3D particle shape modelling and optimization through proper orthogonal decomposition

Based on proper orthogonal decomposition (POD), a new method is presented in order to statistically characterize arbitrary particle shapes using an optimal choice of shape functions identified on a set of 1000 digitized railway ballast particles obtained through 3D Scan. The coefficients of the POD expansion enable a description of ballast grains with varying levels of accuracy. On exploiting the knowledge of their statistical distribution we are able, implementing an appropriate multivariate kernel density estimation method, to generate irregular particles with similar morphological features. The description and generation methods are validated by comparing statistical distributions of basic characteristics: surface area, volume, average radius, elongation, flatness, and aspect ratio. Using suitable geometric descriptors defining local curvatures, we identify which surface points might be regarded as forming faces. This shows that the proposed particle generation method is well suited for irregularly shaped granular materials, as a first geometric definition step, before numerical simulations of their collective mechanical properties are carried out by a Discrete Element code dealing with polyhedral shapes. We illustrate this process with the simple case of the assembling of a granular pack from a loose configuration, by one-dimensional compression, using different levels of accuracy in the representation of grain shape.