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Probability Based Size Effect Representation for Failure in Civil Engineering Structures Built of Heterogeneous Materials

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Computational Methods in Stochastic Dynamics

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 22))

Abstract

In this work we discuss the failure analysis of civil engineering structures built of heterogeneous materials. The material heterogeneities call for a detailed representation of typical micro or meso-structure, which can be provided with the structured FE mesh representation as illustrated herein for 2D case and two-phase material. The building-block of such a representation is the constant stress triangular element that can contain two different phases and phase interface, along with all modifications needed to account for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface. We further show by numerical simulations that the proposed structured FE mesh approach is much more efficient than the non-structured mesh representation. This feature is of special interest for probabilistic analysis, where a large amount of computation is needed in order to provide the corresponding statistics. One such case of probabilistic failure analysis is also considered in this work, where the geometry of the phase interface remains uncertain since it is obtained as the result of the Gibbs random process. This computation is further used to provide the appropriate probabilistic description of material parameters of phenomenological model of localized failure in terms of correlated random fields. Subsequent Monte Carlo computations of failure phenomena in simple tension test performed with such probabilistic phenomenological model clearly show the capability of presented approach to recover the size effects anywhere within a range between the two classical bounds which are Continuum Damage Mechanics and Linear Fracture Mechanics.

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Acknowledgements

This work was supported by the French Ministry of Research. The collaboration with TU Braunchweig research group of H.G. Matthies, especially R. Niekamp and M. Krosche, and PROCOPE program funding are also gratefully acknowledged. AI also acknowledges the Research Award of the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Ecole Normale Superieure de Cachan, LMT, 61 avenue du president Wilson, 94235, Cachan, France

    Adnan Ibrahimbegovic, Jean-Baptiste Colliat, Martin Hautefeuille, Delphine Brancherie & Sergiy Melnyk

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  1. Adnan Ibrahimbegovic
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  2. Jean-Baptiste Colliat
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  3. Martin Hautefeuille
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  4. Delphine Brancherie
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  5. Sergiy Melnyk
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Correspondence to Adnan Ibrahimbegovic .

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Editors and Affiliations

  1. Inst. Structural Analysis &, Seismic Research, National Technical Univ. Athen, Iroon Polytechniou Str. 9, Athens, 157 80, Greece

    Manolis Papadrakakis

  2. , Intitute of Structural Analysis and Seis, National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    George Stefanou

  3. , Institute of Structural Analysis and Se, National Technical University of Athens, Iroon Polytechniou, Zografou Campus 9, Athens, 15780, Greece

    Vissarion Papadopoulos

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Ibrahimbegovic, A., Colliat, JB., Hautefeuille, M., Brancherie, D., Melnyk, S. (2011). Probability Based Size Effect Representation for Failure in Civil Engineering Structures Built of Heterogeneous Materials. In: Papadrakakis, M., Stefanou, G., Papadopoulos, V. (eds) Computational Methods in Stochastic Dynamics. Computational Methods in Applied Sciences, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9987-7_15

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  • DOI: https://doi.org/10.1007/978-90-481-9987-7_15

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