Variational issues in the homogenization of discrete systems
(2007) Multi-scale Computational Methods for Solids and Fluids, ECCOMAS, p.186-191- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1515242
- author
- Ricker, S ; Mergheim, J ; Menzel, Andreas LU and Steinmann, P
- organization
- publishing date
- 2007
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Multi-scale Computational Methods for Solids and Fluids
- pages
- 186 - 191
- conference name
- Multi-scale Computational Methods for Solids and Fluids, ECCOMAS,
- conference location
- ENS-Cachan, France
- conference dates
- 2007-11-28 - 2007-11-30
- language
- English
- LU publication?
- yes
- id
- 5eadaa5e-d120-472f-b4f4-8bf4d8cc310e (old id 1515242)
- alternative location
- http://www.msf.ens-cachan.fr/pdf/MSFCachanEccomas2007.pdf
- date added to LUP
- 2016-04-04 14:12:07
- date last changed
- 2018-11-21 21:18:54
@inproceedings{5eadaa5e-d120-472f-b4f4-8bf4d8cc310e,
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.}},
author = {{Ricker, S and Mergheim, J and Menzel, Andreas and Steinmann, P}},
booktitle = {{Multi-scale Computational Methods for Solids and Fluids}},
language = {{eng}},
pages = {{186--191}},
title = {{Variational issues in the homogenization of discrete systems}},
url = {{http://www.msf.ens-cachan.fr/pdf/MSFCachanEccomas2007.pdf}},
year = {{2007}},
}