MEAM Ph.D. Thesis Defense: “Mechanical Behavior and Fracture of Fibrous Materials at Large Deformations”

The mechanical behavior of fiber network materials is characterized by large deformations before failure and a strain-stiffening stress-strain response. In this thesis, this is investigated using discrete simulations at the microstructural level along with theoretical and computational results from continuum models. Cauchy and first Piola-Kirchhoff stress tensors for discrete networks of central-force elements are defined based on the equivalence of virtual power between the discrete system and its continuum representation. The framework is rigorously validated by demonstrating that non-uniform stress fields computed in discrete simulations of networks with defects and inhomogeneities show excellent agreement with continuum predictions for problems involving both infinitesimal and large, non-linear deformations. Network materials are reported to resist fracture in the presence of cracks, and this property is related to their nonlinear behavior. A computational model for the microstructure of network materials is developed to study the effects of a sharp crack under very large deformations. The computed stress field in the discrete network reproduces the asymptotic crack-tip fields based upon a continuum constitutive model derived from representative volume elements of the discrete network. The dominant stress components as a function of the undeformed distance from the crack follow a singular relation that is similar to the classical (small strain) HRR solution. The scaling exponent is determined completely by the constitutive behavior of individual fibers, which directly relates the macroscopic behavior directly to the microstructure. Finally, a continuum model that predicts macroscopic behavior for arbitrary states of deformation, including damage evolution, is constructed from mesoscopic simulations. The continuum model can access length- and time-scales that are inaccessible in a related class of high-fidelity discrete simulations, which allows prediction of fracture toughness, the material property that determines rupture resistance in the presence of defects.