A paper on stochastic multiscale fracture analysis of three-dimensional functionally graded composites

Given link is for a new moment-modified polynomial dimensional decomposition (PDD) method developed for stochastic multiscale fracture analysis of three-dimensional, particle-matrix, functionally graded materials (FGMs) subject to arbitrary boundary conditions.

The method involves Fourier-polynomial expansions of component functions by orthonormal polynomial bases, an additive control variate in conjunction with Monte Carlo simulation for calculating the expansion coefficients, and a moment-modified random output to account for the effects of particle locations and geometry. A numerical verification conducted on a two-dimensional FGM reveals that the new method, notably the univariate PDD method, produces the same crude Monte Carlo results with a five-fold reduction in the computational effort. Results show that there exist significant variations in the probabilistic characteristics of the stress-intensity factors and fracture-initiation probability along the crack front.

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Link: http://dx.doi.org/10.1016/j.engfracmech.2010.09.006