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A stochastic micromechanical model for fiber-reinforced concrete using maximum entropy principle

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Abstract

A stochastic micromechanical framework is presented to predict the probabilistic behavior of the fiber-reinforced concrete (FRC) using the maximum entropy principle. The FRC is represented as a multiphase composite composed of the aggregate, the interfacial transition zone, the bulk cement paste, and the fiber. The volume fractions of the different constituents are analytically calculated based on the material mix proportions and the aggregate grading. The multilevel homogenization schemes are presented to predict the material’s effective properties considering the effects of the aggregate, the ITZ, and the fibers with the different shapes. By modeling the volume fractions and properties of constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the inherent randomness of effective properties among the different specimens. The maximum entropy distribution is modified to estimate the probability density function of the material’s properties using their different order moments. Numerical examples including the limited experimental validations, the comparisons with existing micromechanical models, the commonly used probability density functions, and the direct Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the material’s effective properties.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (51508404, 51478348, 51278360, 51308407, U1534207). This work is also supported by the National Key Basic Research and Development Program (973 Program, No. 2011CB013800), State Key Laboratory of High Performance Civil Engineering Materials (No. 2015CEM008), Program of Shanghai Science and Technology Commission(15DZ1205003), the 1000 Talents Plan Short-Term Program by the Organization Department of the Central Committee of the CPC, Research Program of State Key Laboratory for Disaster Reduction in Civil Engineering, the Funds of Fundamental Research Plan for the Central Universities.

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Conflict of interest The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Key Laboratory of Advanced Civil Engineering Materials (Tongji University), Ministry of Education, 4800 Cao’an Road, Shanghai, 201804, China

    Qing Chen & Zhengwu Jiang

  2. Shaanxi Provincial Major Laboratory for Highway Bridge and Tunnel, Chang’an University, Xi’an, 710064, Shaanxi, China

    Qing Chen

  3. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, China

    Hehua Zhu & Zhiguo Yan

  4. Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education, Tongji University, 1239 Siping Road, Shanghai, 200092, China

    Hehua Zhu & Zhiguo Yan

  5. Department of Civil and Environmental Engineering, University of California, Los Angeles, CA, 90095, USA

    J. Woody Ju

  6. Department of Civil Engineering, Shanghai Univesitiy, 99 Shangda Road, Shanghai, 200444, China

    Changhong Wang

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  1. Qing Chen
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  2. Hehua Zhu
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  3. J. Woody Ju
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  4. Zhiguo Yan
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Correspondence to Qing Chen, Changhong Wang or Zhengwu Jiang.

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Chen, Q., Zhu, H., Ju, J.W. et al. A stochastic micromechanical model for fiber-reinforced concrete using maximum entropy principle. Acta Mech 229, 2719–2735 (2018). https://doi.org/10.1007/s00707-018-2135-1

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  • DOI: https://doi.org/10.1007/s00707-018-2135-1

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