Evaluation of stress inside a rock is the standard problem in mining engineering.
Rock mass behavior resulting from excavation is determined by how strong and in which directions this rock is stressed by a local geology. To evaluate rock stress prior to mining, one can drill a hole through the rock and measure how the wall of the hole is deformed with respect to its relaxed, stress-free shape.
The original stress at the location of the hole is related to the wall deformation in a complex way, depending on the rock properties and the shape of the wall. Our software simulates rock behavior in these conditions and calculates the stress from the wall shape, rock properties, and deformation data. The figure below demonstrates how accurately our simulations reproduce analytic results when the latter are available, namely when the stress depends linearly on strain and the hole is spherical.
The curved lines in the graph show how the independent components of the stress tensor evolve with iterations. The straight lines indicate randomly generated values of the same components, which were used prior to simulation to determine how the wall is deformed according to the analytic solution.