  Materials with network-like microstructure, including polymers, are the
backbone for many natural and human-made materials such as gels, biological
tissues, metamaterials, and rubbers. Fracture processes in these networked
materials are intrinsically multiscale, and it is computationally prohibitive
to adopt a fully discrete approach for large scale systems. To overcome such a
challenge, we introduce an adaptive numerical algorithm for modeling fracture
in this class of materials, with a primary application to polymer networks,
using an extended version of the Quasi-Continuum method that accounts for both
material and geometric nonlinearities. In regions of high interest, for example
near crack tips, explicit representation of the local topology is retained
where each polymer chain is idealized using the worm like chain model. Away
from these imperfections, the degrees of freedom are limited to a fraction of
the network nodes and the network structure is computationally homogenized,
using the micro-macro energy consistency condition, to yield an anisotropic
material tensor consistent with the underlying network structure. A nonlinear
finite element framework is used to solve the system where dynamic adaptivity
allows transition between the continuum and discrete scales. The method enables
accurate modelling of crack propagation without a priori constraint on the
fracture energy while maintaining the influence of large-scale elastic loading
in the bulk. We demonstrate the accuracy and efficiency of the method by
applying it to study the fracture in different examples of network structures.
We further use the method to investigate the effects of network topology and
disorder on its fracture characteristics. We discuss the implications of our
method for multiscale analysis of fracture in networked material as they arise
in different applications in biology and engineering.
