A continuum model for progressive damage in tough multinetwork elastomers

Recently a class of multinetwork elastomers (MNEs) was developed by swelling a filler polymer network with monomers that are subsequently polymerized to form matrix networks. Such MNEs were reported to possess remarkable stiffness and fracture toughness while maintaining the ability to sustain large deformation as found in simple elastomers. The enhancement in toughness is attained by prestretching the chains of the filler network through the introduction of one or more matrix network(s), thereby promoting energy dissipation through chain scission in the filler network. In this work, a model to capture the mechanical response of MNEs is developed, and validated with experimental data. Prestrech of the polymer chains is incorporated into the model by basing the strain energy density function on the combined effect of swelling and subsequent deformation of the completed MNE. The filler network is modeled as a polydisperse network of breakable polymer chains with nonlinear chain elasticity, while the matrix networks are modeled using the generalized neo-Hookean model. Although the filler network occupies only a small fraction of the material volume, the model shows that it contributes to the majority of the stress. Finally, the hysteresis during cyclic loading is shown to correlate with the accumulation of damage in the filler network during each cycle.