Cornell University

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CAM Colloquium: Chung-Yuen Hui (MAE, Cornell University) - Surface Stresses/Couples in Solid and the Neumann Triangle Balance of Forces

Friday, May 4, 2018 at 3:30pm

Frank H. T. Rhodes Hall, 655

Elasto-capillarity phenomena – solid deformation driven by liquid surface tension – have been extensively studied, but are distinct from phenomena driven by solid surface stress.  In this talk I will illustrate solid surface stress effect on a classic problem: a line force acting on a soft elastic solid, say due to the surface tension of a liquid drop, can cause the forming of a kink which regularizes the otherwise unbounded solution.   Linear theory shows that the applied force is borne entirely by the solid surface stress, not by the elasticity of the substrate; this local balance of three forces is called Neumann’s Triangle.   However, it is not difficult to imagine realistic properties for which this force balance cannot be satisfied.  Here we study how force balance is rescued from the breakdown of naïve Neumann’s Triangle by a combination of (a) large deformations of the bulk solid, and (b) increase in surface stress due to surface elasticity.  I will also raise the possibility that solid surfaces can store energy in bending. An important example is lipid bilayer.   I will demonstrate that a surface that resists bending completely regularizes the stress and strain field underneath the line load – it is continuously differentiable everywhere.

C.Y. Hui graduated from the University of Wisconsin-Madison in physics and mathematics.  He received a master degree in applied math and a Ph. D in solid mechanics, both from Harvard.   He came as an assistant professor to the department of Theoretical and Applied Mechanics in Cornell in 1981 and is currently the Joseph-Ford Professor in Mechanical and Aerospace Engineering.   He has published over 275 journal papers and is currently working on the mechanical behavior of soft materials.

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College of Engineering, Center for Applied Mathematics


engineering, center for applied math, College of Engineering, mae, center for applied mathematics, Mechanical and Aerospace Engineering


Chung-Yuen Hui

Speaker Affiliation

Department of Mechanical and Aerospace Engineering, Cornell University

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