A transient nonlinear finite element framework and implementation of coupled electro-chemo-mechanics of polyelectrolyte hydrogels

Abstract

Polyelectrolyte (PE) hydrogels exhibit complex behavior characterized by large mechanical deformations, nonlinear stress response, solvent transport, and ion diffusion. The interplay between these mechanisms can lead to unexpected swelling dynamics, deformation patterns, and stress response. As such, advanced computational tools are needed for the efficient design of PE hydrogel-based devices, such as actuators and sensors for soft robotics, microfluidic valves, and drug delivery systems. In this work, we develop a numerical framework to simulate the coupled electro-chemo-mechanical behavior of PE hydrogels using finite element analysis. Applying this framework, an electro-chemo-mechanical model for PE hydrogels in a dilute ionic solution is implemented as a user element (UEL) subroutine in Abaqus/Standard. The model and UEL implementation are validated by comparing to experiments in the literature for transient free-swelling of a DMAEA gel in a solution of varying ionic strengths, then applied to study the consolidation behavior under confined compression and the transient bending behavior of a hydrogel bilayer. The simulations show that the ionic strength of the external solution, fixed charge density, and Flory-Huggins parameter play significant roles in the magnitude of the transient swelling and consolidation behavior.