A reduced-dimensional explicit discrete element solver for simulating granular mixing problems

Geometric deep learning for computational mechanics Part I: anisotropic hyperelasticity

“…The vertex weight of a vertex-weighted graph w : V → R m maps an element of the vertex set onto a vector weight where m = 5 for twodimensional cases and m = 9 for three-dimensional cases -considering the dimensions of the position vector and the plastic strain tensor (in Voigt notation). We then run direct numerical simulations of the RVE to collect snapshots of this vertex-weighted graph under different loading cases and prescribed boundary conditions of the RVE, with a coverage requirement similar to those used for constructing orthogonal bases for reduced order simulations via the method of snapshots (Rowley and Marsden, 2000;Zhong and Sun, 2018;Zhong et al, 2021). Assuming that the sampling for the path-dependent behaviors is sufficient, the next step is to establish a pair of mappings between these weighted graphs and their low-dimensional representation.…”

Feasibility Analysis of a POD-Based Reduced Order Model with Application in Eulerian–Lagrangian Simulations

“…Shinde and Vilas, Li et al, , and Schiødt et al employed POD in the Lagrangian framework to characterize the particle flows rather than develop a ROM. Recently, Zhong et al developed an intrusive POD-based ROM for the simplified DEM simulations with a small number of particles. Li et al proposed a nonintrusive POD-based ROM for Eulerian–Lagrangian simulations.…”