Modeling Fracture in Rate-Dependent Polymer Networks: A Quasicontinuum Approach
A. Ghareeb and A. Elbanna
Journal of Applied Mechanics, 88, 111007 (2021).

ABSTRACT
Soft materials, such as rubber and gels, exhibit rate-dependent response where
the stiffness, strength, and fracture patterns depend largely on loading rates.
Thus, accurate modeling of the mechanical behavior requires accounting for
different sources of rate dependence such as the intrinsic viscoelastic behavior
of the polymer chains and the dynamic bond breakage and formation mechanism. In
this chapter, we extend the QC approach presented in Ghareeb and Elbanna (2020,
An Adaptive Quasi-Continuum Approach for Modeling Fracture in Networked
Materials: Application to Modeling of Polymer Networks, J. Mech. Phys. Solids,
137, p. 103819) to include rate-dependent behavior of polymer networks. We
propose a homogenization rule for the viscous forces in the polymer chains and
update the adaptive mesh refinement algorithm to account for dynamic bond
breakage. Then, we use nonlinear finite element framework with
predictor-corrector scheme to solve for the nodal displacements and velocities.
We demonstrate the accuracy of the method by verifying it against fully discrete
simulations for different examples of network structures and loading conditions.
We further use the method to investigate the effects of the loading rates on the
fracture characteristics of networks with different rate-dependent parameters.
Finally, We discuss the implications of the extended method for multiscale
analysis of fracture in rate-dependent polymer networks.