[see e.g. the review by @Javili2013]. The vast majority of numerical treatments of surface elasticity, however, have been limited to the infinitesimal deformation regime. Furthermore, to the best of the authors knowledge, no open-source or commercial finite element implementation of surface elasticity is available.

The objective of this contribution is to detail a finite element implementation of surface elasticity at finite deformations using the open-source library `deal.II` [@Bangerth2007; @Bangerth; @Bangerth2013]. The implementation uses various `deal.II` routines developed to facilitate solving partial differential equations on curved manifolds [see e.g. @DeSimone2009; @Heltai2008] embedded in a higher-dimensional space. The `deal.II` term for this set of routines is *codimension one*. The name follows from the mathematical definition of codimension: if $W$ is a subspace of a linear space or manifold $V$, then the codimension of $W \in V$ is defined by $\text{codim}\, W = \text{dim}\, V - \text{dim}\, W$. The *codimension one* routines greatly simplify the construction of the approximations to the various mathematical operators on the surface, and the geometric description of the surface. This is critical, as the surface deformation gradient (used to parameterize the constitutive response) is rank deficient, and the surface profile can be complex when modelling realistic problems. The 