Elastic and strength properties of statistical volume elements: Determination of isotropic and homogeneous size limits

•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.