The Nanometric and Micrometric Scales of the Structure and Mechanics of Materials Revisited : An Introduction to the Challenge of Fully Deterministic Numerical Descriptions

Amine Ammar (1) , Francisco Chinesta (2) , Pierre Joyot (3)

1 LR - Laboratoire de rhéologie
2 LMSP - Laboratoire de Mécanique des Systèmes et des Procédés
3 ESTIA INSTITUTE OF TECHNOLOGY

Nanoscience and nanotechnology as well as the fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales use descriptions ranging from the quantum to the statistical mechanics. This article revisits the modeling at these scales and points out the main challenges related to the numerical solution of such models that sometimes are discrete but involve an extremely large number of particles (as is the case of molecular dynamics simulations or coarse-grained molecular dynamics) and other times are continuous but defined in highly multidimensional spaces, leading to the well-known curse of dimensionality issues. The curse of dimensionality of some of these deterministic models will be emphasized, and their numerical implications will be addressed in the second part of this work.

Domaines: Mécanique [physics.med-ph]; Matériaux

Amine Ammar, Francisco Chinesta, Pierre Joyot. The Nanometric and Micrometric Scales of the Structure and Mechanics of Materials Revisited : An Introduction to the Challenge of Fully Deterministic Numerical Descriptions. International Journal for Multiscale Computational Engineering, 2008, 6 (3), pp.191-213. ⟨10.1615/IntJMultCompEng.v6.i3.20⟩. ⟨hal-01007372⟩