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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i1.30
pages 19-28

Elastic Softening and Stiffening of Metals Surfaces

L. G. Zhou
Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Hanchen Huang
Rensselaer Polytechnic Institute


Materials surfaces, which dominate nanostructures such as nanoplates, are elastically different from their bulk counterparts. This paper reports elastic softening and stiffening of metals surfaces based on a combination of analytical formulations, molecular statics calculations, and ab initio calculations. The metals in this study include face-centered-cubic Cu, body-centered-cubic W, and hexagonal-close-packed Ti. Two mechanisms dictate the surface elasticity. The bond loss of surface atoms leads to surface softening, and the accompanying bond saturation leads to surface stiffening. For close-packed Cu and Ti the percentage of missing bonds is low, and the bond loss can be compensated for by the bond saturation, leading to possible surface stiffening. On the other hand, open-structure W is unlikely to have stiffer surfaces because each missing bond constitutes a large percentage of the total coordination. In general, a metal surface can be elastically softer or stiffer than the bulk, depending on the competition of bond loss and bond saturation at the surface.