Isogeometric analysis for modelling of failure in advanced composite materials

Isogeometric analysis (IGA) has recently received much attention in the computational mechanics community. The basic idea is to use splines as the basis functions for finite-element calculations. This enables the integration of computer-aided design and numerical analysis and allows for an exact representation of complex, curved geometries. Another feature of isogeometric basis functions, their higher-order continuity, is even more important for the development of shell and continuum shell elements to analyse structural stability and damage in thin-walled composite structures. The higher-order shape functions can be used to implement relatively straightforward but powerful shell elements. In addition, these shape functions contribute to a better representation of stresses in continuum elements. Finally, interfaces and delaminations can be modelled by reducing the order of the isogeometric shape functions by knot-insertion. In this chapter, we will give an overview of the recent developments in IGA for shell and continuum shell formulations.