The Microscopic Insight into Fracturing of Brittle Materials with the Discrete Element Method

Geophysics is an extremely vast field of science that studies the physical processes taking place on Earth or other planets. One of such processes is fracturing of materials. To support these statesments two phenomena can be mentioned. Materials subjected to extreme external conditions, such as ice or rock masses, after exceeding their certain strength parameters, start to fracture, which is manifested by glaciers calving or catastrophic earthquakes.
    Despite the huge scientific progress made in recent decades, many issues in geophysics are still unexplained. The commonly used laboratory and field research methods have their limitations. Therefore, in recent years, a relatively new research technology, the numerical modelling, has raised the interest. The rapidly increasing power of computers allows to create more and more sophisticated models and study phenomena to which traditional research methods do not give access.
    In this work, the analysis of the issue of material fracturing in geophysical applications was undertaken. The Discrete Element Method was used, which is ideally suited for simulating the fracturing process, because it assumes a discrete model of matter (consisting of particles), and also allows to considerate all kinds of issues related to particle rotations and movements. The research consisted of two stages. In the first one, it was attempted to simulate material cracking during three different material tests: uniaxial compression, Brazilian test and uniaxial stretching. The aim was to obtain data that cannot be obtained during laboratory measurements. These include: particles energy – kinetic energies of linear and rotational motions, as well as, potential energies of bonds between particles; dependencies between microscopic parameters of bonds and particles, and macroscopic parameters of the whole material, as well as the influence of particle size on material behaviour under the influence of external loading.
     In the second stage of the research, the transition to the extremely important and current problem of climate change was undertaken. As a result of global warming, glaciers lose more of their mass as a result of the so-called calving, i.e., the phenomena when the block of ice breaks off and falls into the water. Again, the essence of this process is the fracturing, and the DEM method can be very useful for analysing this process. As part of the research, a DEM model of calving glacier was created. Various scenarios were analysed when blocks of different sizes fall from different heights. Inside glacier and water, a network of receivers was created, measuring accelerations during the entire simulation. An attempt was made to determine how two parameters related to calving (the size of the falling down block of ice and the height from which the fall occurs) affect the acceleration of water and glacier particles.
     The obtained data provided information about materials fracturing. As part of the uniaxial compression simulation, it was found that the fracturing materials are characterized by a constant relationship between different potential energies of bonds between particles, regardless of their macroscopic parameters. The highest potential energies occurred during compression and shearing between particles, the smallest in relation to bending and rotations. In the case of the Brazilian test, the linear relationship between the critical stress (at which the fracture occurs) and the inverse of the size of the smallest particles forming the material is probably the most interesting. In the uniaxial stretching test, three classes of material cracking were discovered, depending on the bonds parameters between the particles. Simulations of glacier calving provided information about the propagation of the signals in a material similar to water and ice.

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CONTENTS

Acknowledgements, ...3
Abstract, ...4
Streszczenie, ...5
1. Introduction, ...7
2. Fracturing of materials, ...9
    2.1 Types of deformation, ...9
    2.2 Basics of the fracture mechanics, ...10
3. The discrete element method, ...14
    3.1 Numerical modelling of physical processes, ...14
    3.2 Overview of Discrete Element Method, ...15
    3.3 ESyS-Particle, ...17
4. Discrete element simulations of solid materials under external load, ...25
    4.1 Introduction, ...25
    4.2 Uniaxial compression, ...28
    4.3 Brazilian test, ...42
    4.4 Uniaxial stretching, ...50
    4.5 Conclusions, ....65
5. Discrete element simulations of glacier calving, ...67
    5.1 Introduction, ...67
    5.2 Simulation settings, ...72
    5.3 Simulations results, ...76
    5.4 Conclusions, ...89
6. Summary and conclusions, ...90
Appendix A. Okeanos supercomputer, ...93
Appendix B. Anatomy of the ESyS-Particle and GenGeo scripts, on the example of glacier calving simulation, ...97
    Slurm script for supercomputer, ...98
    Simulation geometry generated with GenGeo, ...98
    Explanation of GenGeo script, ...101
    ESyS-Particle script written in Python, ...106
    Mesh file generating bottom wall for glacier, ...113
    Mesh file generating bottom wall for water, ...113
    Mesh file generating left wall for water, ...113
    Mesh file generating right wall for water, ...114
    Explanation of ESyS-Particle script, ...114
References, ...119