Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties

X. -Y. Zhou, P. D. Gosling, C. J. Pearce, L. Kaczmarczyk, Z. Ullah

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Quantifying uncertainty in the overall elastic properties of composite materials arising from randomness in the material properties and geometry of composites at microscopic level is crucial in the stochastic analysis of composites. In this paper, a stochastic multi-scale finite element method, which couples the multi-scale computational homogenization method with the second-order perturbation technique, is proposed to calculate the statistics of the overall elasticity properties of composite materials in terms of the mean value and standard deviation. The uncertainties associated with the material properties of the constituents are considered. Performance of the proposed method is evaluated by comparing mean values and coefficients of variation for components of the effective elastic tensor against corresponding values calculated using Monte Carlo simulation for three numerical examples. Results demonstrate that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by randomness in the constituent material properties.
LanguageEnglish
Pages84-105
JournalComputer Methods in Applied Mechanics and Engineering
Volume300
DOIs
Publication statusAccepted/In press - 18 Aug 2015

Fingerprint

Homogenization method
Composite materials
Materials properties
Perturbation techniques
Tensors
Elasticity
Statistics
Finite element method
Geometry

Keywords

  • Composites
  • Effective elastic properties
  • Computational multi-scale homogenization
  • Stochastic finite element method
  • Perturbation technique

Cite this

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title = "Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties",
abstract = "Quantifying uncertainty in the overall elastic properties of composite materials arising from randomness in the material properties and geometry of composites at microscopic level is crucial in the stochastic analysis of composites. In this paper, a stochastic multi-scale finite element method, which couples the multi-scale computational homogenization method with the second-order perturbation technique, is proposed to calculate the statistics of the overall elasticity properties of composite materials in terms of the mean value and standard deviation. The uncertainties associated with the material properties of the constituents are considered. Performance of the proposed method is evaluated by comparing mean values and coefficients of variation for components of the effective elastic tensor against corresponding values calculated using Monte Carlo simulation for three numerical examples. Results demonstrate that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by randomness in the constituent material properties.",
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Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties. / Zhou, X. -Y.; Gosling, P. D.; Pearce, C. J.; Kaczmarczyk, L.; Ullah, Z.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 300, 18.08.2015, p. 84-105.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties

AU - Zhou, X. -Y.

AU - Gosling, P. D.

AU - Pearce, C. J.

AU - Kaczmarczyk, L.

AU - Ullah, Z.

PY - 2015/8/18

Y1 - 2015/8/18

N2 - Quantifying uncertainty in the overall elastic properties of composite materials arising from randomness in the material properties and geometry of composites at microscopic level is crucial in the stochastic analysis of composites. In this paper, a stochastic multi-scale finite element method, which couples the multi-scale computational homogenization method with the second-order perturbation technique, is proposed to calculate the statistics of the overall elasticity properties of composite materials in terms of the mean value and standard deviation. The uncertainties associated with the material properties of the constituents are considered. Performance of the proposed method is evaluated by comparing mean values and coefficients of variation for components of the effective elastic tensor against corresponding values calculated using Monte Carlo simulation for three numerical examples. Results demonstrate that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by randomness in the constituent material properties.

AB - Quantifying uncertainty in the overall elastic properties of composite materials arising from randomness in the material properties and geometry of composites at microscopic level is crucial in the stochastic analysis of composites. In this paper, a stochastic multi-scale finite element method, which couples the multi-scale computational homogenization method with the second-order perturbation technique, is proposed to calculate the statistics of the overall elasticity properties of composite materials in terms of the mean value and standard deviation. The uncertainties associated with the material properties of the constituents are considered. Performance of the proposed method is evaluated by comparing mean values and coefficients of variation for components of the effective elastic tensor against corresponding values calculated using Monte Carlo simulation for three numerical examples. Results demonstrate that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by randomness in the constituent material properties.

KW - Composites

KW - Effective elastic properties

KW - Computational multi-scale homogenization

KW - Stochastic finite element method

KW - Perturbation technique

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DO - 10.1016/j.cma.2015.10.020

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