Multi-Scale Modeling of Heterogeneous Materials and the Validation Challenge

Article Preview

Abstract:

This paper considers multi-scale modeling strategies for heterogeneous materials while also highlighting the problems of determining experimentally the micro-scale properties and validating such techniques. Multi-scale modeling techniques enable us to capture the influence of (evolving) heterogeneous material microstructures on the overall macroscopic behavior. This paper discusses computational multi-scale modeling techniques for problems both with and without poor scale separation. In developing these powerful multi-scale modeling techniques, the obvious challenge of validating both the material behavior at multiple scales and the associated scale transition methodologies, using advances in material characterization and experimental mechanics, comes into sharp focus and this will be briefly explored here.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

345-350

Citation:

Online since:

August 2011

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2011 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] F. Feyel, Multiscale FE2 elastoviscoplastic analysis of composite structures, Computational Materials Science, 16: 344–354, (1999).

DOI: 10.1016/s0927-0256(99)00077-4

Google Scholar

[2] V. Kouznetsova, M. Geers, W. Brekelmans, Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, 54: 1235–1260, (2002).

DOI: 10.1002/nme.541

Google Scholar

[3] C. Miehe, A. Koch, Computational micro-to-macro transitions of discretised microstructures undergoing small strains, Archive of Applied Mechanics, 72: 300–317, (2002).

DOI: 10.1007/s00419-002-0212-2

Google Scholar

[4] Ł. Kaczmarczyk, C.J. Pearce, N. Bićanić, Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization, International Journal for Numerical Methods in Engineering, 74: 506–522, (2008).

DOI: 10.1002/nme.2188

Google Scholar

[5] Ł. Kaczmarczyk, C.J. Pearce, N. Bićanić, Studies of microstructural size effect and higher-order deformation in second-order computational homogenization, Computers and Structures, (2008).

DOI: 10.1016/j.compstruc.2008.08.004

Google Scholar

[6] T. Belytschko, S. Loehnert, J.H. Song, Multiscale aggregating discontinuities: A method for circumventing loss of material stability, International Journal for Numerical Methods in Engineering, 73: 869–894, (2008).

DOI: 10.1002/nme.2156

Google Scholar

[7] I. Gitman, H. Askes, L. Sluys, Coupled-volume multi-scale modelling of quasi brittle material, European Journal of Mechanics A/Solids, 27: 302–327, (2008).

DOI: 10.1016/j.euromechsol.2007.10.004

Google Scholar

[8] C. Miehe, C. Bayreuther, On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers, International Journal for Numerical Methods in Engineering, 71: 1135–1180, (2007).

DOI: 10.1002/nme.1972

Google Scholar

[9] Ł. Kaczmarczyk, C.J. Pearce, N. Bićanić, E. de Souza Neto, Numerical multiscale solution strategy for fracturing heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, 199(17-20): 1100 – 1113, (2010).

DOI: 10.1016/j.cma.2009.11.018

Google Scholar

[10] Ł. Kaczmarczyk, C.J. Pearce, A corotational hybrid-Trefftz stress formulation for modelling cohesive cracks, Computer Methods in Applied Mechanics and Engineering, 198(15-16): 1298 – 1310, (2009).

DOI: 10.1016/j.cma.2008.11.018

Google Scholar

[11] M.R.A. van Vliet, Size Effect in Tensile Fracture of Concrete and Rock, PhD thesis, Delft University of Technology, (2000).

Google Scholar

[12] W. Zhu, J.J. Hughes, N. Bicanic and C.J. Pearce, Nanoindentation mapping of mechanical properties of cement paste and natural rocks, Materials Characterization, 58(11-12): 1189-1198, (2007).

DOI: 10.1016/j.matchar.2007.05.018

Google Scholar