From the resulting deformed coordinate positions, the average displacement of the two halves at the inner edge on the big end of the cut can be calculated (the digital equivalent of the opening measurement in the experimental version of the rapid splitting test). A cut perpendicular (the second mesh) to the first was made, with the same stress field remained identical to that in the first instance. The two openings provide theoretical results of multiple testing of the same individual, without one test influencing another. 

Simulating populations

A simulated population here refers to a set of 1000 simulated individual samples which have a (simulated) rapid splitting test mean of \(1513\pm\ 20\ \mu\epsilon\) and a standard deviation of \(630\pm5\ \mu\epsilon\).
In order for the theoretical sample described in Section \ref{294131} to be created (which is needed to provide the individuals of the populations), the four input values in Equation \ref{eq:stress_surface} need to be defined. For each sample they are calculated from a multivariate normal distribution (Equation \ref{eq:multinorm}). The generation of the normal distribution takes the mean matrix which is constant for all samples regardless of their population, and the Covarience matrix which is made up of a population specific input variance and two correlations, CAdj and COpp, describe how related each of the four evenly spaced stress points on the circumference of the sample are at the populations level (see Figure \ref{210238} for a visual representation). The input variance is manipulated to give the output population a standard deviation of \(630\pm5\ \mu\epsilon\) (Note that the output population means are all between \(1494\) and \(1531\ \mu\epsilon\)).