Visco-hyperelastic swelling and mechanical behavior of tough pH-sensitive hydrogels: Theory development and numerical implementation

Abstract

Tough pH-sensitive hydrogels with noncovalent bonds have been developed in recent years as a promising structural material. They are involved in many engineering devices and natural phenomena due to their attractive properties. In this paper, we develop an electro-chemo-mechanical theory for swelling and mechanical behavior of tough pH-sensitive hydrogels. Due to its large deformation and time-dependent properties, we treat the hydrogel as a single-phase incompressible visco-hyperelastic material. We employ the Nernst-Planck equation to capture the flux of the ionic species through hydrogel boundaries. In this work, we are focused on the macro-size pH-sensitive hydrogels. Due to the Debye length, we assume the electro-neutrality condition both inside and outside of the hydrogel. Therefore, to find the concentration of co-ions and counter-ions inside the hydrogel, we use the Donnan equilibrium. We utilize the Generalized Maxwell model along with the Yeoh strain energy function to characterize the visco-hyperelastic behavior of the hydrogel. Hydrogel swells mainly due to the osmotic pressure. In this theory, we relate the osmotic pressure to the swelling ratio and apply the swelling ratio as a constraint in the strain energy function. After presenting the theory, we implement the theory in a nonlinear finite element framework for simulation. Our proposed theory can capture the transient dual swelling response of the hydrogel in various pH values as well as the time-dependent and self-healing behavior of the hydrogel.