Identification of stochastic material properties in multiscale modelling

Wacław Kuś¹ , Tadeusz Burczyński^1,2

¹Silesian University of Technology, Department for Strength of Materials and Computational.
²Cracow University of Technology, Institute of Computer Science, Cracow, Poland.

DOI:

https://doi.org/10.7494/cmms.2011.4.0376

Abstract:

The paper is devoted to multiscale identification of material properties in microscale. The identification process allows one to identify properties (like material constants, geometry) in microscale on the basis of measurements performed for macroscale. The presented approach assumes stochastic material properties in microscale. The identification problem is formulated as minimization of a functional which represents a distance between measured and theoretical values of displacements and strains. The Monte Carlo method combined with the finite element method is used to obtain theoretical displacements and strains values. The identification problem is solved with use of an evolutionary algorithm.

Cite as:

Kuś, W., & Burczyński, T. (2011). Identification of stochastic material properties in multiscale modelling. Computer Methods in Materials Science, 11(4), 524 – 530. https://doi.org/10.7494/cmms.2011.4.0376

Article (PDF):

Keywords:

Identification, Stochastic, Multiscale, Finite element method

References:

Burczyński, T., 1995, The Boundary Element Method, WNT Warsaw 1995 (in Polish).

Burczyński, T., 1995a, Boundary element method in stochastic shape design sensitivity analysis and identification of uncertain elastic solids, Engineering Analysis with Boundary Elements, 15, 151-160.

Burczyński, T., Beluch, W., Długosz, A., Orantek, P., Skrobol, A., 2006, Inteligent computing in inverse problems, Computer Assisted Mechanics and Engineering Sciences, 13, 161-206.

Burczyński, T., Kuś, W., 2009, Microstructure optimization and identification in multi-scale modeling, eds, J. Eberhardsteiner et al. ECCOMAS Multidisciplinary Jubilee Symposium – New Computational Challenges in materials, Structures and Fluids, Computational Methods in Applied Science, Springer Science, 169-181.

Burczyński, T., Orantek, P., 2009, Uncertain identification problems in the context of granular computing, eds, Bargiela, A., Pedrycz, W., Human-Centric Information Processing, 182, Springer-Verlag, 329-350.

Burczyński, T., Skrzypczyk, J., 1999, Theoretical and computa¬tional aspects of the stochastic Boundary Element Method, Computer Methods in Applied Mechanics and Engineering, 168, 321-344.

Kamiński, M., Kleiber, M., 2000, Perturbation based stochastic finite element method for homogenization of two-phase elastic composites, Computer and Structures, 78, 811-836.

Kuś, W., Burczyński, T., 2008, Parallel bioinspired algorithms in optimization of structures, Lecture Notes in Computa¬tional Sciences, 4967, 1285-1292.

Kleiber, M., Hien, T.D., 1992, Stochastic Finite Element Meth¬od, Wiley.

Kuś, W., Długosz, A., Burczyński, T., 2011, OPTIM – Library of bioinspired optimization algorithms in engineering applications, Computer Methods in Material Science, 11, 1,9-15.

Kuś, W., Burczyński, T., 2010, Bioinspired algorithms in multiscale optimization, eds, Kuczma, M., Wilmański, K, Computer Method in Mechanics, Springer, 183-192.

Madej,L., Mrozek, A., Kus, W., Burczyriski. T.. Pietrzyk, M., 2008, Concurrent and upscaling methods in multi scale modelling – case studies, Computer Methods in Material Science, 8, 1, 1-15.

Papoulis, A., 1991, Probability, Random Variables and Stochastic Processes. McGrawHill, New York.

Sakata, S., Ashida, F., 2011, Hierarchical stochastic homogenization analysis of a particle reinforced composite material considering non-uniform distribution of microscopic random quantities, Computational Mechanics, 48, 529-540.

Terada, K., Kikuchi, N., 2001, A class of general algorithms for multi-scale analyses for heterogeneous media, Computer Methods in Applied Mechanics and Engineering, 190, 5427-5464.

Zienkiewicz, O. C, Taylor, R. L., Zhu, J. Z., 2005, The Finite Element Method: Its Basis and Fundamentals, 6th Edition, Butterworth-Heinemann.