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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

Lookup NU author(s): Dr Xiaoyi Zhou, Professor Peter Gosling



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


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.

Publication metadata

Author(s): Zhou X-Y, Gosling PD, Pearce CJ, Kaczmarczyk L, Ullah Z

Publication type: Article

Publication status: Published

Journal: Computer Methods in Applied Mechanics and Engineering

Year: 2016

Volume: 300

Pages: 84–105

Print publication date: 01/03/2016

Online publication date: 17/11/2015

Acceptance date: 15/10/2015

Date deposited: 09/11/2015

ISSN (print): 0020-7683

ISSN (electronic): 1879-2146

Publisher: Pergamon Press


DOI: 10.1016/j.cma.2015.10.020


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Funder referenceFunder name
EP/K026925/1UK Engineering and Physical Sciences Research Council (EPSRC)