extreme Behaviors in Fibrous Material Remodeling: Auxetic to Non-Auxetic Transition and Phase Segregation

Fibrous materials, prevalent in biological tissues and engineered composites, undergo remodeling in response to mechanical loads, leading to plastic changes in fiber orientation. A previously developed continuum model describes this remodeling process. Building on that framework, the present study examines the extreme behaviors of such materials. Analytical results for the homogeneous response under tensile loading reveal three distinct classes: in class (A), fibers asymptotically approach a specific angle; in class (B), fibers align perpendicularly to the load direction; and in class (C), fibers align either with the load direction or perpendicularly, depending on their initial orientation. Numerical simulations are employed to analyze the non-homogeneous material response in a standard tensile test, demonstrating how differences in behavior arise from the material class and the initial fiber orientation distribution. This investigation focuses on the extreme behaviors of material classes (A) and (C), emphasizing phase segregation and transitions between auxetic and non-auxetic behavior.