A compact anisotropic model for the mechanical response of double network hydrogels

Double-network (DN) hydrogels combine exceptional toughness with tissue-like softness, making them promising materials for biomedical and soft engineering applications. In this work, we present a novel constitutive model for predicting their mechanical response under general multiaxial loading conditions. At the microscopic scale, the two interlaced polymer networks are represented by effective semiflexible (worm-like) chains, capturing the cooperative behavior of the stiff, brittle first network and the soft, extensible second one. Irreversible damage is modeled as a progressive increase in the effective contour length of these chains, enabling the reproduction of the characteristic softening and Mullins effects observed experimentally. The macroscopic behavior is obtained through affine microsphere-based homogenization, ensuring a thermodynamically consistent formulation with a minimal number of material parameters. Despite its simplicity, the model accurately reproduces uniaxial and biaxial responses reported in the literature and demonstrates predictive capability across different loading paths. Furthermore, the identified parameters exhibit systematic trends with varying crosslinking densities, highlighting the potential of the proposed framework for the rational design of DN hydrogels with tailored mechanical properties.