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.
Highlights
Given the opportunities they present to design for high-performance, composite materials have found extensive applications in a broad range of engineering fields
A stochastic multi-scale finite element method is proposed for the homogenization analysis of composite materials when randomness in the material constituent properties is taken into consideration
The computational homogenization scheme proposed in [29,5], which introduces a hierarchy of boundary conditions at the microscale and allows for direct treatment of micro-to-macro transitions, is adopted to estimate the overall elasticity property
Summary
Given the opportunities they present to design for high-performance, composite materials have found extensive applications in a broad range of engineering fields. Several studies of uncertainty analysis using the multi-scale finite element method have been reported, where stochastic analyses have been undertaken using Monte-Carlo simulation with different finite element schemes [15,16,17,18,19,20] Such an approach can become expensive in terms of computational time, especially for large numbers of variables, which is common for composites. In order to obtain better predictive modelling of material behaviour, and to deal with variability in the material properties of each component of the composite, a stochastic multi-scale method is developed by integrating the perturbation based stochastic finite element with a multi-scale computational homogenization method for the probabilistic prediction of the mechanical properties of a composite material. Conclusions drawn from the present study are provided in the last section
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