The attached paper was recently accepted for publication in Journal of the Mechanics and Physics of Solids.

 The concept of surface energy is widely used to understand numerous aspects of material behavior:
fracture, self-assembly, catalysis, void formation, microstructure evolution and size-effect exhib-
ited by nano structures. Extensive work exists on deriving homogenized constitutive responses
for macroscopic composites—relating effective properties to various microstructural details. In the
present work, we focus on homogenization of surfaces. Indeed, elucidation of the effect of surface
roughness on the surface energy, stress and elastic behavior is relatively under-studied and quite
relevant to the behavior of both nanostructures and bulk material where surfaces are involved in
some form or fashion. We present derivations that relate both periodic and random roughness to
the effective surface elastic behavior. We find that the residual surface stress is hardly affected by
roughness while the superficial elastic properties are dramatically altered and, importantly, they
may also change sign—this has significant ramifications in the interpretation of sensing based on
frequency measurement changes. Interestingly, even if the bare surface has a zero surface elasticity
modulus, roughness is seen to endow it with one. Using atomistic calculations, we verify the quali-
tative validity of the obtained theoretical insights. We show, through an illustrative example, that
the square of resonance frequency of a cantilever beam with rough surface can decrease almost by
a factor of two compared to a flat surface.