Different research areas rely on different physical approaches to study the micromechanical stability of materials and the nucleation and propagation of avalanche processes. These include coarse-grained elastoplastic or phase-field models in finite element (FEM) or lattice representations; discrete element (DEM) simulation of molecular dynamics representing amorphous or granular materials; fracture and interface propagation; simple conceptual representations of natural processes and solutions in the mean-field approximation. Some numerical and analytical results reveal a certain degree of universality across models and phenomena. Other features appear to be sensitive to the modeling approach, or its parameters. Of particular interest are the limitations of each modeling approach, such as the role of topological constraints in crystalline and granular matter, the dimensional embedding of the model and the range of interactions.
This section calls for recent results and reviews on the state of the art in the micromechanical modelling of avalanche dynamics across research areas, with an emphasis on universal features and the particular advantages, limitations and forecasting capabilities of each approach.