Multi-scale method for the crack problem in microstructural materials

  • The paper deals with numerical computation of a crack problem posed on microstructural heterogeneous materials that contain multiple phases in the microstructure. The mechanical failure of such materials is a natural multi-scale effect since cracks typically nucleate in regions of defects on the microscopic scale. The modeling strategy for solving the crack problem concerns simultaneously the macroscopic and microscopic models. Our approach is based on an efficient combination of the homogenization technique and the mesh superposition method (s-version of the finite element method). The homogenized model relies on a double-scale asymptotic expansion of the displacements field. The mesh superposition method uses two independent (global and local) finite element meshes and the concept of superposing the local mesh arbitrarily onto the global continuous mesh. The crack is treated by the local mesh and the homogenized material model is considered on the global mesh. Numerical experimentsThe paper deals with numerical computation of a crack problem posed on microstructural heterogeneous materials that contain multiple phases in the microstructure. The mechanical failure of such materials is a natural multi-scale effect since cracks typically nucleate in regions of defects on the microscopic scale. The modeling strategy for solving the crack problem concerns simultaneously the macroscopic and microscopic models. Our approach is based on an efficient combination of the homogenization technique and the mesh superposition method (s-version of the finite element method). The homogenized model relies on a double-scale asymptotic expansion of the displacements field. The mesh superposition method uses two independent (global and local) finite element meshes and the concept of superposing the local mesh arbitrarily onto the global continuous mesh. The crack is treated by the local mesh and the homogenized material model is considered on the global mesh. Numerical experiments for problems on biomorphic microcellular ceramic templates with porous microstructures of multiple materials constituents are presented.show moreshow less

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Metadaten
Author:Ronald H. W. HoppeGND, Svetozara I. Petrova
URN:urn:nbn:de:bvb:384-opus4-10837
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1283
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-19)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston, University of Applied Sciences Bielefeld, Bulgarian Academy of Sciences Sofia
Release Date:2009/07/21
Tag:homogenization; elasticity; mesh superposition; crack; extended FEM
GND-Keyword:Mikrostruktur; Rissausbreitung; Mathematische Modellierung; Finite-Elemente-Methode
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand