A Stochastic Multiscale Method for the Elastodynamic Wave Equation Arising from Fiber Composites

A Stochastic Multiscale Method for the Elastodynamic Wave Equation Arising from Fiber Composites

Ivo Babuska, Mohammad Motamed, and Raul Tempone, A Stochastic Multiscale Method for the Elastodynamic Wave Equation Arising from Fiber Composites, Computer Methods in Applied Mechanics and Engineering, Volume 276, 1 July 2014, Pages 190–211
Ivo Babuska, Mohammad Motamed, and Raul Tempone
Fiber composites, multiscale simulation, stochastic elastic wave equation, uncertainty quantification
2014
We present a stochastic multilevel global-local algorithm for computing elastic waves propagating in fiber-reinforced composite materials. Here, the materials properties and the size and location of fibers may be random. The method aims at approximating statistical moments of some given quantities of interest, such as stresses, in regions of relatively small size, e.g. hot spots or zones that are deemed vulnerable to failure. For a fiber-reinforced cross-plied laminate, we introduce three problems (macro, meso, micro) corresponding to the three natural scales, namely the sizes of laminate, ply, and fiber. The algorithm uses the homogenized global solution to construct a good local approximation that captures the microscale features of the real solution. We perform numerical experiments to show the applicability and efficiency of the method.
Feb. 2014