Effect of Volume Element Geometry on Convergence to a Representative Volume

To accurately simulate fracture, it is necessary to account for small-scale randomness in the properties of a material. Apparent properties of statistical volume element (SVE) can be characterized below the scale of a representative volume element (RVE). Apparent properties cannot be defined uniquely for an SVE, in the manner that unique effective properties can be defined for an RVE. Both constitutive behavior and material strength properties in SVE must be statistically characterized. The geometrical partitioning method can be critically important in affecting the probability distributions of mesoscale material property parameters. Here, a Voronoi tessellation-based partitioning scheme is applied to generate SVE. Resulting material property distributions are compared with those from SVE generated by square partitioning. The proportional limit stress of the SVE is used to approximate SVE strength. Superposition of elastic results is used to obtain failure strength distributions from boundary conditions at variable angles of loading. This article is available in the ASME Digital Collection at https://doi.org/10.1115/1.4043753.