Variational issues in the homogenization of discrete systems

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Abstract

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.

Details

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mechanical Engineering
Original languageEnglish
Title of host publicationMulti-scale Computational Methods for Solids and Fluids
Pages186-191
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes
EventMulti-scale Computational Methods for Solids and Fluids, ECCOMAS, - ENS-Cachan, France
Duration: 2007 Nov 282007 Nov 30

Conference

ConferenceMulti-scale Computational Methods for Solids and Fluids, ECCOMAS,
CountryFrance
CityENS-Cachan
Period2007/11/282007/11/30