Aleatory uncertainty in constitutive modeling refers to the intrinsic variability in material properties caused by differences in micromorphology (e.g., grain orientation or size, microcracks, inclusions, etc.) from sample to sample. Accordingly, a numerical simulation of a nominally axisymmetric problem must be run in full 3D (non-axisymmetric) mode if there is any possibility of a bifurcation from stability.

Dynamic indentation experiments, in which a spherical ball impacts to top free surface of a cylindrical specimen, nicely illustrate that fracture properties must have spatial variability — in fact, the intrinsic instability that leads to radial cracking is regarded by the Utah CSM group as a potential inexpensive means of inferring the spatial frequency of natural variations in material properties.

Radial cracking in dynamic indentation experiments.

Below is shown results of a conventional smeared damage model applied using spatially perturbed strength and energy release properties. This demonstrated ability to control radial cracking frequency in the simulations suggest that dynamic indentation experiments represent a practical means of parametrizing models that account for aleatory uncertainty.

Simulation of radial cracking using different levels of variability in the fracture strength to demonstrate a direct correlation with radial crack spacing.