SummaryThe modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family of large ill-conditioned linear systems. In this paper we study strategies to efficiently solve to linear system based on non-overlapping domain decomposition methods. We present a review of most employed approaches and their strong connections. We outline their mechanical interpretations as well as the practical issues when willing to implement and use them. Numerical properties are illustrated by various assessments from academic to industrial problems. An hybrid approach, mainly designed for multifield problems, is also introduced as it provides a general framework of such approaches.

This paper introduces a computational strategy to solve structural problems featuring nonlinear phenomena that occur within a small area, while the rest of the structure retains a linear elastic behavior. Two finite element models are defined: a global linear model of the whole structure, and a local nonlinear "submodel" meant to replace the global model in the nonlinear area. An iterative coupling technique is then used to perform this replacement in an exact but non-intrusive way, which means the model data sets are never modified and the computations can be carried out with standard finite element software. Several ways of exchanging data between the models are discussed and their convergence properties are investigated on two examples.