Adhesive contact of the Hertzian indenter with an incompressible elastic substrate bi-directionally stretched along the indenter principal planes of curvature is considered in the Johnson–Kendall–Roberts theoretical framework. An approximate model is constructed by examining energy release rate conditions only on the edges of the minor and major axes of the contact ellipse. The effect of weak coupling between fracture modes I and II is introduced using a phenomenological mode-mixity function. This study was motivated by the need to model a passive–adhesive mechanism in cell mechanics on stretchable substrates.
Proceedings of the Royal Society A: https://royalsocietypublishing.org/doi/full/10.1098/rspa.2019.0507
ResearchGate link: https://www.researchgate.net/publication/338891646_Elliptical_adhesive_contact_under_biaxial_stretching