Abstract
The relevant relations pertaining to hyperelastodynamics are stated in spatial and material setting. Thereby the spatial setting allows for the computation of the spatial motion problem, whereas the material setting allows for the consideration of the material motion problem. Thus the former serves to compute the dynamic response of a hyperelastic continuum due to given data, while the latter serves to consider any possible nonsmoothness in the solution to the former. It is the aim of this treatise to establish a formalistic framework that (i) highlights the intriguing duality of the spatial and material setting, and (ii) provides the necessary tools for an elegant transition between the spatial and material setting. To this end, the essential vehicle of the present approach is the variational approach which is firstly applied to hyperelastostatics and secondly to hyperelastodynamics. By adopting a tedious but strict formalism a number of new aspects are discovered.
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