Eq. 2 is the cumulative Weibull distribution with scale parameter S 0 and shape parameter m ; Ψ Ψ = ∫ ∫ V [ σ σ ^ ^ ( ξ ξ ) ] m d V ( ξ ξ ) = constant factor depending on the structure geometry, V = structure volume; ξ ξ = relative (size-independent) coordinate vectors, σ σ ^ ^ ( ξ ξ ) = dimensionless stress field (dependent on geometry), scaled so that the maximum stress be 1; n d = number of spatial dimensions ( n d = 1, 2 or 3); l 0 = material characteristic length representing the effective size of the RVE (typically about 3 inhomogeneity sizes).