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International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

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International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012002175
pages 327-342


Ulrike Schmidt
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, 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

Краткое описание

In this work a multiscale approach is introduced which allows for the identification of small scale mechanical properties by means of large scale test data. The proposed scheme is based on the computational homogenization method in which a small scale representative volume element is related to each large scale material point and the large scale material response is directly obtained via homogenization of the small scale field variables. Application of this computational homogenization method usually requires that the microstructure of the material be well characterized, i.e., that the constitutive behavior of all constituents of the heterogeneous material is known. This condition is circumvented here by the solution of an inverse optimization problem, which provides the fine scale material properties as a result. Therefore the objective function compares large scale experimental results to field values, simulated with the computational homogenization method. Discrete analytical expressions for the sensitivities are derived, and the performance of different gradient-based optimization algorithms is compared for linear elastic problems with various microstructures.

Ключевые слова: multiscale, homogenization, parameter identification


  1. Optimization Toolbox User's Guide - Version 5.0, The MathWorks.

  2. Burczyrński, T. and Kuś, W., Identification of material properties in multiscale modelling. DOI: 10.1088/1742-6596/135/1/012025

  3. Cioranescu, D. and Donato, P., An Introduction to Homogenization.

  4. Coleman, T. and Li, Y., On the convergence of reflective newton methods for large-scale nonlinear minimization subject to bounds.

  5. Coleman, T. and Li, Y., An interior, trust region approach for nonlinear minimization subject to bounds. DOI: 10.1137/0806023

  6. Costanzo, F., Gray, G., and Andia, P., 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

  7. Feyel, F. and Chaboche, J.-L., Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. DOI: 10.1016/S0045-7825(99)00224-8

  8. Fish, J. and Ghouali, A., Multiscale analytical sensitivity analysis for composite materials. DOI: 10.1002/1097-0207(20010228)50:6<1501::AID-NME84>3.0.CO;2-0

  9. Giusti, S., Novotny, A., de Souza Neto, E., and Feij&#243;o, R., Sensitivity of the macroscopic elasticity tensor to topological microstructural changes. DOI: 10.1016/j.jmps.2008.11.008

  10. Hill, R., Elastic properties of reinforced solids: Some theoretical principles. DOI: 10.1016/0022-5096(63)90036-X

  11. Kanout&#233;, P., Boso, D., Chaboche, J., and Schrefler, B., Multiscale methods for composites: A review. DOI: 10.1007/s11831-008-9028-8

  12. Kouznetsova, V., Brekelmans,W., and Baaijens, F., Approach to micro-macro modeling of heterogeneous materials. DOI: 10.1007/s004660000212

  13. Lillbacka, R. and Ekh, E. M., Calibration of a multiscale material model based on macroscale test data.

  14. Mahnken, R. and Stein, E., A unified approach for parameter identification of inelastic material models in the frame of the finite element method. DOI: 10.1016/0045-7825(96)00991-7

  15. Macconi, M., Morini, B., and Porcelli, M., Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities. DOI: 10.1016/j.apnum.2008.03.028

  16. Miehe, C. and Koch, A., Computational micro-to-macro transitions of discretized microstructures undergoing small strains. DOI: 10.1007/s00419-002-0212-2

  17. Miehe, C., Schr&#246;der, 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

  18. Morini, B. and Porcelli, M., TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities. DOI: 10.1007/s10589-010-9327-5

  19. Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. DOI: 10.1016/j.cma.2006.08.015

  20. Oskay, C. and Fish, J., On calibration and validation of eigendeformation-based multiscale models for failure analysis of heterogeneous systems. DOI: 10.1007/s00466-007-0197-3

  21. Possart, G., Presser, M., Passlack, S., Geiss, P., Kopnarski, M., Brodyanski, A., and Steinmann, P., Micro-macro characterisation of DGEBA-based epoxies on the way to polymer interphase modelling. DOI: 10.1016/j.ijadhadh.2008.10.001

  22. Ricker, S., Mergheim, J., and Steinmann, P., On the multiscale computation of defect driving forces. DOI: 10.1615/IntJMultCompEng.v7.i5.70

  23. Smit, R., Brekelmans,W., and Meijer, H., Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling. DOI: 10.1016/S0045-7825(97)00139-4

  24. Sundararaghavan, V. and Zabaras, N., Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multiscale homogenization. DOI: 10.1016/j.ijplas.2006.01.001

  25. Terada, K., Hori, M., Kyoya, T., and Kikuchi, N., Simulation of the multi-scale convergence in computational homogenization approaches. DOI: 10.1016/S0020-7683(98)00341-2

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