*codimension one* routines allow the surface of the body to be treated as an independent two-dimensional manifold embedded in three-dimensional space. The constitutive model for the surface implemented here allows the surface to behave in a solid- or fluid-like manner. For solid-like behaviour, the surface free energy resembles a classical neo-Hookean model. The neo-Hookean model is extended to include surface tension and thereby account for fluid-like effects.

Certain aspects of the implementation presented here for the volume contributions are similar to those discussed in the online tutorial (step\_44) on a three-field formulation for (near-incompressible) finite elasticity (see [www.dealii.org/developer/doxygen/deal.II/step\_44.html](www.dealii.org/developer/doxygen/deal.II/step_44.html)).

The finite element formulation is implemented within the total Lagrangian framework and a Bubnov–Galerkin spatial discretization of the volume and surface employed. The surface is assumed material (i.e. it acts like a membrane permanently attached to the underlying solid volume). The nonlinear problem is solved using a Newton–Raphson procedure wherein the tangent contributions from both the volume and surface are computed exactly. A curvilinear-coordinate-based finite element methodology for the problem of surface elasticity was developed in a companion paper [@Javili-in-review]. Extensive theoretical details and references are provided. For additional information on the admissible range for the surface material parameters, see @Javili2012c. In 