Variational issues in the homogenization of discrete systems

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


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.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

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


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