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Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-carlo method

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Abstract

The computationally random homogenization analysis of a two-phase heterogeneous materials is addressed in the context of linear elasticity where the randomness of constituents’ moduli and microstructural morphology together with the correlation among random moduli are fully considered, and random effective quantities such as effective elastic tensor and effective stress as well as effective strain energy together with their numerical characteristics are then sought for different boundary conditions. Based on the finite element method and Monte-carlo method, the RVE with randomly distributing particles determined by a numerical convergence scheme is firstly generated and meshed, and two types of boundary conditions controlled by average strain are then applied to the RVE where the uncertainty existing in the microstructure is accounted for simultaneously. The numerical characteristics of random effective quantities such as coefficients of variation and correlation coefficients are then evaluated, and impacts of different factors on random effective quantities are finally investigated and revealed as well.

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Acknowledgments

The first author gratefully acknowledges the support of the Alexander von Humboldt Stiftung through a ‘Humboldt Research Fellowship for Postdoctoral Researchers’ for a research stay at the Leibniz Universität Hannover. The support of Natural Science Foundation of China to the project (JJ0500110405) “Random homogenization of heterogeneous materials with infinitesimal and finite deformation” is also gratefully acknowledged.

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Authors and Affiliations

  1. Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, P.O.Box: 187, Xi’an , 710071, People’s Republic of China

    Juan Ma, Jie Zhang & Liangjie Li

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, 30167 , Hannover, Germany

    Peter Wriggers & Shahab Sahraee

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  1. Juan Ma
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  2. Jie Zhang
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  3. Liangjie Li
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Correspondence to Juan Ma.

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Ma, J., Zhang, J., Li, L. et al. Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-carlo method. Comput Mech 54, 1395–1414 (2014). https://doi.org/10.1007/s00466-014-1065-6

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  • DOI: https://doi.org/10.1007/s00466-014-1065-6

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