Constitutive modeling for polymer hydrogels: A new perspective and applications to anisotropic hydrogels in free swelling

Abstract

Abstract The paper presents a modified theoretical framework for isotropic and anisotropic deformation of hydrogels in both steady and transient states. By applying the kinematic constraint between the mechanical and chemical fields in the second law of thermodynamics, a unified constitutive equation could be obtained, which is capable to describe the isotropic or anisotropic deformation of hydrogels at the same time. Also, the diffusion equation for solvent molecules is modified based on the constraint and the Lagrange multiplier used to force the constraint is avoided being introduced in the free energy function. The theoretical framework is specialized to describe the steady swelling behaviors of anisotropic hydrogels and the corresponding solution properties for the equations of free swelling are discussed. The anisotropic-swelling behaviors for several kinds of configurations are investigated, including hydrogel blocks and a cylindrical tube with one or two families of reinforced fibers. We find that the swelling of anisotropic hydrogels shows rich behaviors even for the simple configurations in free states, such as selective expansion/shrinkage and anomalous residual stress. An agreement between the results obtained by the constitutive equations and experiments for the transversally isotropic swelling demonstrates the effectiveness of the constitutive model.