Indentation of layered soft electroactive media

Novel layered soft electroactive materials/structures have various special functions and features which can be uniquely applied to different modern science and engineering fields. In this paper, three-dimensional full-field solutions for the indentation characterization of layered soft electroactive media are presented by using a newly established semi-analytical approach. This approach is based on the integration of the Fourier-Bessel series system of vector functions, the dual-variable and position method and the Green's function. For illustration, the flat-ended indentation of a layered neo-Hookean ideal dielectric half-space, incorporating interfacial imperfections and material inhomogeneity between adjacent layers, is taken as an example. The present method is first verified by comparing with the exact solution for a reduced homogeneous case and then applied to multi-layered half-spaces with varying interfacial conditions, ranging from the frictionless contact case to the perfectly bonded case, and with linearly/exponentially graded shear moduli within the layers. The effects of the material compressibility and the interfacial imperfections on the full-field responses are investigated through one-layer and twolayer half-space models, respectively. The imperfections are found to play as barriers in the propagation of indentation-induced distortion within the layered structure. The comparison between the incremental von Mises stress for 20-layer and 100-layer half-spaces further highlights the positive significance of increasing layers to prevent stress mismatches in such structures. Most interestingly, with the advantage of much lower cost on fabrication, the layered structure with sufficient layers is quantitively demonstrated to achieve desired performance comparable to the continuously graded one. We believe that the present study not only establishes a good reference for characterizing the properties of soft multi-field coupled materials/structures containing material inhomogeneity and/or imperfections but also provides a benchmark pattern for addressing related complex boundary-value problems.