# An Adaptive Quasi-Continuum Approach for Modeling Fracture in Networked Materials: Application to Modeling of Polymer Networks

## TL;DR

This paper introduces an adaptive quasi-continuum method for modeling fracture in networked materials like polymers, combining local detail near cracks with homogenized bulk behavior for efficient multiscale analysis.

## Contribution

The paper presents a novel adaptive numerical algorithm that integrates explicit local modeling with homogenized global behavior for fracture analysis in networked materials.

## Key findings

- Accurate modeling of crack propagation without predefined fracture energy.
- Efficient multiscale approach combining discrete and continuum models.
- Insights into how network topology affects fracture characteristics.

## Abstract

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.