A Phase Field Model for the Damage and Fracture of Multiple Network Elastomers

This work develops a continuum phase field model for predicting the damage initiation and crack propagation in multiple network elastomers. Previous researches have revealed that failure of multiple network elastomers involves microscopic damage initiation by the chain scission of filler network and macroscopic fracture by penetrating crack of matrix network. However, most existing models for multiple network elastomers only deal with its finite deformation and strain softening process, which are unable to capture the initiation and propagation of cracks. In this work, to bridge the microscopic damage and the macroscopic fracture of multiple network elastomers in the finite deformation model, we incorporate the phase field variable of crack surface density to model the crack propagation and the internal damage variable to model the chain scission. By forming a multi-field variational framework, the developed model can be used to simulate the macroscopic deformation and fracture of multiple network elastomers. Through a finite element implementation of the phase field model, previous experiment results obtained from uniaxial tension and unilateral fracture can be well predicted. Moreover, experimentally observed damage zone formed by sacrificing filler network to achieve toughening effect is also numerically illustrated in simulation, giving much clearer pictures for the contributions of different energy dissipation mechanisms.