The Young-Laplace equation associated with transverse shear stress within the surface layer of a solid

ABSTRACT

The Young-Laplace equation was firstly established based on a liquid film without shearing resistance. It is not valid for a solid. By taking into account the in-plane shearing and transverse shearing within a surface layer, we reconstruct the Young-Laplace equation for a solid. This new version shows that the equilibrium of a solid surface is determined by the bulk stress, the surface membrane stress and the transverse shear stress acting together. The transverse shear stress depends on the gradient of the Gaussian curvature of the surface and the strain. The intrinsic membrane stress and transverse shear stress cause residual stresses to appear in the interior of the solid. The intrinsic transverse shear stress occurs only in a non-spherical shaped body.