Indentation on a constrained electroactive gel - Xia, Guozhan (Journal of the mechanics and physics of solids, 2025)
Electroactive gel (EAG), a smart material with tunable physical properties, has attracted increasingly more attention in various engineering fields. This paper presents the analytical solutions for the frictionless contact between a rigid spherical indenter and a block of constrained swollen EAG, which is also subject to a transverse electric field. The classical JKR model is extended to involve the additional energy penalty accounting for surface tension in the equilibrium state. With the new results in surface Green's function established in advance for electromechanical orthotropic materials, typical indentation relations are derived in terms of elementary functions for electrically conducting and insulating cases, respectively. The whole analysis is performed based on the gel endowed with a Flory-Rehner energy density function to signify the feasibility of our method. The theoretical predictions are first verified by comparing to the finite element simulations, and then focus on the influences of biasing fields on the indentation relations and the geometric characteristics during contact, including the eccentricity, the pull-out force, and the relevant critical distance at beginning of separation. It is noteworthy that the disappearance of indentation force does not necessarily correspond to the initiation of surface instability for the orthotropic material, which may attribute to the absence of external Maxwell stress. A novel critical criterion with a more comprehensive form is proposed instead to not only cover the traditional perspective but also be applicable for more general cases. We believe that the contact model proposed here serves a theoretical base for the indentation-based characterization method of EAGs and a wide range of kindred functional soft materials.