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The potentially significant role of the surface of an elastic body in theoverall response of the continuum can be described using the mature theory ofsurface elasticity. The objective of this contribution is to detail the finiteelement approximation of the underlying governing equations (both in the volumeand on its surface) and their solution using the open-source finite elementlibrary deal.II. The fully-nonlinear (geometric and material) setting isconsidered. The nonlinear problem is solved using a Newton--Raphson procedurewherein the tangent contributions from the volume and surface are computedexactly. The finite element formulation is implemented within the totalLagrangian framework and a Bubnov-Galerkin spatial discretization of the volumeand the surface employed. The surface is assumed material. A map between thedegrees of freedom on the surface and on the boundary of the volume is used toallocate the contribution from the surface to the global system matrix andresidual vector. The deal.II library greatly facilitates the computation of thevarious surface operators, allowing the numerical implementation to closelymatch the theory developed in a companion paper. Key features of the theory andthe numerical implementation are elucidated using a series of benchmark exampleproblems. The full, documented source code is provided.

A finite element implementation of surface elasticity at finite strains using the deal.II library