The full, documented source code is provided.'
author:
- |
    Andrew McBride${}^\text{a}$, Ali Javili${}^\text{b}$, Paul Steinmann${}^\text{b}$, Daya Reddy${}^\text{a}$\
    [${}^\text{a}$Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa]{}\
    [${}^\text{b}$Chair of Applied Mechanics, University of Erlangen–Nuremberg, Germany]{}
bibliography:
- 'Elibrary.bib'
title: 'A finite element implementation of surface elasticity at finite strains using the deal.II library'
---

Introduction
============

The surface elasticity theory of @Gurtin1975 has been widely used to account for the role that the surface of an elastic body can play in the overall response of the continuum. Integral to the theory is the derivation of a set of governing equations and constitutive relations that describe the behaviour of the surface of the bulk object. The role of surface elasticity and the size-dependence of the elastic response has received considerable attention recently [see e.g. @Duan2009; @Weissmuller2010]. This resurgence of interest in the mechanics of surfaces can be largely attributed to the increasing number of applications involving nanoscale structures. In such applications scale effects are observed due to the significant surface-to-volume ratio. Classical continuum formulations are unable to account for these effects as they lack an inherent length scale.

The theory of surface elasticity is well understood 