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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping and Y. Tsompanakis
Chapter 5

Virtual Experiments and a Statistically Equivalent Representative Volume Element for Macroscopic Constitutive Laws

M. Šejnoha, J. Vorel, R. Valenta and J. Zeman

Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic

Full Bibliographic Reference for this chapter
M. Šejnoha, J. Vorel, R. Valenta, J. Zeman, "Virtual Experiments and a Statistically Equivalent Representative Volume Element for Macroscopic Constitutive Laws", in B.H.V. Topping and Y. Tsompanakis, (Editor), "Civil and Structural Engineering Computational Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 5, pp 131-155, 2011. doi:10.4203/csets.28.5
Keywords: random composites, statistically equivalent periodic unit cell, homogenization, multiscale modeling, masonry, concrete, mastic asphalt.

Although often assumed in the micromechanical modeling of materials, the true periodic microstructures can be associated with only a limited number of carefully fabricated material systems. In practice, a majority of construction materials currently used for the design of engineering structures can be classified as random, either natural or artificially made, composites with complex microstructures over a wide range of length scales from nanometers to meters. To span such large size differences the general scope of hierarchical modeling has been promoted over the last two decades as the main driving force for structural design.

On the one hand, such a modeling venture opens the way to the introduction of a fundamentally different theoretical framework for the description of material behavior at a particular scale of interest and, if combined with proper averaging, to address the structural response without the need for calibrating the necessary macroscopic constitutive model used on the structural level. On the other hand, one may still offer several arguments as to why this compelling approach is not a practical tool or even admissible for large scale analyses. First, unless restricted to simple academic examples, it is still too computationally demanding. Second, in some modes of deformation such as strain localization the fully coupled homogenization schemes appear theoretically inadequate.

Therefore, even despite tremendous changes in the modeling of details of construction materials including fabrication processes, the large scale analysis of actual engineering structures still relies on the phenomenological description of the macroscopic material behavior. However, instead of deriving the model parameters from an arduous and expensive macroscopic experimental study we offer an appealing alternative to providing such material data by using a virtual testing tool established as an integrated set of models, algorithms and procedures for the prediction of mechanical properties of materials on an arbitrary scale. At the minimum a successful application of this strategy requires the synergy of the formulation of a certain representative volume element and advanced micromechanical modeling. This can be demonstrated as a cooperation of the following four tasks:

  • Small scale laboratory testing to provide for material data of individual constituents of the composite. These micromechanical tests are faster, cheaper and, in combination with a computer model, relatively easy to generalize as they rely on intrinsic properties of composite components.
  • Construction of the material database to store both local (phase) and homogenized (macroscopic) data.
  • Construction of a certain representative volume element (RVE) of a real material sample used in numerical simulations [1].
  • Numerical simulation of a large scale laboratory experiment exploiting the concept of periodic fields to derive material data needed in the macroscopic analysis [2].

Such a virtual laboratory tool is then expected not only to greatly reduce the number of laboratory tests at the macrolevel but also to improve the effectiveness of existing laboratory tests and speed up the introduction of new materials. In the present paper the generality of the virtual testing tool is advocated through the application of this approach to random masonry [3], concrete and asphalt mixtures - all falling into the category of random composites. The last material system in particular is addressed in sufficient detail to demonstrate how the results of the virtual testing tool can be brought directly to points of practical application [4].

J. Zeman, M. Šejnoha, "From random microstructures to representative volume elements", Modelling and Simulation in Materials Science and Engineering, 15(4), S325-S335, 2007.
J. Zeman, M. Šejnoha, "Numerical evaluation of effective properties of graphite fiber tow impregnated by polymer matrix", Journal of the Mechanics and Physics of Solids, 49(1), 69-90, 2001.
J. Novák, J. Zeman, M. Šejnoha and J. Šejnoha, "Pragmatic multi-scale and multi-physics analysis of Charles Bridge in Prague", Engineering Structures, 30(11), 3365-3376, 2008.
R. Valenta, "Micromechanical modeling of asphalt mixtures", Faculty of Civil Engineering, Czech Technical University in Prague, 2011.

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