Multiscale modelling and computational strategies for composites

In the field of the structural analysis of composites, from the design of materials and structures to manufacturing, there has been increasing interest in material models which are described on a smaller scale than that of the macroscopic structural level. The first challenge, which depends on the design objective, consists of building an efficient, yet simple, ‘material’ model for the small scale chosen. The main damage mechanisms and their evolution must be described correctly. We use two very different composite materials to illustrate the state-ofthe- art of this field, the advantages and disadvantages of multiscale models and the current status of the research. The use of such material models leads to problems with extremely large numbers of degrees of freedom. This poses a second challenge, which is to design alternative computational strategies capable of solving such engineering problems. The goal is to reduce the calculation cost drastically while, at the same time, trying to increase robustness. The second and main part of the paper deals with this challenge and its present answers which are mechanics-based multiscale computational strategies with homogenization in space and in time. The paper should be seen as an overview of the state-of-the-art and the challenges facing the field of modelling and computation for composites