TY - JOUR

T1 - Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure

AU - Ma, Juan

AU - Sahraee, Shahab

AU - Wriggers, Peter

AU - De Lorenzis, Laura

N1 - Funding information: 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.

PY - 2015/3/31

Y1 - 2015/3/31

N2 - 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.

AB - 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.

KW - Finite deformations

KW - Montecarlo method

KW - Multiscale analysis

KW - Randomness and correlation

KW - Stochastic homogenization

UR - http://www.scopus.com/inward/record.url?scp=84937814236&partnerID=8YFLogxK

U2 - 10.1007/s00466-015-1136-3

DO - 10.1007/s00466-015-1136-3

M3 - Article

AN - SCOPUS:84937814236

VL - 55

SP - 819

EP - 835

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

IS - 5

ER -