Description:
<jats:p>In this paper, the use of <jats:italic>hp</jats:italic>‐basis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, <jats:italic>C</jats:italic><jats:sup><jats:italic>k</jats:italic></jats:sup> <jats:italic>hp</jats:italic>‐basis functions based on classical B‐splines and a new approach for the construction of <jats:italic>C</jats:italic><jats:sup>1</jats:sup> <jats:italic>hp</jats:italic>‐basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new <jats:italic>C</jats:italic><jats:sup>1</jats:sup> approach also includes varying polynomial degrees. The properties of the <jats:italic>hp</jats:italic>‐basis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the <jats:italic>C</jats:italic><jats:sup><jats:italic>k</jats:italic></jats:sup> <jats:italic>hp</jats:italic>‐basis functions based on B‐splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.</jats:p>