Engineering Transactions, 67, 2, pp. 213–226, 2019
10.24423/EngTrans.1012.20190502

Response Surfaces in the Numerical Homogenization of Non-Linear Porous Materials

Witold BELUCH
Silesian University of Technology
Poland

Marcin HATŁAS
Silesian University of Technology
Poland

The paper deals with the numerical homogenization of structures made of non-linear porous material. Material non-linearity causes a significant increase in computational costs for numerical homogenization procedure. An application of the response surface methodology allows a significant reduction of the computational effort providing good approximation precision. Finite element method commercial software is employed to solve the boundary-value problem in both scales. Due to the significant reduction in computing time, the proposed attitude may be applied for different optimization and identification tasks for inhomogeneous, non-linear media, especially with the use of global optimization methods.
Keywords: numerical homogenization; response surface; porous material; non-linear material
Full Text: PDF

References

Liu L.S., Chen G.F., Porous materials. Processing and applications, Elsevier, 2014.

Wen C.E., Mabuchi M., Yamada Y.Y., Shimojima K., Chino Y., Asagina T., Processing of biocompatible porous Ti and Mg, Scripta Materialia, 45(10): 1147–1153, 2001, https://doi.org/10.1016/S1359-6462(01)01132-0.

Ishizaki K., Porous Materials: Process Technology and Applications, Springer, Boston, 1998.

Kouznetsova V., Computational homogenization for the multi-scale analysis of multi-phase materials, PhD. thesis, Technische Universiteit Eindhoven, 2002.

Weise T., Global optimization algorithms. Theory and application, 2nd ed., Thomas Weise, Germany, 2009.

Beluch W., Długosz A., Multiobjective and multiscale optimization of composite materials by means of evolutionary computations, Journal of Theoretical and Applied Mechanics, 54(2): 397–409, 2016, doi: 10.15632/jtam-pl.54.2.397.

Beluch W., Burczyński T., Two-scale identification of composites' material constants by means of com-putational intelligence methods, Archives of Civil and Mechanical Engineering, 14(4): 636–646, 2014, https://doi.org/10.1016/j.acme.2013.12.007.

Beluch W., Hatłas M., Multiscale evolutionary optimization of Functionally Graded Materials, [in:] Proceedings of the 3rd Polish Congress of Mechanics (PCM) and 21st International Conference on Com-puter Methods in Mechanics (CMM), Chapter 15, pp. 83–86, CRC Press/Balkema, 2016.

ANSYS 3D DesignXplorer 18.0 software documentation, ANSYS 2017.

ANSYS Mechanical 18.2 software documentation, ANSYS 2017.

Zohdi T., Wriggers P., An introduction to computational micromechanics, Springer, 2004.

Dormieux L., Lemarchand E., Kondo D., Brach S., Strength criterion of porous media: Application of homogenization techniques, Journal of Rock Mechanics and Geotechnical Engineering, 9(1): 62–73, 2017, https://doi.org/10.1016/j.jrmge.2016.11.010.

Fritzen F., Forest S., Böhlke T., Kondo D., Kanit T., Computational homogenization of elasto-plastic porous metals, International Journal of Plasticity, 29: 102–119, 2012, https://doi.org/10.1016/j.ijplas.2011.08.005.

Terada K., Hori M., Kyoya T., Kikuchi N., Simulation of the multi-scale convergence in computational homogenization approaches, International Journal of Solids and Structures, 37(16): 2285–2311, 2000.

Ptaszny J., Fedeliński P., Numerical homogenization by using the fast multipole boundary element meth-od, Archives of Civil Mechanical Engineering, 11(1): 181–193, 2011, https://doi.org/10.1016/S1644-9665(12)60182-4.

Zienkiewicz O.C., Taylor R.L., The finite element method, vol. 1–3, Butterworth, Oxford, 2000.

Czyż T., Dziatkiewicz G., Fedeliński P., Górski R., Ptaszny J., Advanced computer modelling in microme-chanics, Silesian University of Technology Press, Gliwice, 2013.

Hill R., Elastic properties of reinforced solids: Some theoretical principles, Journal of Mechanics and Physics of Solids, 11: 357–372, 1963, https://doi.org/10.1016/0022-5096(63)90036-X.

Nemat-Nasser S., Hori M., Micromechanics: Overall properties of heterogeneous materials, Elsevier, 1999.

Jiang T., Shao J., On the incremental approach for nonlinear homogenization of composite and influ-ence of isotropization, Computational Material Science, 46(2): 447–451, 2009.

Ilic S., Hackl K., Application of the multiscale FEM to the modeling of the nonlinear multiphase materi-als, Journal of Theoretical and Applied Mechanics, 47: 537–551, 2009.

Terada K., Kikuchi N., Nonlinear homogenization method for practical applications, American Society of Mechanical Engineers, Applied Mechanics Division, 212: 1–16, 1995.

Kleijnen J.P.C., Kriging metamodeling in simulation: A review, European Journal of Operational Re-search, 193: 707–716, 2009.

Myers R.H., Montgomery D.C., Anderson-Cook C.M., Response surface methodology. Process and product optimization using designed experiments, Wiley, 2009.

Bradley N., The response surface methodology, PhD thesis, Indiana University South Bend, 2007.

Vapnik V., The support vector method of function estimation, [in:] J.A.K. Suykens, J. Vandewalle [Eds], Nonlinear modeling, Springer, Boston, MA, 1998.




DOI: 10.24423/EngTrans.1012.20190502

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland