On the incremental equations in surface elasticity

Yu, Xiang; Fu, Yibin

Abstract

We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau–Rayleigh and Wilkes instabilities in a solid cylinder.

• Journal Article Type: Article
• Acceptance Date: Dec 27, 2023
• Online Publication Date: Feb 16, 2024
• Deposit Date: Mar 22, 2024
• Publicly Available Date: Mar 22, 2024
• Journal: Mathematics and Mechanics of Solids
• Print ISSN: 1081-2865
• Electronic ISSN: 1741-3028
• Publisher: SAGE Publications
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1177/10812865231226183
• Keywords: Mechanics of Materials, General Materials Science, General Mathematics