A nonlinear continuum framework for constitutive modeling of active polymer gels

Abstract

Chemo-mechanical transduction is one of the key mechanisms that has formed the basis for designing bio-inspired self-driven synthetic systems from soft materials. Polymer hydrogels that use Belousov–Zhabotinsky (BZ) reaction are a unique class of dynamical reaction–diffusion (RD) systems that can continuously transduce internal chemical energy, from the reaction, to produce sustained mechanical work. In particular, BZ gels represent a complex nonlinear chemo-mechanical system, wherein, the autocatalytic oscillatory BZ reaction drives the rhythmic mechanical deformations through polymer-solvent inter–diffusion. The objective of our work is to develop a standardized finite element (FE) framework for chemically driven active hydrogels that captures nonlinear elastic deformations with limited chain extensibility. The distinguishing feature of our approach is that, unlike other approaches, it combines reaction kinetics, solvent transport, elastodynamics of the polymeric network, and polymer-solvent friction under a unified FE framework. Moreover, we adapt our approach to a specific case of BZ gels and capture their swelling-deswelling characteristics. We first implement our FE framework in MATLAB that subsequently, forms the basis for constructing a three-dimensional user element subroutine (3D-UEL) in ABAQUS. Ultimately, through our simulations, we are able to capture all the essential features of BZ gels that includes chemically driven mechanical deformations. In addition, we also demonstrate that our 3D-UEL efficiently captures the chemo-mechanical response of “stent-shaped” BZ gels–a non-standard 3D geometry. In essence, our FE approach not only allows us to simulate BZ gels but also provides a template for other active, dynamical, RD-based systems, driven by chemo-mechanical transduction, irrespective of internal or external mechanisms.