Elasticity and Wave Propagation in Granular Materials

Particle simulations are able to model behavior of granular materials, but are very slow when large-scale phenomena and industrial applications of granular materials are considered. Even with the most advanced computational techniques, it is not possible to simulate realistic numbers of particles in large systems with complex geometries. Thus, continuum models are more desirable, where macroscopic field variables can be obtained from a micro-macro averaging procedure. However, aspects of microscopic scale are neglected in classical continuum theories (restructuring, geometric non linearity due to discreteness, explicit control over particle properties). The focus of this work is the investigation of elastic and dissipative behavior of isotropic, dense assemblies. In particular, the attention is devoted on the effect of microscopic parameters (e.g. stiffness, friction, cohesion) on the macroscopic response (e.g. elastic moduli, attenuation). The research methodology combines experiments, numerical simulations, theory. One goal is to extract the macroscopic material properties from the microscopic interactions among the individual constituent particles; for simple enough systems this can often be done using techniques from mechanics and statistical physics. While these simplified models can not capture all aspects of technically relevant realistic grains the fundamental physical phase transitions can be studied with these model systems. Complex mixtures with more than one particle species can exhibit enhanced mechanical properties, better than each of the ingredients. The interplay of soft with stiff particles is one reason for this, but requires a more accurate formation of the interaction of deformable spheres. A new multi-contact approach is pro- posed which shows a better agreement between experiments and simulations in comparison to the conventional pair interactions. The study of wave propagation in granular materials allows inferring many fundamental properties of particulate systems such as effective elastic and dissipative mechanisms as well as their dispersive interplay. Measurements of both phase velocities and attenuation provide complementary information about intrinsic material properties. Soft-stiff mixtures, with the same particle size, tested in the geomechanical laboratory, using a triaxial cell equipped with wave transducers, display a discontinuous dependence of wave speed with composition. The diffusive characteristic of energy propagation (scattering) and its frequency dependence (attenuation) are past into a reduced order model, a master equation devised and utilized for analytically predicting the transfer of energy across a few different wavenumber ranges, in a one-dimensional chain

Sound characteristics of disordered granular disks: Effects of contact damping

We investigate numerically the sound properties of disordered dense granular packings in two dimensions. Employing linear equations of motion and excluding contact changes from our simulations, we demonstrate time evolution of sinusoidal standing waves of granular disks. We varied the strength of normal and tangential viscous forces between the disks in contact to explore the dependence of sound characteristics such as dispersion relations, attenuation coefficients, and sound speeds on the contact damping. For small wave numbers, the dispersion relations and sound speeds of acoustic modes are quite insensitive to the damping. However, a small dip in the phase speed of the transverse mode decreases as the viscous force in normal direction increases. In addition, the dispersion relation of the rotational mode differs qualitatively from the theoretical prediction for granular crystals. Therefore, disordered configurations with energy dissipation play a prominent role in sound properties of granular materials. Furthermore, we report how attenuation coefficients depend on the contact damping and quantify how they differ from the prediction of lattice theory. These improved relations, based on our numerical results, can in future be compared to advanced theories and experiments

Elastic waves in particulate glass-rubber mixture: Experimental and numerical investigations/studies

In this paper we study by wave propagation the elastic response of granular mixtures made of soft and stiff particles subjected under hydrostatic pressure/stress. This allows inferring fundamental properties of granular materials such as elastic moduli and dissipation mechanisms. We compare physical experiments in a triaxial cell equipped with piezoelectric wave transducers and Discrete Element Method simulations (DEM). In the experimental part, dense, static packings made of monodisperse glass and rubber beads are prepared at various levels of hydrostatic stress and species fractions. Small perturbations are generated on one side and the time of flight through the glass-rubber mixtures are measured to quantify the effect of the mixture composition on the elastic moduli. Interestingly, the experiments show that the behavior is non-linear and nonmonotonic with increasing percentage of rubber particles. Wave velocity and modulus remain fairly constant when increasing the fraction of rubber to 30%, while they experience a sudden drop between 30% and 60%, to become again constant between 60% to 100%. DEM simulations offer deeper insights into the micromechanics in and at the transition between the glass- and rubber-dominated regimes. The simplest analysis with Hertzian spherical particles of different stiffness is performed as a preliminary step. The behavior of mixtures with high glass content is very well captured by the simulations, without need of any additional calibration, whereas the complex interaction between rubber and glass leave open questions for further study

Influence of dry cohesion on the micro- and macro-mechanical properties of dense polydisperse powders & grains

Understanding how cohesive granular materials behave is of interest for many industrial applications, such as pharmaceutical or food and civil engineering. Models of the behaviour of granular materials on the microscopic scale can be used to obtain macroscopic continuum relations by a micro-macro transition approach. The Discrete Element Method (DEM) is used to inspect the influence of cohesion on the micro and macro behaviour of granular assemblies by using an elasto-plastic cohesive contact model. Interestingly, we observe that frictional samples prepared with different cohesion values show a significant difference in pressure and coordination number in the jammed regime; the differences become more pronounced when packings are closer to the jamming density, i.e. the lowest density where the system is mechanically stable. Furthermore, we observe that cohesion has an influence on the jamming density for frictional samples, but there is no influence on the jamming density for frictionless samples

Raw data of wave propagation experiments using glass-rubber mixtures

We studied by wave propagation the elastic response of granular mixtures made of soft and stiff particles subjected under hydrostatic pressure/stress. This allows inferring fundamental properties of granular materials such as elastic moduli and dissipation mechanisms

Raw data of wave propagation experiments using glass-rubber mixtures

We studied by wave propagation the elastic response of granular mixtures made of soft and stiff particles subjected under hydrostatic pressure/stress. This allows inferring fundamental properties of granular materials such as elastic moduli and dissipation mechanisms