Coupled Chemo-Mechanical Swelling Behavior of PH-Sensitive Hollow Cylinder Hydrogels under Extension–Torsion and Internal Pressure: Analytical and 3D FEM Solutions

Abstract

The coupled transient chemo-mechanical behavior as well as the large deformation behavior under various complex load conditions must be taken into account when designing a functional responsive polymer actuator or sensor. One sort of deformation that can be used to characterize the properties of materials with complicated behavior, like soft hydrogels, is coupled extension and torsion with internal pressure. It is important to thoroughly research the complex kinetics of pH-hydrogels with coupled diffusion and massive deformation behavior. The transient behavior of cylindrical hydrogels under coupled extension–torsion with internal pressure under indifferent conditions is proposed in this work using a reliable semi-analytical method. In this regard, an analytical solution is offered to inspect this problem, which is used as a common experimental methodology for the characterization and modeling of polymeric materials. The results show that the rate of deformation and the physical characteristics of the material have a substantial impact on the cylindrical hydrogel’s transient behavior under coupled extension–torsion and internal pressure. For the same problem, a 3D finite element study was done to assess the analytical solution. The accuracy of our method is supported by the results’ agreement in both the FE analysis and the proposed approach. However, offering such a solution for this complex problem is of tremendous relevance given the significantly cheaper computational cost of analytical methods when compared to FEM. Additionally, the calculations indicate a complex reaction force and moment because the hydrogel experiences nonlinear Poynting-type effects in this deformation domain. The suggested semi-analytical procedure’s resilience behavior is demonstrated by the visualization of the effects of various material properties. This method can be used to calibrate constitutive models and to develop and improve hydrogel structures.

pH-Sensitive Hydrogel Bilayers: Investigation on Transient Swelling-Induced Bending through Analytical and FEM Approaches

“…The Nernst-Planck equation takes the form of [34] Figure 13. A pH-responsive hydrogel in its dry state (reference) and its swollen state (current) in response to external pH stimuli, the network contains acidic groups, co-ions, counter-ions, and fixed charges [17].…”

“…Ionizable acidic groups in pH-sensitive hydrogels give rise to fixed charges and mobile ions, forming an electrical double layer in the domain. This layer surrounds the hydrogel and scales with Debye's length, which is in the nanoscale range [17]. The behavior of smaller hydrogels can be strongly influenced by this layer, while for larger macroscopic hydrogels that are several micrometers or more in size, the left-hand side of Equation ( 4) can generally be ignored outside of the double layer.…”

“…To simplify the notation, differentiation with respect to the referential coordinate (X 2 ) is denoted by the prime symbol. The porosity of the gel is defined according to a model proposed by [17].…”

“…Since the model is one-dimensional, α remains fixed throughout the analysis (α = 1). The hydrogel's chemical reactions facilitate the determination of the reversible binding concentration of ion k to the polymer chains (c b k ) through the following equation [17]:…”

“…Considerable attention has been given to the analysis of the finite deformation of hydrogels, including the bending of a block [15,16], torsion, extension, and inflation of hydrogel cylinders [17], inflation of a cylinder [18] and spherical membrane [19,20], have been carried out. One of particular interest in studying hydrogel deformation behaviors is the study of hydrogel-based bilayers and their finite bending triggered by swelling [21].…”