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Homogenization of random heterogeneous media with inclusions of arbitrary shape modeled by XFEM

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Abstract

The paper deals with the homogenization of random heterogeneous media with arbitrarily shaped inclusions simulated with the extended finite element method (XFEM) coupled with Monte Carlo simulation (MCS). The implementation of XFEM is particularly suitable for this type of problems since there is no need to generate a new finite element mesh at each MCS. The inclusions are randomly distributed and oriented within the medium while their shape is implicitly modeled by the iso-zero of an analytically defined random level set function, which also serves as the enrichment function in the framework of XFEM. Homogenization is performed based on Hill’s energy condition and MCS. The homogenization involves the generation of a large number of random realizations of the microstructure geometry based on a given volume fraction of the inclusions and other parameters (shape, spatial distribution and orientation). The influence of the inclusion shape on the effective properties of the random media is highlighted. It is shown that the statistical characteristics of the effective properties can be significantly affected by the shape of the inclusions especially in the case of large volume fraction and stiffness ratio.

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Acknowledgments

This work is implemented within the framework of the research project “MICROLINK: Linking micromechanics-based properties with the stochastic finite element method: a challenge for multiscale modeling of heterogeneous materials and structures” - Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State. The provided financial support is gratefully acknowledged. M. Papadrakakis acknowledges the support from the European Research Council Advanced Grant “MASTER–Mastering the computational challenges in numerical modeling and optimum design of CNT reinforced composites” (ERC-2011-ADG 20110209). Special thanks are also due to Professor Haim Waisman for providing the computer code of the XFEM model for inclusions of elliptical shape.

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Authors and Affiliations

  1. School of Civil Engineering, Institute of Structural Analysis & Antiseismic Research, National Technical University of Athens, 9 Iroon Polytechneiou, Zografou Campus, 15780, Athens, Greece

    Dimitris Savvas, George Stefanou & Manolis Papadrakakis

  2. Department of Civil Engineering, Institute of Structural Analysis & Dynamics of Structures, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    George Stefanou

  3. Department of Civil Engineering & Engineering Mechanics, Columbia University, New York, NY, 10027, USA

    George Stefanou & George Deodatis

Authors
  1. Dimitris Savvas
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  2. George Stefanou
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  3. Manolis Papadrakakis
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  4. George Deodatis
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Correspondence to George Stefanou.

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Savvas, D., Stefanou, G., Papadrakakis, M. et al. Homogenization of random heterogeneous media with inclusions of arbitrary shape modeled by XFEM. Comput Mech 54, 1221–1235 (2014). https://doi.org/10.1007/s00466-014-1053-x

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  • DOI: https://doi.org/10.1007/s00466-014-1053-x

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