固体的杨-拉普拉斯方程
The Young-Laplace's equation for solid
摘要：
在液膜无剪切阻力的基础上，建立了杨氏-拉普拉斯方程。它不适用于固体。通过考虑表面层内的面内剪切和横向剪切，重建了描述固体表面的杨氏-拉普拉斯方程。本文提出了一种新的杨-拉普拉斯方程。结果表明，固体的表面平衡是由体应力、表面膜应力和表面横向应力共同决定的。横向剪应力取决于表面高斯曲率的梯度和应变。薄膜内应力和表面横向剪应力使固体内部产生残余应力。内禀表面横向剪应力只发生在非球形体中。
英文摘要：
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.
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