Micromechanical modeling of the multi-axial deformation behavior in double network hydrogels

Abstract The Mullins-type damage behaviors in double network hydrogels have attracted a broad research interest in recent years. However, most of current works focus on characterizing and modeling the uniaxial deformation behaviors of these materials. In this work, we combine experimental and theoretical approaches to investigate the anisotropic damage behaviors of double network hydrogels revealed in multi-axial deformation conditions. We demonstrate that an isotropic damage model based on the eight-chain model and the network alteration theory fails to capture the stress response in multi-axial loading tests. An anisotropic damage theory based on the microsphere model has also been developed, while both the affine and non-affine approaches are adopted to obtain the micro-macro mapping. The results show that the affine microsphere model cannot describe the experimental results in pure shear and unequal biaxial tests. Remarkably, the non-affine microsphere model with three parameters captures all the important features of the experimental observations. This is because the non-affine model accurately predicts the directional damage of the primary cross-linked network. The non-affine microsphere model is also able to describe the damage cross-effect in double network hydrogels. The developed theoretical framework can promote the fundamental understanding of the anisotropic damage behaviors in various types of tough gels.