A Micromechanically Based Constitutive Model for the Inelastic and Swelling Behaviors in Double Network Hydrogels

Abstract

This paper presents a micromechanically based constitutive model within the framework of the continuum mechanics to characterize the inelastic elastomeric and swelling behaviors of double network (DN) hydrogels, such as the stresssoftening, necking instability, hardening, and stretchinduced anisotropy. The strainenergy density function of the material is decomposed into two independent contributions from the tight and brittle first network and the soft and loose second network, each of which is obtained by integrating the strain energy of onedimensional (1D) polymer chains in each direction of a unit sphere. The damage process is derived from the irreversible breakages of sacrificial chains in the first network and characterized by the directional stretchdependent evolution laws for the equivalent modulus and the locking stretch in the nonGauss statistical model of a single polymer chain. The constitutive model with the optimizedmaterial evolution law predicts stress–stretch curves in a good agreement with the experimental results during loading, unloading, and reloading paths for both ionic and covalent DN hydrogels. The deformationinduced anisotropy is investigated and demonstrated by the constitutive model for the free swelling of damaged specimen. The constitutive model is embedded into the finiteelement (FE) procedure and proved to be efficient to model the necking and neck propagation in the planestrain uniaxial elongation. Based on the procedure, the effects of imperfection and boundary conditions on the loading path and the material evolution during different stages of deformation are investigated.