Modulating adhesion strength in multi-ferroic composite materials: Insights from adhesive contact with arbitrary profile indenters

Adhesion control is a critical aspect of various applications, from industrial adhesion devices to the locomotion of insects on ceilings and walls. Multi-ferroic materials, which encompass mechanical, electrical, and magnetic properties, offer approaches for reversible adhesion control. This study presents a comprehensive theoretical framework for adhesive contact in multi-ferroic composite materials when subjected to axisymmetric rigid indenters with arbitrary profiles. We analytically derive the physical fields for various contact models, including Hertz contact, Johnson–Kendall–Roberts (JKR), and Maugis–Dugdale (MD) adhesive models. The obtained energy release rates indicate that the electric and magnetic potentials can modulate adhesion strength. The Griffith energy balance relation is employed to derive the indentation forces and penetration depths, which can be extended to a range of common indenters. Notably, the classical approximations fail when using small spherical indenters, but the study provides valid alternatives. The influence of amplitude and wavelength on contact behavior is explored, with greater effects observed for larger or smaller values. For cosine-shaped indenters, equivalence to flat-ended cylindrical punches is established under specific conditions. The study also reveals that the power indices for power-law-shaped indenters change the influence of electric and magnetic potentials on pull-off forces. These findings provide a theoretical fundament associated with the biomimetic and artificial adhesive systems and the modern testing techniques.