In this paper, we consider the derivation of the modified Wenzel’s and Cassie’s equations for wetting phenomena on rough surfaces from a three-dimensional phase field model. We derive an effective boundary condition by asymptotic two-scale homogenization technique when the size of the roughness is small. The modified Wenzel’s and Cassie’s equations for the apparent contact angles on the rough s...

We investigate, using the framework of Γ-convergence, a phase-field model proposed in [Torabi et al, Proc. R. Soc. A, 2009] for strongly anisotropic systems; in particular, we prove a full Γ-convergence result for an anisotropic Modica-Mortolatype energy.

High cycle fatigue has become the leading cause of failure in gas turbine engine blades in recent years [1]. The majority of these failures were associated with surface damage such as foreign object damage (FOD). Therefore, the ability of a material to resist impact damage and the subsequent fatigue propagation of any cracks that may result has become a crucial design consideration. Substantial...