We investigate the fragmentation response of a thin ring subjected to radially expanding loads. Material strength is represented as a random field. By adjusting the covariance function, we can systematically incorporate various forms of material heterogeneity, such as the length scale of variations, roughness, and the extent of fluctuations. The specific stochastic variation of material properties at the macroscale is translated into macroscopic quantities of interest (QoIs), including dynamic strength and fracture toughness. Our objective is to determine the distribution of these QoIs. Under quasi-static loading conditions, macroscopic strength is determined using the weakest link model, which posits that the overall strength equals the minimum local strength. We will explore how the characteristics of the local strength distribution and correlation function inform the parameters of the Weibull model applicable to quasi-static strength. This will be contrasted with the strength distribution at higher loading rates and its dependence on the mean local strength.
We utilize probabilistic neural networks (PNNs) to model aleatoric uncertainty, which captures the intrinsic variability in the input-output relationships of the system. This uncertainty stems from the underlying variation of microscale material properties, represented by a random field strength parameter. Unlike traditional neural networks that produce deterministic outputs, PNNs generate probability distributions for the target variable, enabling the estimation of predicted means and confidence intervals in regression tasks. With the trained PNNs, we predict the distributions of dynamic strength, toughness, and mean fragment size. For lower loading rates, these distributions will be compared to those predicted by the weakest link model for quasi-static loading conditions.
