Mechanical Properties of Fibrous Network Materials

We discuss mechanical behavior of specific fibrous network materials, including the evolution of tension in fibrin clots, compression of pulmonary emboli, and fracture of Whatman filter paper. The first material, fibrin clots, consist of random networks of fibrin fibers. When clots form by polymerization they develop tensile pre-stresses. We construct a mathematical model for the evolution of tension in isotropic fibrin gels. As the fiber diameter grows over time, properties which depend on it, such as the stored energy per unit length of a single fiber, the force-stretch relation of a fiber, and therefore the tension in the network as a whole, also evolve over time. The second fibrous network is pulmonary emboli, which consist of random networks of fibrin fibers with fluid-filled pores and red blood cells (RBCs). Stress-strain responses of human pulmonary emboli under cyclic compression were measured, revealing that emboli exhibit hysteretic stress-strain curves characteristic of foams. We describe the hysteretic response of emboli using a model of phase transitions, in which the compressed embolus is segregated into coexisting rarefied and densified phases whose fractions change as compression progresses. Our model takes into account RBC rupture in compressed emboli and stresses due to fluid flow through their small pores. The mechanical response of emboli is shown to vary depending on their RBC content. The third fibrous network is Whatman filter paper. The effect of humidity on properties such as out-of-plane fracture toughness of Whatman filter paper is studied for a broad range of relative humidities. Crack growth is modeled using traction-separation laws, whose parameters are fitted to experiments. Additionally, a novel model is developed to capture the high peak and sudden drop in the experimental force measurement caused by the existence of an initiation region, an imperfect zone ahead of a nascent crack. The relative effect of each independent parameter is explored to better understand the humidity dependence of the traction-separation parameters. The materials studied have biological, clinical, and industrial applications, and the methods described here are also applicable to other fibrous network materials