MDS-UQ is a nonintrusive multiscale solver based on reduced order homogenization in combination with Karhunen-Loeve expansion and stochastic collocation method based on sparse grid. MDS-UQ has been verified against the Latin Hypercube Monte-Carlo method. MDS-UQ considers parameters describing constitutive equations and microstructure architecture as random variables.
Figure 1 depicts a plate with a crack where both the strength of the matrix and fiber are assumed as random fields with a mean and standard deviation depicted in the table on the right. Figure UQ2 shows the error in the mean and standard deviation of the overall composite plate strength as a function of the number of realization. In the sparse grid approach, realizations are carried out in the quadrature points of the random space.