Cost-effective and accurate interlaminar stress modeling of composite Kirchhoff plates via immersed isogeometric analysis and equilibrium

The interest for composites has constantly grown in recent years, especially in the aerospace and automotive industries, as they can be moulded in complex form and geometry, as well as exhibit enhanced engineering properties. Nevertheless, despite the accelerated diffusion of laminated composites, the design of these materials is often restrained by the lack of cost-effective modeling techniques. In fact, the existing numerical strategies allowing for cheap simulations of laminated structures usually fail to directly capture out-of-plane through-the-thickness stresses, which are typically responsible for failure modes such as delamination. In this context, a stress recovery approach based on equilibrium has been recently shown to be an efficient modeling strategy in the framework of isogeometric analysis. Since immersed approaches like the finite cell method have been proven to be a viable alternative to mesh-conforming discretization for dealing with complex/dirty geometries as well as trimmed surfaces, we herein propose to extend the stress recovery approach combining the finite cell method, isogeometric analysis and equilibrium to model the out-of-plane behavior of Kirchhoff laminated plates. Extensive numerical tests showcase the effectiveness of the proposed approach.