Mechanics of composites with finite length crimped fibers dispersed in a soft matrix

Abstract

Collagen-containing tissues show strain hardening behavior due to the alignment and the waviness of collagen fibers. As the fibers uncrimp and align with stretching, they become increasingly load-bearing and make the tissue strain hardening. We consider the mechanics of analogous synthetic composites comprising stiff crimped fibers dispersed in a soft elastomeric matrix. A novel workflow is developed wherein a random configuration of hundreds of finite-length crimped fibers embedded in a soft matrix can be created, meshed, and then simulated by 3D finite element methods. We show that the mechanical behavior of these composites is affected by the degree of fiber crimp, the fiber volume fraction, and fiber orientation. The degree of reinforcement of the soft matrix was found to increase with volume fraction of the fibers, and with better alignment of the fibers along the tension direction. Fibers with larger crimp amplitude were found to show strain hardening behavior, i.e. contribute little to the stress at small strain, but much more at large strain. The Holzapfel-Gasser-Ogden model is shown to capture the stress-strain behavior adequately. Further, we show that simulations of a single fiber embedded in a soft matrix can approximately predict the mechanical behavior of multifiber composites at much reduced computational cost. Such composites of chopped crimped fibers offer the benefit of reproducing the mechanical behavior of tissues, while still being flow-processable.