| Abstract: |
| Since the study of surface tension by Gibbs, it has become clear that surface stresses must be accounted for when modeling elastic bodies at small length scales. In this talk we report on a recently proposed mathematical model of a bulk solid containing a boundary surface with strain-gradient surface elasticity. The partial differential equations governing equilibrium states are the Euler-Lagrange equations associated to a Lagrangian energy functional with a novel surface energy density depending on the deformed surface`s relative curvature, stretching, and stretching gradient. After considering its mathematical precursors and properties, we then discuss its promise for modeling fracture without the pathological singularities arising in more classical models. |
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