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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v7.i5.70
pages 457-474

On the Multiscale Computation of Defect Driving Forces

Sarah Ricker
Applied Mechanics, University of Kaiserslautern, 67653 Kaiserslautern, Germany
Julia Mergheim
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, Germany
Paul Steinmann
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, Germany

ABSTRACT

In the present contribution, the computational homogenization scheme is extended toward the homogenization of configurational quantities like the Eshelby stress and material node point forces. Configurational mechanics is concerned with changes of the material configuration of continuum bodies and has numerous applications in defect mechanics, as, e. g., it can be shown that the material force at a crack tip corresponds to the J-integral and thus yields a criterion for crack propagation. In the theoretical part of this work, the differences between the homogenization of the direct and the inverse motion problem are elaborated. Therefore focus is put onto the influence of microscopic material interfaces and material body forces on the averaged field values. The theoretical results are illustrated by various numerical examples, which on one hand compare the homogenized configurational quantities for different microstructures, and on the other hand, point out which features of the microstructure influence the macroscopic configurational quantities.

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