Доступ предоставлен для: Guest
Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
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

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012002946
pages 361-373

INVERSE ANALYSIS FOR MULTIPHASE NONLINEAR COMPOSITES WITH RANDOM MICROSTRUCTURE

Sandra Klinge
Institute of Mechanics, Ruhr-University Bochum, D-44780 Bochum, Germany

Краткое описание

The contribution considers the application of inverse analysis to the identification of the material parameters of nonlinear composites. For this purpose a combination of the Levenberg-Marquardt method with the multiscale finite element method is used. The first one belongs to the group of gradient-based optimization methods, and the latter is a numerical procedure for modeling heterogeneous materials which is applicable in the case when the ratio of characteristic sizes of the scales tends to zero. Emphasis is placed on the investigation of problems with an increasing number of unknown materials parameters, as well as on the manifestation of the ill-posedness of inverse problems. These effects first occurred in the case of three-phase materials. The illustrative examples are concerned with cases where such a combination of experimental data is used that effects of ill-posedness are alleviated and a unique solution is achieved.

ЛИТЕРАТУРА

  1. Bazaraa, M. S., Sherali, H., and Shetty, C. M., Nonlinear Programming: Theory and Algorithms.

  2. Bertsekas, D., Nonlinear Programming.

  3. Chaterjee, A., An introduction to the proper orthogonal decomposition.

  4. Feyel, F., A multilevel finite element method FE2 to describe the response of highly nonlinear structures using generalized continua. DOI: 10.1016/S0045-7825(03)00348-7

  5. Fish, J. and Fan, R., Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading. DOI: 10.1002/nme.2355

  6. Fish, J. and Kuznetsov, S., Computational continua. DOI: 10.1002/nme.2918

  7. Hadamard, J., Lectures on Cauchy's Problem in linear partial differential equations. DOI: 10.1063/1.3061337

  8. Haupt, R. and Haupt, S. E., Practical Genetic Algorithms. DOI: 10.1002/0471671746

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

  10. Hill, R., On constitutive macro-variables for heterogeneous solids at finite strain. DOI: 10.1098/rspa.1972.0001

  11. Huet, C., Application of variational concepts to size effects in elastic heterogeneous bodies. DOI: 10.1016/0022-5096(90)90041-2

  12. Ilic, S., Application of the Multiscale FEM to the Modeling of Composite Materials.

  13. Ilic, S., Parameter identification for two-phase nonlinear composites.

  14. Ilic, S., User Manual for the Multiscale FE Program MSFEAP.

  15. Ilic, S. and Hackl, K., Application of the multiscale FEM to the modeling of nonlinear multiphase materials.

  16. Ilic, S. and Hackl, K., Solution-precipitation creep - extended FE implementation. DOI: 10.1007/978-90-481-9195-6_8

  17. Ilic, S., Hackl, K., and Gilbert, R. P, Application of the multiscale FEM to the modeling of cancellous bone. DOI: 10.1007/s10237-009-0161-6

  18. Kabanikhin, S., Definitions and examples of inverse and ill-posed problems. DOI: 10.1515/JIIP.2008.019

  19. Klinge, S. and Hackl, K., Application of the multiscale FEM to the modeling of nonlinear composites with a random microstructure. DOI: 10.1615/IntJMultCompEng.v10.i3

  20. Kost, B., Optimierung mit Evoultionsstrategien.

  21. Luenberger, D. and Ye, Y., Linear and Nonlinear Pogramming.

  22. Michel, J. and Suquet, P., Computational analysis of nonlinear composites structures using the nonuniform transformation fields analysis. DOI: 10.1016/j.cma.2003.12.071

  23. 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

  24. Miehe, C., Schröder, 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

  25. Nocedal, J. and Wright, S. J., Numerical Optimization. DOI: 10.1007/b98874

  26. Oden, J. and Zohdi, T., Analysis and adaptive modeling of highly heterogeneous elastic structures. DOI: 10.1016/S0045-7825(97)00032-7

  27. Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2006.08.015

  28. 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

  29. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in Fortran.

  30. Rojas, R., Neural Networks.

  31. Scherer, A., Neurale Netze.

  32. Schröder, J., Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilit ätsproblemen.

  33. Schwefel, H. P., Evolution and Optimum Seeking.

  34. Simo, J. C. and Hughes, T. J. R., Computational Inelasticity.

  35. Talbi, E. G., A taxonomy of hybrid metaheuristics. DOI: 10.1007/978-3-642-30671-6_1

  36. Terada, K. and Kikuchi, N., A class of general algorithms for multi-scale analysis of heterogeneous media. DOI: 10.1016/S0045-7825(01)00179-7

  37. Topping, B. H. V. and Bahreininejad, A., Neural Computing for Structure Mechanics.

  38. Yu, X. and Gen, M., Introduction to the Evolution Algorithms.

  39. Yuan, Z. and Fish, J., Towards realization of computational homogenization in practice. DOI: 10.1002/nme.2074

  40. Yuan, Z. and Fish, J., Hierarchical model reduction at multiple scales. DOI: 10.1002/nme.2554

  41. Yuan, Z. and Fish, J., Multiple scale eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2008.12.038

  42. Yvonet, J. and He, Q.-C., The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains. DOI: 10.1016/j.jcp.2006.09.019

  43. Zienkiewicz, O. C. and Taylor, R. L., The Finite Element Method.

  44. Zohdi, T., Wriggers, P., and Huet, C., A method of substructuring large-scale computational micromechanical problems. DOI: 10.1016/S0045-7825(01)00189-X