We study the fragmentation response of a thin ring undergoing radially expanding loading, as the analysis can be carried out in 1D and all the domain undergoes a spatially uniform and temporally increasing loading. We assume that the underlying material properties are random fields. Through adjustments to the covariance function used, various forms of material heterogeneity, e.g. length scale of variations, roughness, span of variations, can systematically be incorporated in the model. We present fragmentation response in terms of material properties (fracture strength and length scales), random field (correlation length and point-wise span) and loading rate. Some macroscopic QoIs are fracture energy loss, maximum average stress, and fragmentation size distribution.
Forming the relation between the input parameters and output QoIs is quite challenging due to multiple factors including the high dimension of input space, expensive fracture simulations, and the need to simulate many such forward simulations to accurately propagate statistics from the input fields to output QoIs. We will design a machine learning workflow to identify the required data size and learning algorithms for extracting input-output relationships. We will reduce the size of the input space while controlling tradeoffs between computational and statistical efficiency. Moreover, we consider the problem of model selection by searching through a wide array of learning algorithms along with various evaluation metrics to measure the generalization error of the designed system. The results reveal interesting interplays between the form of the underlying length scales. The ML results facilitated understanding how the fracture response of the material shifts from the weakest link to a microstructural average response as the loading rate increases and how the shape of the probability distribution of macroscopic strength changes as a function of loading rate and microstructural property distributions.
2025-04-09 09:00:00
