Capillary-induced deformation of an initially stressed neoHookean solid: A sessile liquid droplet

Abstract The development in lab-on-a-chip and flexible electronics has attracted great interest to understand the fluid-structure interaction. In this work, we analyze the capillary-induced deformation of an initially stressed neo-Hookean solid with an axisymmetric, sessile droplet on the surface in the framework of the incremental deformation theory. The neo-Hookean material is subjected initially to uniformly biaxial loading (stretching or compressing). Using the incremental deformation theory and the concept of breadth, we derive an explicit solution of the normal displacement component of the surface of the initially stressed neo-Hookean solid, which consists of a scaling factor and a shape function. The scaling factor decreases with the increase of the biaxial stretch, leading to the decrease in the deformation induced by the sessile droplet. The initially biaxial compression of the neo-Hookean solid increases the scaling factor. There is a critical-initial compression loading, at which the surface deformation changes from convex shape to concave shape. Increasing the ratio of the breadth to the radius of the contact zone between the sessile droplet and the initially stressed neo-Hookean solid increases the maximum value of the shape function.