Abstract
This paper presents a homogenization-based hybrid uncertain analysis method (HHUAM) for the prediction of the effective elastic tensor for microscopic material properties with uncertain‑but‑bounded parameters. For those uncertain‑but‑bounded parameters related to the microscopic material properties, the ones with sufficient statistic information are modelled as bounded random variables, and those without enough statistics to build the probability density functions are defined as interval variables. Based on the finite element framework for homogenization method, the effective elastic tensor with bounded hybrid uncertain parameters can be expanded by using Gegenbauer series expansion. The variation ranges of the expectation and variance of the effective elastic tensor can be obtained due to the orthogonality relationship of Gegenbauer polynomials. Two numerical cases are carried out to verify the effectiveness and the efficiency of the HHUAM. The influence of the bounded hybrid uncertainties in microstructures on homogenized macroscopic elastic properties of heterogeneous materials is also investigated.
Published Version
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