A Multiaxial Theory of Double Network Hydrogels

The incorporation of a stiff and brittle phase into a soft and flexible polymer network makes double network hydrogels remarkably tougher than the conventional one. It also induces a stress softening in cyclic loading, which is seemingly identical to that of filled rubbers. Therefore, material models proposed for double network hydrogel are mostly based on continuum damage theories of filled elastomers. However, recent experimental studies clearly distinguish double network hydrogels from filled elastomers by the damage cross-effect in multiaxial deformation. In this paper, a micromechanical model for double network hydrogels under multiaxial deformation is proposed on the basis of the analytical network-averaging concept. Accordingly, the directional fracture of the first network results from cumulative damage in all directions. Furthermore, the strong interpenetration of the two networks is taken into account. The proposed analytical model includes very few physically motivated material constants and demonstrates excellent agreement with comprehensive experimental data of double network hydrogels under multiaxial loading conditions.