A constitutive model for the large deformation of a self-healing gel

Abstract

We developed a 3D finite strain constitutive model to study the deformation of a hydrogel that contains two types of molecular crosslinks with one set of crosslinks much stronger than the other. Upon mechanical loading, the weaker crosslinks first break but can reform after breakage, thus endowing the gel with self-healing ability. An example is a recently developed ionically cross-linked triblock copolymer hydrogel, where ionic cross-links can form between the polyelectrolyte mid-blocks due to electric interaction. These physical bonds provide an additional set of crosslinks, which is analogous to the tightly cross-linked network in a double network gel and is necessary for toughness enhancement. However, unlike covalent bonds, these ionic cross-links can reform after they break. By keeping track of the time evolution of the breakage and reformation of these physical crosslinks, our model is able to address the macroscopic softening (hardening) behavior due to breaking (healing) of the physical bonds. In particular, we demonstrate our model for a uni-axial tensile test and show that strain softening in a tensile test can be suppressed by sufficiently slow loading rates. Our model is also able to capture the hysteresis and plasticity in a loading-unloading cycle.