On the incorporation of curvature effects into the isogeometric analysis of fibre-reinforced solids

Abstract

In the context of engineering on the micro- and nanoscale, size-dependency is an important characteristic of material behaviour. In order to avoid complex experiments and predict size effects in simulations instead, classic continuum approaches are extended by the introduction of a length scale, e.g. through the consideration of gradient contributions. For the particular case of fibre-reinforced materials, such a gradient-enhanced approach can be achieved by introducing the fibre curvature as an additional kinematic quantity. This implies that basis functions with a global continuity higher than C0 are required for a finite element-based approach which accounts for these fibre curvature effects. The present contribution shows that the isogeometric finite element method can provide a framework for the simulation of the respective higher-gradient continua.