Details
| Original language | English |
|---|---|
| Pages (from-to) | 495-510 |
| Number of pages | 16 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 198 |
| Issue number | 3-4 |
| Publication status | Published - 13 Sept 2008 |
Abstract
In this contribution, methods of computing the macroscopic tangent that is required in multiscale volumetric homogenization problems are investigated. A condensation procedure that employs the tangent information from the microscale finite element analysis is derived within a special framework where deformation controlled boundary conditions in micromechanical testing are enforced via the penalty method. The developed methodology is demonstrated by sample macroscale problems in the context of the multilevel finite element strategy. Due to the high memory allocation costs that the condensation procedure induces, a perturbation procedure is developed based on a minimal number of micromechanical tests. Results from the condensation and perturbation procedures are compared for sample infinitesimal and finite deformation inelasticity problems and the algorithmic consistency of the macroscopic tangent with the evolution of the macroscopic stress is discussed. It is shown that the ability to compute the macroscopic tangent can also be employed to construct a stress controlled micromechanical testing procedure.
Keywords
- Macroscopic tangent computation, Multiscale analysis, Volumetric homogenization
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 198, No. 3-4, 13.09.2008, p. 495-510.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the computation of the macroscopic tangent for multiscale volumetric homogenization problems
AU - Temizer, I.
AU - Wriggers, Peter
N1 - Funding information: Support for this work was provided by the German Research Foundation (DFG) under Grant No. WR 19/36-1.
PY - 2008/9/13
Y1 - 2008/9/13
N2 - In this contribution, methods of computing the macroscopic tangent that is required in multiscale volumetric homogenization problems are investigated. A condensation procedure that employs the tangent information from the microscale finite element analysis is derived within a special framework where deformation controlled boundary conditions in micromechanical testing are enforced via the penalty method. The developed methodology is demonstrated by sample macroscale problems in the context of the multilevel finite element strategy. Due to the high memory allocation costs that the condensation procedure induces, a perturbation procedure is developed based on a minimal number of micromechanical tests. Results from the condensation and perturbation procedures are compared for sample infinitesimal and finite deformation inelasticity problems and the algorithmic consistency of the macroscopic tangent with the evolution of the macroscopic stress is discussed. It is shown that the ability to compute the macroscopic tangent can also be employed to construct a stress controlled micromechanical testing procedure.
AB - In this contribution, methods of computing the macroscopic tangent that is required in multiscale volumetric homogenization problems are investigated. A condensation procedure that employs the tangent information from the microscale finite element analysis is derived within a special framework where deformation controlled boundary conditions in micromechanical testing are enforced via the penalty method. The developed methodology is demonstrated by sample macroscale problems in the context of the multilevel finite element strategy. Due to the high memory allocation costs that the condensation procedure induces, a perturbation procedure is developed based on a minimal number of micromechanical tests. Results from the condensation and perturbation procedures are compared for sample infinitesimal and finite deformation inelasticity problems and the algorithmic consistency of the macroscopic tangent with the evolution of the macroscopic stress is discussed. It is shown that the ability to compute the macroscopic tangent can also be employed to construct a stress controlled micromechanical testing procedure.
KW - Macroscopic tangent computation
KW - Multiscale analysis
KW - Volumetric homogenization
UR - http://www.scopus.com/inward/record.url?scp=55649093757&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2008.08.018
DO - 10.1016/j.cma.2008.08.018
M3 - Article
AN - SCOPUS:55649093757
VL - 198
SP - 495
EP - 510
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - 3-4
ER -