Surface stress drives large material deformation to smooth compliant solids

Surface stress is a fundamental property affecting the interfacial mechanics of compliant solid structures. Previous experiments demonstrating how surface stress rounds and flattens sharp features have been largely limited to the two-dimensional (2D) and nearly planar case, studying rectangular ridges of initial height h₀ and initial width w₀, where h₀/w₀ is small (h₀/w₀ << 1). We microfabricate three-dimensional (3D) compliant structures with non-negligible aspect ratio (h₀/w₀ ~ 1) and observe that micropillar grids made of a compliant polymer in contact with air undergo spacing-dependent deformation, which is largest at low spacings and reaches a constant value at large spacings. This spacing-dependent behavior suggests an elastocapillary interaction between the structures at small spacing, whereas the asymptotic value suggests a limiting distance over which long-range interactions between pillars apply. The existing analytical solution for low aspect ratio structures appears to underpredict deformation for structures with higher aspect ratio, so we employ three-dimensional finite element analysis to model the large deformation. Our numerical results show large rotation within the material, explaining the discrepancy between our data and a low-amplitude theory. Finite element analysis also offers intriguing insights into the problem, such as predicting stress field maps and investigating the competition between bulk and surface energy.