A continuum lagrangian finite deformation computational framework for modeling granular flows

Granular flows are ubiquitous in many natural and engineering processes, from the formation of sand dunes to how chemicals are transported inside a factory. Such phenomena are characterized by complex interactions between the individual grains and surrounding fluids, multi-phase and heterogeneous materials, diverse physics, and large deformations. Due to these factors, analytical models and laboratory-scale experiments provide very limited information on the behavior of real-life scale problems. An alternative then is to rely on numerical methods to simulate granular flows. However, the current state-of-the-art computational frameworks available suffer from limitations, usually related to the large deformations involved. In this work, we develop a new computational framework to simulate granular flows which provides a unified approach to incorporating the multi-physics and multi-phase materials involved in a large deformation setting, while enabling large scale simulations efficiently. This framework is comprised of three main "ingredients, " namely, (1) a particle method, (2) a continuum large deformation theory, and (3) an implementation paradigm to support high performance computing. These ingredients translate into a finite deformation formulation based on the multiplicative split of the deformation gradient within the smoothed particle hydrodynamics (SPH) class of methods. The code was developed in Python to make use of user friendliness and enable easy maintenance and adaptation to multiple users' needs. It was also developed to make use of the most common parallel computing paradigms, in particular OpenMP, MPI and GPU processing. This is the first time a finite deformation formulation was applied in the context of the SPH method to simulate granular flows. The advantages of the new framework include computational efficiency, bypassing the limitations of objective stress rates, and ameliorating the well known SPH issue of tensile instability. Moreover, the framework proposed is structured more closely to what is usually encountered in the context of finite element method (FEM) implementations, in particular the constitutive update routines. This unified structure with FEM allows constitutive formulations often applied to such method to be directly applied to the SPH framework. Because this is the first time a framework like this was proposed, it had to be thoroughly validated. In order to validate the framework then, we performed a series of simulations of well known laboratory-scale experiments whose data are readily available for comparison of quantitaative results. Since the framework is intended to be applicable to real-life, large scale problems, we also validated the framework with a real case of debris flow and showed that the framework is capable of recovering the most important quantitative and qualitative features of the flow, such as flow velocity and duration, initiation zones and mobilized volumes of sediment, depositional configuration, and failure sequence. Furthermore, it was shown that the code is scalable, efficient, and ready for deployment as an open source resource for scientists and engineers in many fields, ranging from geotechnical engineering to land use policy and natural hazards risk assessment

Advisor: Borja Ronaldo I. (Ronaldo Israel)
Linder Christian (Engineering professor) 
Segall Paul