An implicit stress gradient plasticity model for describing mechanical behavior of planar fiber networks on a macroscopic scale

The plasticity behavior of fiber networks is governed by complex mechanisms. This study examines the effect of microstructure on the macroscopic plastic behavior of two-dimensional random fiber networks such as strong-bonded paper. Remote load is a pure macroscopic mode I opening field, applied via a boundary layer assuming small scale yielding on the macroscopic scale. It is shown that using a macroscopic classical homogeneous continuum approach to describe plasticity effects due to (macroscopic) singular-dominated strain fields in planar fiber networks leads to erroneous results. The classical continuum description is too simple to capture the essential mechanical behavior of a network material since a structural effect, that alters the macroscopic stress field, becomes pronounced and introduces long-ranging microstructural effects that have to be accounted for. Because of this, it is necessary to include a nonlocal theory that bridges the gap between microscopic and macroscopic scales to describe the material response in homogeneous continuum models. An implicit stress gradient small deformation plasticity model, which is based on a strong nonlocal continuum formulation, is presented here that has the potential to describe the plasticity behavior of fiber networks on a macroscopic scale. The theory is derived by including nonlocal stress terms in the classical associated J2-theory of plasticity. The nonlocal stress tensor is found by scaling the local Cauchy stress tensor by the ratio of nonlocal and local von Mises equivalent stresses. The model is relatively easy to implement in ordinary finite element algorithms for small deformation theory. Fairly good agreements are obtained between discrete micromechanical network models and the derived homogeneous nonlocal continuum model.