Modeling fracture in rate-dependent polymer networks: A quasi-continuum approach

Soft materials, such as rubber and gels, exhibit rate-dependent response where the stiffness, strength and fracture patterns may depend 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. Here, we extend the QC approach presented in Ghareeb and Elbanna [Journal of the Mechanics and Physics of Solids, 137, 103819 (2020)] 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 mechanisms. Finally, we discuss the implications of rate dependence on engineering crack path and geometry in polymer-like networks.