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International Journal for Multiscale Computational Engineering

Publicado 6 números por año

ISSN Imprimir: 1543-1649

ISSN En Línea: 1940-4352

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Indexed in

On the Multiscale Computation of Defect Driving Forces

Volumen 7, Edición 5, 2009, pp. 457-474
DOI: 10.1615/IntJMultCompEng.v7.i5.70
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SINOPSIS

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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CITADO POR
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  3. Blanco Pablo J., Sánchez Pablo J., de Souza Neto Eduardo A., Feijóo Raúl A., Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models, Archives of Computational Methods in Engineering, 23, 2, 2016. Crossref

  4. de Souza Neto E.A., Blanco P.J., Sánchez P.J., Feijóo R.A., An RVE-based multiscale theory of solids with micro-scale inertia and body force effects, Mechanics of Materials, 80, 2015. Crossref

  5. Liu Chenchen, Reina Celia, Variational coarse-graining procedure for dynamic homogenization, Journal of the Mechanics and Physics of Solids, 104, 2017. Crossref

  6. Kuhn Charlotte, Müller Ralf, Klassen Markus, Gross Dietmar, Numerical homogenization of the Eshelby tensor at small strains, Mathematics and Mechanics of Solids, 25, 7, 2020. Crossref

  7. Saeb Saba, Steinmann Paul, Javili Ali, Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound, Applied Mechanics Reviews, 68, 5, 2016. Crossref

  8. Liu Chenchen, Reina Celia, Dynamic homogenization of resonant elastic metamaterials with space/time modulation, Computational Mechanics, 64, 1, 2019. Crossref

  9. Liu Chenchen, Reina Celia, Discrete Averaging Relations for Micro to Macro Transition, Journal of Applied Mechanics, 83, 8, 2016. Crossref

  10. Müller Ralf, Kuhn Charlotte, Klassen Markus, Andrä Heiko, Staub Sarah, Indicators for the Adaptive Choice of Multi-Scale Solvers Based on Configurational Mechanics, in Multi-scale Simulation of Composite Materials, 2019. Crossref

  11. Ricker Sarah, Mergheim Julia, Steinmann Paul, Müller Ralf, A comparison of different approaches in the multi-scale computation of configurational forces, in Recent Progress in the Mechanics of Defects, 2010. Crossref

  12. Ricker Sarah, Mergheim Julia, Steinmann Paul, Müller Ralf, On the Homogenization of Material Forces, PAMM, 11, 1, 2011. Crossref

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