Modeling the mechanics and rheology of porous and granular media: an elastoplastic continuum approach

The complex mechanics of porous and granular media play a significant role in various industrial processes and natural phenomena. As an example, understanding the mechanics of how failure occurs, localizes and propagates in porous brittle solids under various conditions is crucial in comprehending the preceding mechanisms of earthquakes and the release of rock and snow avalanches. Capturing the complete evolution of gravitational mass movements like snow avalanches as they transition from solid-like to fluid-like behavior is challenging. This requires constitutive models that account for the relevant mechanical processes as well as versatile computational schemes capable of accommodating the phase change.

In this thesis, various aspects of porous and granular media mechanics, primarily motivated by snow and the desire to accurately model snow avalanches, are approached with the material point method (MPM). This relatively young numerical continuum scheme dating back roughly three decades has experienced very recent enhancements which contributed to significant improvement of its initial deficiencies. Here, MPM is employed 1) to explain and quantify the mechanics and mechanical properties of elastoplastic porous media through simulations of their microstructure and 2) on a macroscopic scale to simulate granular mass movements.

In the proposed microstructure-based approach, it will be demonstrated that MPM permits the investigation of both small and large deformation characteristics of irregular porous media with a continuous solid skeleton. Tackling such problems has previously been difficult, with mesh-based schemes suffering from extreme mesh-distortion under large deformations and discrete methods requiring a non-trivial segmentation into (bonded) grains. As an application, the large plastic consolidation in porous brittle materials is examined as a function of a wide range of porosities, from around 25% to 75%, as well as other microstructural properties. Notably, a universality in two-dimensional consolidation is reported. In addition, a diverse set of compaction patterns is reproduced depending on material properties and loading rate. These patterns include the propagating and reflection compaction bands observed in previous experiments with snow and granular packs. Based on the simulation results, the compaction band speed is found to follow a power law depending on the yield stress to inertia stress ratio.

On the macroscopic scale, a novel elasto-viscoplastic constitutive law is formulated and implemented in a two- and three-dimensional MPM, allowing for the modeling of granular solids and their transition to a liquid state which may be both cohesive and compressible. This model, conceived as a combination of critical state soil mechanics (describing granular solids) and the mu(I)-rheology (describing granular liquids), is highly relevant for snow avalanches. In view of validation, the model is compared to analytical calculations and