Comparison of Mullins Effect between Tough Double Network Hydrogels and Filled Elastomers under Various Types of Deformation

The distinctive features of the Mullins effect between the double network (DN) hydrogels (Mai et al., Macromolecules 51, 5245–5257, 2018) and filled elastomers (Mai et al., Soft Matter 13, 1966–1977, 2017) are revealed by cyclic stretching measurement with various extension modes, i.e., uniaxial, planar, unequal and equal biaxial stretching. The modulus reduction, energy dissipation (D), and dissipation factor (Δ, the ratio of dissipated energy to input strain energy) in each loading-unloading cycle are evaluated. The result indicates that the cross-effect of strains (λ_iλ_j; i,j =x,y,z and i ≠ j) on Δ is pronounced in the DN gels whereas it is minimal in the filled elastomers. Interestingly, the modulus reduction relative to initial modulus and Δ in each cycle almost agree with each other in the DN gels, but they are considerably different in filled elastomers. This discrepancy reflects that the modulus reduction and dissipation factor are different in the main origin for the filled elastomers, while both of them totally stem from the purely elastic fracture of the chains in rigid and brittle DN gels networks.