Mechanics of random fiber networks

Paper has a multiscale structure, including a spectrum of features: macrofluctuations (scale of tens, hundreds, thousands ... of meters), streaks (scale of meters), flocs (scale of centimeters), single cellulose fibers (scale of millimeters), cellulose fiber being a composite helically wound from fibrils (scale of tens of microns), fibrils (submicron scale), and molecular chains (tens through thousands of Angstroms). This complexity is the root cause of various size-scale effects in mechanics (elasticity and strength) of paper. We outline a micromechanics model of paper which provides a bridge from the scale of interacting fibers to a statistical continuum approximation. The model accounts for a 3-D random geometry of fiber networks with any degree of fiber flocculation, and employs a Timoshenko beam with torsion for each fiber segment (between two contiguous fiber-fiber bonds). The fiber-fiber bonds are treated as either rigid or flexible. The model involves a computational mechanics of thousands of fibers, in which global failure occurs on microscale through fracture of a fiber segment and/or fracture of a fiber-fiber bond. We also report on the scale effects and statistics of effective mechanical (elastic and strength) responses due to a nonuniform paper formation.