Immersed Boundary Analysis of Models with Internal State Variables: Applications to Hydrogels

Summary

Research on Soft Active Materials (SAMs) has flourished in recent years driven mainly by potential applications to actuation systems, tissue engineering, and soft robotics. These applications benefit from the unique properties of SAMs such as large deformations, a wide range of stimulants, and high motion complexities. Hydrogels are among the dominant members of SAMs. Their highly nonlinear chemo-mechanical transient behavior is described by equations that include rates of internal state variables representing the local swelling state of the gel. Hence, the simulation of hydrogels requires intricate numerical approaches with stabilization schemes. This paper presents an immersed boundary analysis technique to simulate models with internal state variables. A hydrogel model is used as an example to describe the components of the proposed technique. Level sets define the material layout on a fixed background mesh and a generalized version of the extended finite element method predicts the response. The influence of the internal state variables on the stability of the physical analysis is examined. While focusing on an XFEM approach for hydrogels, the presented theory can be extrapolated to similar applications using models with internal state variables (e.g., shape memory polymers) and other immersed boundary analysis technique (e.g., CutFEM).