Publicado 6 números por año
ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352
Indexed in
On the Multiscale Computation of Defect Driving Forces
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.
-
Rice, J. R., A path independent integral and the approximate analysis of strain concentrations by notches and cracks. DOI: 10.1115/1.3601206
-
Hill, R., On constitutive macro-variables for heterogeneous solids at finite strain. DOI: 10.1098/rspa.1972.0001
-
Nemat-Nasser, S., and Hori, M., Micromechanics: Overall Properties of Heterogeneous Materials.
-
Hill, R., Elastic properties of reinforced solids: Some theoretical principles. DOI: 10.1016/0022-5096(63)90036-X
-
Suquet, P. M., Elements of homogenization for inelastic solid mechanics. DOI: 10.1007/3-540-17616-0_15
-
Guedes, J.-M., and Kikuchi N., Preprocessing and postprocessing for materials based on the homogenisation method with adaptive finite element methods. DOI: 10.1016/0045-7825(90)90148-F
-
Terada, K., and Kikuchi, N., Nonlinear homogenization method for practical applications.
-
Gosh, S., Lee, K., and Moorthy, S., Multiple scale analysis of heterogeneous elastic structures using homogenisation theory and voronoi cell finite element method. DOI: 10.1016/0020-7683(94)00097-G
-
Feyel, F., and Chaboche, J.-L., FE<sup>2</sup> multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. DOI: 10.1016/S0045-7825(99)00224-8
-
Miehe, C., Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation. DOI: 10.1002/nme.515
-
Miehe, C., and Koch, A., Computational microto- macro transitions of discretized microstructures undergoing small strains. DOI: 10.1007/s00419-002-0212-2
-
Miehe, C., Schotte, J., and Lambrecht, M., Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. DOI: 10.1016/S0022-5096(02)00016-9
-
Miehe, C., Computationalmicro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. DOI: 10.1016/S0045-7825(02)00564-9
-
Fish, J., and Yu, Q., Multiscale damage modeling for composite materials: Theory and computational framework. DOI: 10.1002/nme.276
-
Smit, R. J. M., Brekelmanns, W. A. M., and Meijer, H. E. H., Prediction of the large-strain mechanical response of heterogeneous polymer systems: Local and global deformation behaviour of a representative volume element of voided polycarbonate. DOI: 10.1016/S0022-5096(98)00089-1
-
Miehe, C., Schr ¨oder, J., and Schotte, J., , Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. DOI: 10.1016/S0045-7825(98)00218-7
-
Schröder, J., Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Instabilitäten.
-
Kouznetsova, V., Brekelmans, W. A. M., and Baaijens, F. P. T., An approach to micro-macro modeling of heterogeneous materials. DOI: 10.1007/s004660000212
-
Eshelby, J. D., The force on an elastic singularity. DOI: 10.1098/rsta.1951.0016
-
Maugin, G. A., Material Inhomogeneities in Elasticity.
-
Gurtin, M. E., Configurational Forces as Basic Concepts of Continuum Physics.
-
Kienzler, R., and Herrmann, G., Mechanics in Material Space with Applications to Defect and Fracture Mechanics.
-
Steinmann, P., Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. DOI: 10.1016/S0020-7683(00)00203-1
-
Steinmann, P., Ackermann, D., and Barth, F. J., Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting. DOI: 10.1016/S0020-7683(00)00381-4
-
Denzer, R., Barth, F. J., and Steinmann, P., Studies in elastic fracture mechanics based on the material force method. DOI: 10.1002/nme.834
-
Miehe, C., Schröder, J., and Becker, M., Computational homogenization analysis in finite elasticity: Material and structural instabilities on the micro- and the macro scales of periodic composites and their interaction. DOI: 10.1016/S0045-7825(02)00391-2
-
Costanzo, F., Gray, G. L., and Andia P. C., On the definitions of effective stress and deformation gradient for use in MD: Hill’s macrohomogeneity and the virial theorem. DOI: 10.1016/j.ijengsci.2004.12.002
-
Ricker Sarah, Mergheim Julia, Steinmann Paul, Müller Ralf, A comparison of different approaches in the multi-scale computation of configurational forces, International Journal of Fracture, 166, 1-2, 2010. Crossref
-
NGUYEN VINH PHU, STROEVEN MARTIJN, SLUYS LAMBERTUS JOHANNES, MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS, Journal of Multiscale Modelling, 03, 04, 2011. Crossref
-
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
-
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
-
Liu Chenchen, Reina Celia, Variational coarse-graining procedure for dynamic homogenization, Journal of the Mechanics and Physics of Solids, 104, 2017. Crossref
-
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
-
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
-
Liu Chenchen, Reina Celia, Dynamic homogenization of resonant elastic metamaterials with space/time modulation, Computational Mechanics, 64, 1, 2019. Crossref
-
Liu Chenchen, Reina Celia, Discrete Averaging Relations for Micro to Macro Transition, Journal of Applied Mechanics, 83, 8, 2016. Crossref
-
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
-
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
-
Ricker Sarah, Mergheim Julia, Steinmann Paul, Müller Ralf, On the Homogenization of Material Forces, PAMM, 11, 1, 2011. Crossref
-
Steinmann Paul, Introduction, in Spatial and Material Forces in Nonlinear Continuum Mechanics, 272, 2022. Crossref