Abstract Uncertainty in experimental measurements makes it challenging to determine which features are intrinsic to the phenomenon and which are most stable and reliable. Granular materials, such as sand, form a complex system in which the forces between individual particles influence the material's macroscopic behavior. However, these forces are also subject to uncertainty, as repeated measurements can yield different results. In this paper, we investigate how to model and visually analyze the uncertain structure of forces in granular materials. We adopt different perspectives on uncertainty by considering it as variance, probability, or additional variable. For a nuanced analysis of granular material data, we propose combining visualizations that represent these perspectives into a single visual analytics approach. We integrate uncertainty‐aware spatial visualizations that convey the probability of features, visualizations of derived measures and their variance over changes in the packing fraction, and overviews of varying probability thresholds. Finally, we evaluate our proposed approach in a case study conducted together with geotechnical engineers for the example of a 2D ensemble of photoelastic disks.

This paper presents an interactive analysis framework for exploring data from photoelastic disk experiments, which serve as a model for two-dimensional granular materials. Granular materials, composed of discrete particles such as sand or gravel, exhibit behaviors resembling fluid or solid states depending on the system configuration. These behaviors arise from interparticle contact forces, which form complex force networks that govern the material's macroscopic behavior. Our framework is specifically designed to analyze such 2D ensembles of dynamic force networks, enabling the identification and characterization of their underlying structures. The framework is built around a topology-based, multiscale data segmentation in terms of force chains and cycles. The analysis methods are structured across three levels: (1) multiscale analysis of individual instances under specific loading conditions, (2) detailed exploration of single experiments encompassing a series of loading and unloading cycles, and (3) comparative analysis across experiments conducted under similar and differing setups. We demonstrate the capabilities of our framework with a case study for each of these levels.

We present a visual analysis environment based on a multi-scale partitioning of a 2d domain into regions bounded by cycles in weighted planar embedded graphs. The work has been inspired by an application in granular materials research, where the question of scale plays a fundamental role in the analysis of material properties. We propose an efficient algorithm to extract the hierarchical cycle structure using persistent homology. The core of the algorithm is a filtration on a dual graph exploiting Alexander’s duality. The resulting partitioning is the basis for the derivation of statistical properties that can be explored in a visual environment. We demonstrate the proposed pipeline on a few synthetic and one real-world data set.