The Young-Laplace's equation for solid

TL;DR

This paper extends the Young-Laplace's equation to solids by incorporating in-plane and transverse shear stresses, accounting for residual stresses and surface curvature effects in solid materials.

Contribution

It reconstructs the Young-Laplace's equation for solids, including shear stresses and curvature effects, which was not addressed in the original liquid-based formulation.

Findings

New version of Young-Laplace's equation for solids proposed

Surface equilibrium depends on bulk, membrane, and transverse stresses

Residual stresses arise from intrinsic surface shear stresses

Abstract

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