An efficient binning scheme with application to statistical crack mechanics

作者：Huq F; Brannon R^*; Graham Brady L

来源：International Journal for Numerical Methods in Engineering, 2016, 105(1): 33-62.

DOI：10.1002/nme.4959

• damage
• fracture
• probabilistic mechanics
• scale bridging
• upscaling
• statistical crack models
• numerical integration
• MPM/PIC mapping schemes
• binning
• data decimation

A computational scheme is developed for sampling-based evaluation of a function whose inputs are statistically variable. After a general abstract framework is developed, it is applied to initialize and evolve the size and orientation of cracks within a finite domain, such as a finite element or similar subdomain. The finite element is presumed to be too large to explicitly track each of the potentially thousands (or even millions) of individual cracks in the domain. Accordingly, a novel binning scheme is developed that maps the crack data to nodes on a reference grid in probability space. The scheme, which is clearly generalizable to applications involving arbitrary numbers of random variables, is illustrated in the scope of planar deformations of a brittle material containing straight cracks. Assuming two random variables describe each crack, the cracks are assigned uniformly random orientations and non-uniformly random sizes. Their data are mapped to a computationally tractable number of nodes on a grid laid out in the unit square of probability space so that Gauss points on the grid may be used to define an equivalent subpopulation of the cracks. This significantly reduces the computational cost of evaluating ensemble effects of large evolving populations of random variables.

• 出版日期2016-1-6