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Variational issues in the homogenization of discrete systems

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Author

Summary, in English

The main objective of this work is the application of variational concepts to microscopic multiple particle systems (MPS) which are assigned to corresponding points of a macroscopic continuum. Due to this underlying micro-structure it is not sufficient to simulate the macroscopic behavior with pre-assumed (overall) material parameters, or rather constitutive-law-based standard methods. Therefore, the challenge is to determine macroscopic material behaviors, by means of e.g. stresses and numerical tangent-stiffnesses, based on the analysis of the underlying multiple particle system. With the assistance of the applied variational principle and the so-called continuization, which corresponds to the limit of an infinite number of particles in the system, the analogy of homogenization of discrete and continuous micro-systems is elaborated. Within this work we focus on the so-called computational homogenization scheme, which provides the stage for a coupling between a macroscopic system simulated by the Finite Element Method and different microscopic simulation techniques.

Department/s

Publishing year

2007

Language

English

Pages

186-191

Publication/Series

Multi-scale Computational Methods for Solids and Fluids

Document type

Conference paper

Topic

  • Mechanical Engineering

Conference name

Multi-scale Computational Methods for Solids and Fluids, ECCOMAS,

Conference date

2007-11-28 - 2007-11-30

Conference place

ENS-Cachan, France

Status

Published