particular, the validity of negative surface parameters, which have been reported in the literature, is assessed.

While the majority of the numerical examples presented in the literature are performed on academic problems, one intended and novel application of the code presented here is to describe realistic nanostructures with complex surface geometry. This requires an efficient and parallelized code. In order to realise this objective, various numerical operations in the volume and on the surface are parallelized (within a shared memory paradigm) using the Threading Building Blocks library (TBB) [@TBB]. Aspects of the extension of this framework to a distributed environment is discussed briefly.

The structure of the paper is as follows. The key kinematic concepts are recalled in Section \[sec\_kinematics\]. Thereafter, the independent hyperelastic constitutive relations governing the response of both the volume and the surface are summarised. The strong form of the governing equations and their restatement in weak form as a Newton scheme are presented in Section \[sec\_governing\_equations\]. The linearized weak form provides the basis for the fully-discrete problem introduced in Section \[sec\_fully\_discrete\]. Details of the numerical implementation within the `deal.II` library are given in Section \[sec\_numerical\_implementation\]. Four numerical examples are presented in Section \[sec\_numerical\_results\]. They serve to 