Nonlinear Visco-Poroelasticity of Gels With Different Rheological Parts

Abstract

A polymeric gel contains a crosslinked polymer network and solvent. Gels can swell or shrink in response to external stimuli. Two typical kinetic processes are involved during the deformation of gels: the viscoelastic and poroelastic responses. Viscoelasticity of gels is generated from local rearrangement of the polymers, while poroelasticity is generated from solvent migration. The coupled time-dependent behaviors of gels can be formulated by coupling a spring-dashpot model with a diffusion–deformation model. Different combinations of spring and dashpot and different ways of dealing with the coupling between solvent migration and rheological models—either through the spring or dashpot—induce significantly different constitutive behaviors and characteristic time-dependent responses of gels. In this work, we quantitatively study how different rheological models coupled with solvent migration affect the transient behavior of gels. We formulate the visco-poroelastic gel theory for the Maxwell model, the Kelvin–Voigt model, and the generalized standard viscoelastic model. In addition, for generalized standard viscoelastic model, we also discuss the different coupling through the secondary spring or the dashpot. The models are implemented into finite element codes, and the transient-state simulations are performed to investigate the time-dependent deformation and frequency-dependent energy dissipation of different rheologically implemented gel models. The result shows that different combinations of spring and dashpot give the gel solid-like properties and liquid-like properties under different time scales; in addition, the coupling of solvent migration with the dashpot in the rheological model results in restrictions of solvent migration under certain length scales.