A multiscale model for the multiaxial anisotropic damage of double-network gels

Double-network (DN) gels possess exceptional mechanical properties and hold great promise as innovative soft materials due to their peculiar inherent structure made of a first highly cross-linked brittle short-chain network and a second flexible loosely cross-linked long-chain network. The stretch-induced molecular ordering in DN gels causes anisotropic effects along with complex interactions between the two networks. This paper attempts to contribute to the understanding of the history-dependent anisotropic multiaxial damage behavior of DN gels. A multiscale model is formulated for the constitutive description of the internal network physics in DN gels, such as the stretch-induced molecular ordering and damage, in connection to their multiaxial mechanics. The scission mechanism in the short-chain network is considered at the chain-scale using statistical mechanics by treating the breakage of internal molecular bonds as an energy activation process related to the thermal oscillation and stimulated by the chain stretch. The transition scale microsphere-based method is employed to realize the transition from the short-chain scale to the network scale while considering the statistical variability in chain lengths and their evolution due to the chain rearrangement consecutive to the progressive chain scission events. A two-phase microstructure representation allows accounting for the presence of the superimposed long-chain network along with the effective coupling due to mutual interpenetration of the two networks. The model capabilities to capture the biaxial behavior of gel material systems are critically evaluated by comparing the model outputs with a few available experimental observations under various loading modes highlighting both internal network coupling and anisotropic damage. The relevance of the proposed approach is highlighted by the favorable alignment of the model simulations with experimental observations of gel systems subjected to uniaxial stretching along orthogonal directions and exhibiting history-dependent anisotropic features induced by prior biaxial loading. The damage and rearrangement micro-mechanisms are discussed with respect to the model in connection to loading history.