MCE Ph.D. Thesis Seminar

Constitutive modeling in granular materials has been historically based on macroscopic experimental observations that while being usually effective to predict the bulk behavior of these type of materials, suffer of important limitations when it comes to understand the physics behind grain-to-grain interactions that induces the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s, helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanism furnishing the grain scale. However, one the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres and polyhedra have been typically used.

Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there remains a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but can rather directly unravel the micro-mechanical origin of macroscopic behavior.

Thus, in order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements and velocities), providing an across-the-scale basis for a better understanding and modeling of granular media.

In the same way, we introduce a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method.

Then,  after calibrating LS-DEM with respect to real experimental results, we exploit part of its potentiality to study the dependency of critical state (CS) parameters such as critical state line (CSL) slope , CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digitalized grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.