Exact axisymmetric adhesive contact analysis for a pre-deformed soft electroactive half-space

In this paper, three-dimensional exact solutions of adhesive contact between a pre-deformed compressible soft electroactive half-space and an axisymmetric rigid indenter are presented. The change of surface adhesion energy during the contact is examined by using the modified JKR model, which accounts for the real contact area instead of the projected area. With the help of new results in the potential theory method, all physical (field) variables are derived in terms of elementary functions for three common types of axisymmetric indenters (flat-ended, conical, and spherical). The analytical contact relations for different indenter geometries and material properties are provided and summarized in Tables 2 and 3 to serve a solid base for revealing the underlying electromechanical mechanism of soft electroactive materials. For numerical illustration, neo-Hookean isotropic electroactive material is considered. The simulation results clearly demonstrate that both the mechanical and electric biasing fields significantly affect the indentation measurement of the electroactive material. Moreover, at either micro- or nano-scale, adhesion plays a prominent role in the indentation responses. It is of interest that, even without adhesion, the normal stress somewhere in the contact region may become tensile under a prescribed pre-stretch when the biasing electric displacement exceeds a certain value. This abnormal phenomenon actually corresponds to surface instability of the half-space under the biasing field. In the case of adhesive contact, other than the surface instability, the value of surface adhesion energy between the probe and the sample will impose a constraint on the validity of indentation analysis within the linear elastic regime.