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M. Šejnoha, V. Šmilauer, J. Nemecek and L. Kopecký
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic
Keywords: Mori-Tanaka method, self-consistent method, differential scheme, alcali activated fly ash, natural wood, metallic foam, image analysis, nanoindentation, multi-scale homogenization.
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The field of composite materials now offers a tremendous variability
and complexity of microstructures depending on their particular
application. Nevertheless, it still shows a number of common features
which brings various material systems to the same footing, at least from
their analysis point of view. The latter issue has been repeatedly
exploited particularly in connection with systems described by limited
data often reduced to volume fractions and material
properties of individual phases and assumptions as to their statistically
uniform arrangement.
Introduction of images of real microstructures into the analysis
opened the way for more rigorous quantification of
microstructures as well as more advanced
modelling strategies based on statistically equivalent representation
of microstructural details using computational
models [1] often formulated in the hierarchical
manner to account for multiple scales [2]. The use
of advanced computational strategies was further supported by novel
techniques such as nanoindentation for the determination of material
properties of composite constituents on the level of microns. Note
however that combining image analysis, nanoindentation and
hierarchical modelling is by no means limited to complex and time
consuming computations. As a contrast, the use of analytical models such
as self-consistent and
Mori-Tanaka methods is sufficient in many
practical applications particularly if benefiting from the above three
features. Combining these features (image analysis, nanoindentation and
analytical micromechanical models) leads to reliable estimates of the
bulk response of heterogeneous materials which is the principal objective of
this paper.
Since learning from examples is the most simple way towards
understanding, this paper may also serve as a tutorial for the
application of various averaging schemes to the derivation of
effective properties of heterogeneous materials which show multiple
scales. To that end, several vastly dissimilar material systems are
examined. In particular, the calculation of Young's modulus as a function
of the degree of hydration of alkali-activated fly
ash [3] is discussed first followed by the
application of micromechanical modelling of natural
wood [4] and closes with a reference to
metallic foams [5].
By discussing the quality of the theoretical predictions in comparison
with available experimental data the paper introduces the reader to
the concept of a virtual testing tool as an integrated set of
models, algorithms and procedures for the prediction of mechanical
properties on an arbitrary scale.
- 1
- J. Zeman, M. Šejnoha, "From random microstructures to representative volume elements", Modelling and Simulation in Materials Science and Engineering, 15(4), S325-S335, 2007.
- 2
- J. Sýkora, T. Krejcí, J. Kruis, M. Šejnoha, "Computational homogenization of non-stationary transport processes in masonry structures", Journal of Computational and Applied Mathematics, 2011. (Accepted)
- 3
- V. Šmilauer, P. Hlavácek, Škvára F., L. Kopecký, J. Nemecek, "Micromechanical multiscale model for alkali activation of fly ash and metakaolin", Journal of Material Sciece, 46(20), 6545-6555, 2011.
- 4
- K. Hofstetter, C. Hellmich, J. Eberhardsteiner, "Continuum micromechanics estimation of wood strength", Proc. Appl. Math. Mech, 6, 75-78, 2006.
- 5
- J. Nemecek, V. Králík, J. Vondrejc, J. Nemeceková, "Identification of micromechanical properties on metal foams using nanoindentation", in B. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 125, 2011. doi:10.4203/ccp.96.125
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