Isogeometric analysis (IGA) is a novel analysis paradigm which unifies the two cornerstones of computational engneering, computer-aided analysis (e.g. the finite element method) and computer-aided deisgn (CAD). The fundamental idea of IGA is to directly use the CAD parametrization of a geometric design for the puropose of analysis. This in contrast to the traditional situation, in which a CAD geometry is meshed to obtain an analysis-suitable geometric description. The rigorous elimination of the meshing step benefits the design-through-analysis process, especially for complex designs. Additionally, the smoothe spline basis functions inherited from CAD have various advantageous properties compared to the basis functions used in traditional finite elements.

Isogeometric analysis has proven to be a versatile tool for failure analysis. On the one hand, the excellent control over the inter-element continuity conditions enables a natural incoperation of continuum constitutive relations that incorporate higher-order strain gradients, as in gradient plasticity or damage. An additional length scale parameter, associated with the width of a failure process zone, emerges in such formulations. When the width of a failure process zone is negligible compared to the size of a specimen, a sharp (or discrete) description of the failure process is more appropriate. The possibility of enhancing a spline basis with discontinuities by means of knot insertion makes IGA a suitable candidate for modeling such discrete cracks. In this contribution, both possibilities are discussed and illustrated by example ranging from micro-scale failure mechanisms such as fiber-matrix debonding to macro-scale fracture processes.