Abstract
•Use mesoscale elements to statistically characterize elastic and fracture behavior.•Establish convergence metrics appropriate to define isotropic and heterogeneous limits.•Compare representative volume sizes with respect to heterogeneity and anisotropy.•Develop methods to decrease inaccuracy introduced by mesoscale partitioning scheme.•Relate volume element homogenization to stochastic partial differential equations.
In this paper, a method is presented to describe the statistical behavior of mesoscale material property fields, which are useful in macroscopic fracture simulation. The use of representative volume element-based properties can result in unsatisfactory fracture patterns because this approach eliminates random variations. In contrast, statistical volume elements can approximate random and inhomogeneous material properties. We compare two material property convergence metrics based on 1) vanishing variations of a property and 2) the convergence of property mean value versus volume element size. We examine the trends with which the properties of a two-phase composite tend toward homogeneous and isotropic limits. Compared to fracture properties, elastic properties reach their homogeneous and isotropic limit at smaller sizes. Accordingly, a volume element size can be chosen such that only the apparent fracture strength remains random and inhomogeneous. This reduces the computational cost and has proven useful in capturing realistic fracture results. In addition, the geometry of the mesoscale partitioning scheme has an important effect on homogenized properties. The intersection of straight edges with inclusions results in nonphysical size effects, increases anisotropy of properties, and results in 30 to 60 times larger representative volume elements compared to a partitioning scheme based on Voronoi homogenization.