features of the formulation using four example problems. The first example is the Cook’s membrane problem. This is a widely-used benchmark. The purpose of the example is to provide detailed information for a series of uniformly refined meshes. Neo-Hookean type surface effects are considered. The second example illustrates neo-Hookean type surface effects in a nanowire undergoing significant tensile extension. Surface tension is omitted, i.e. $\h{\gamma} \equiv 0$. The third example of a liquid bridge explores the role of isotropic surface tension in a membrane surrounding a thin-walled cylinder with vanishing material properties. This example is a good benchmark for membrane problems as an analytical solution is available. It is however not ideally suited to problems in surface elasticity as, by definition, we require the energetic surface to be the boundary of a volume. The fourth example illustrates neo-Hookean type surface effects in a nanoscale plate with a realistic rough surface. This example is used to assess the performance of the implementation for relatively complex and realistic geometries.

The constitutive relations are given in Summary \[constiutive\_relations\]. Trilinear and bilinear elements are used in the volume and on the surface, respectively. This can be modified in the input parameter file. These results 