Anthony Nouy

On a Multiscale Computational Strategy with Time and Space Homogenization for Structural Mechanics

A new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale. This strategy, which involves homogenization in space as well as in time, could replace in several domains of application the standard homogenization techniques, which are generally limited to the space domain. It is an iterative strategy which calls for the resolution of problems on both a micro (fine) scale and a macro (homogenized) scale. In this paper, we review the bases of this approach and present improved approximation techniques to solve the micro- and macro-problems.

A Multiscale Computational Approach for Contact Problems

We introduce a two-scale computational strategy for the resolution of contact problems with friction, possibly with numerous contact surfaces; the structure studied may also be highly heterogeneous. The description of “micro” and “macro” quantities is performed on the interfaces arising from the decomposition of the structure studied into an assembly of substructures and interfaces. The efficiency and robustness of the method are illustrated on several examples. This iterative computational strategy is suitable for parallel computing; it can be interpreted as a mixed multilevel domain decomposition method. Its scalability has been demonstrated and comparisons with other domain decomposition methods are also given.

Une stratégie de calcul multiéchelle avec homogénéisation en espace et en temps

Resume Une nouvelle strategie de calcul multi-echelle est proposee pour analyser les structures dont le comportement est decrit a une echelle fine tant en temps quen espace (par exemple : les structures composites). Au moins pour un certain nombre de questions, elle devrait se substituer avantageusement aux techniques standards dhomogeneisation et de reanalyse locale qui en general sont limitees au domaine spatial. Le but est ici de decrire les bases de cette approche. Pour citer cet article : P.xa0Ladeveze, A.xa0Nouy, C. R. Mecanique 330 (2002) 683–689.

On a Computational Strategy with Time-Space Homogenization for Heterogeneous Materials

A new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale. This strategy, which involves homogenization in space as well as in time, could replace in several domains of application the standard homogenization techniques, which are generally limited to the space domain and present some drawbacks. It is an iterative strategy which calls for the resolution of problems on both a micro (fine) scale and a macro (homogenized) scale. Here, we review the bases of this approach and present improved approximation techniques to solve the micro and macro problems.