Analytical solution for adhesive contact of magneto-electro-elastic composites under an axisymmetric power-law indenter: A Maugis–Dugdale framework

Abstract

Switchable adhesion in response to external stimuli plays a critical role in various applications such as transfer printing, climbing robots and soft gripper. Multiferroic composites can give specific responses to mechanical-electro-magnetic loadings due to their multi-field coupling effects, which offers new routines to achieve tunable adhesion. In this work, the classical Maugis–Dugdale (M−D) adhesion model is extended to address the axisymmetric adhesive contact problem between a multiferroic composite half-space and an axisymmetric power-law indenter with real shape index n. By virtue of the superposition principle and Griffith energy balance, analytical solutions of the physical quantities at the contact surface and the relationships among the indentation force, contact radius and indentation depth for M−D-n model are obtained. The Derjaguin–Muller–Toporov (DMT)-n solutions applicable to multiferroic composites are derived from the corresponding M−D-n solutions as the limiting cases, which are new to literature and acquired in this work for the first time. The effects of the electromagnetic properties and the profile of the indenter on adhesion behaviors are discussed. It is found that the electromagnetic properties of the indenter have hardly influence on adhesion behaviors in the absence of electromagnetic loadings, which means that one can replace the multi-field coupling adhesion solutions with the purely elastic adhesion solutions in nanoindentation characterization of multiferroic composites under this circumstance. The profile of the indenter has a prominent effect on the transition behavior from DMT-n solution to JKR-n solution. The adhesion enhancing effect induced by the electromagnetic loadings diminishes with increasing the shape index of the indenter and the magnitude of the generalized Tabor parameter. The results obtained from this work not only lay the theoretical basis for nanoindentation technique in characterizing material properties of multiferroic composites, but also possess potential application value in switchable adhesion.