Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved

On a multiscale strategy and its optimization for the simulation of combined delamination and buckling

This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated surfaces. In order to achieve an accurate prediction of the quasi-static response, a very refined discretization of the structure is required, leading to the resolution of very large and highly nonlinear numerical problems. In this paper, a nonlinear finite element formulation along with a parallel iterative scheme based on a multiscale domain decomposition are used for the computation of 3D mesoscale models. Previous works by the authors already dealt with the simulation of multiscale delamination assuming small perturbations. This paper presents the formulation used to include geometric nonlinearities into this existing multiscale framework and discusses the adaptations that need to be made to the iterative process in order to ensure the rapid convergence and the scalability of the method in the presence of buckling and delamination. These various adaptations are illustrated by simulations involving large numbers of DOFs