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Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure

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Abstract

In this work, stochastic homogenization analysis of heterogeneous materials is addressed in the context of elasticity under finite deformations. The randomness of the morphology and of the material properties of the constituents as well as the correlation among these random properties are fully accounted for, and random effective quantities such as tangent tensor, first Piola–Kirchhoff stress, and strain energy along with their numerical characteristics are tackled under different boundary conditions by a multiscale finite element strategy combined with the Montecarlo method. The size of the representative volume element (RVE) with randomly distributed particles for different particle volume fractions is first identified by a numerical convergence scheme. Then, different types of displacement-controlled boundary conditions are applied to the RVE while fully considering the uncertainty in the microstructure. The influence of different random cases including correlation on the random effective quantities is finally analyzed.

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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 (11102143) is also sincerely acknowledged. The first author would like to acknowledge Professor Ilker Temizer for his code of lecture “Micromechanics” at Leibniz Universität Hannover as well. L. De Lorenzis would like to acknowledge the European Research Council, ERC Starting Researcher Grant “INTERFACES”, Grant Agreement N. 279439.

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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

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

    Juan Ma, Shahab Sahraee & Peter Wriggers

  3. Institute of Applied Mechanics, Technische Universität Braunschweig, 38106, Braunschweig, Germany

    Laura De Lorenzis

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  1. Juan Ma
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  2. Shahab Sahraee
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  3. Peter Wriggers
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  4. Laura De Lorenzis
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Correspondence to Juan Ma.

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Ma, J., Sahraee, S., Wriggers, P. et al. Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure. Comput Mech 55, 819–835 (2015). https://doi.org/10.1007/s00466-015-1136-3

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  • DOI: https://doi.org/10.1007/s00466-015-1136-3

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