Some elements of microstructural mechanics G. Cailletaud a , S. Forest a, * , D. Jeulin b , F. Feyel a,c , I. Galliet a , V. Mounoury a , S. Quilici a a Centre des Mat eriaux, Ecole des Mines de Paris/CNRS, UMR 7633, BP 87, F-91003 Evry, France b Centre de Morphologie Math ematique, Ecole des Mines de Paris, 35 rue Saint-Honor e, F-77305 Fontainebleau, France c ONERA DMSE/LCME, 22 Avenue de la Division Leclerc, BP 72, F-92322 Ch^ atillon Cedex, France Received 15 April 2002; received in revised form 14 October 2002; accepted 10 November 2002 Abstract Microstructural mechanics combines the computational methods of structural mechanics and materials sciences. It is dedicated to the mechanics of heterogeneous materials. On the one hand, it can be used to compute industrial com- ponents for which the size of the heterogenities is of the order of magnitude of the size of the structure itself or of holes or notches. On the other hand, the computation of representative volume elements of heterogeneous materials enables one to predict the influence of phase morphology and distribution on the linear or non-linear effective properties, having in view microstructure optimization. Such computations provide the local stress–strain fields that can be used to predict damage or crack initiation. This work focuses on the modern tools available for reconstructing realistic three-dimen- sional microstructures and for computing them, including parallel computing. The choice of the local non-linear constitutive equations and the difficulty of identification of the corresponding parameters remain the weakest link in the methodology. The main example detailed in this work deals with polycrystalline plasticity and illustrates the tremen- dous heterogeneity of local stress and strain, and the effect of grain boundary or free surfaces. The computations are finally used to calibrate a simplified homogenization polycrystal model. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Structural mechanics; Microstructures; Materials; Parallel computing; Finite element; Constitutive behaviour; Viscoplas- ticity; Polycrystal 1. Objectives The mechanics of heterogeneous materials has longly been limited to the derivation of simplified schemes to include some aspects of the micro- structure into the prediction of their effective properties [1]. The tremendous increase of com- putational capabilities has strongly favoured the development of numerical simulations based on a more realistic description of microstructure. The computation of microstructures within the frame- work of continuum mechanics has now gained the level of a scientific ‘‘discipline’’ in its own. We call it in this work ‘‘microstructural mechanics’’, as a reference to the longstanding and now classical structural mechanics. Microstructural mechanics combines the tools of computational structural Computational Materials Science 27 (2003) 351–374 www.elsevier.com/locate/commatsci * Corresponding author. Tel.: +33-1-6076-3051; fax: +33-1- 6076-3150. E-mail address: samuel.forest@mat.ensmp.fr (S. Forest). 0927-0256/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0927-0256(03)00041-7