Abstract

The nature of fracture phenomena strongly limits engineering solutions to cases, a little bit beyond the regime of linear fracture mechanics. Nevertheless, fracture in brittle disordered materials, dominated by simultaneously growing and dynamically competing cracks is rather ubiquitous [1,2]. From the dynamics of single crack propagation, through the statistics of crack ensembles to the rapid fragmentation of materials, Discrete Element Methods (DEM) helped to enrich the understanding over the past decades. Models of seemingly simple rigid body dynamics with simple contact and cohesive interactions proved to be surprisingly successful for representing dynamic fracture and fragmentation phenomena, emerging from the complex systems dynamics. Today, applications of DEM make a substantial contribution for explaining the mechanical response and breaking phenomena of heterogeneous materials under various types of loading conditions beyond single crack growth [3,4]. Various particle geometries, material response, ways to treat repulsive and cohesive behaviour and of course loss of cohesion, lead to a flexible tool-set of approaches. Strategies for higher order agglomeration, coupling with other simulation techniques for continuum domains or other particle based methods extended the reach of DEM significantly. Ranging from the slowly changing, sub-critical loads to the highly energetic fragmentation, DEM proved to be an indispensable tool for such investigations. In this talk a brief review on the motivations and basic ideas behind the DEM approach to cohesive particulate matter is given. Different ways of introducing cohesion and its loss are discussed in light of fracture in frictional and non-frictional materials beyond the Griffith length of stable crack growth. Among the widespread applications of DEM for the fracture of heterogeneous materials, focus is given on impact comminution of aggregated matter [4]. By providing an improved understanding of comminution processes e.g. in impact mills, one of the energetically least efficient processes on the global scale could be improved – by the use of particle mechanics. It is shown, that a critical impact velocity vcr exists, separating the fracture from the fragmentation regime. Below the critical velocity, fragmentation by repeated impacts can be described by a Basquin type low cycle fatigue law, above vcr Power-law fragment size distributions emerge. This behaviour is robust even for multi-phase materials. In a comparative study it is finally demonstrated, how the milling efficiency can be increased for the same system only by manipulating the shock wave configurations via vibrating targets.

Abstract

This talk addresses the application of SPH to problems of hydro-fracturing and fluid-structure interaction. Simulating a hydraulic-fracture propagating in a rock with in-situ joint sets is particularly challenging. Traditional continuum modeling techniques have the advantage of using classical non- linear material models, however they often fail to accurately capture the complexity of the geometry and path of multiple intersecting fractures. In particular, mesh dependence of the fracture path, closing of an opened fracture and shear, present difficulties using these techniques. The use of the smoothed particle hydrodynamics (SPH) method for these problems is relatively recent. Mesh free methods, such as SPH, have the potential to overcome the previously mentioned difficulties of mesh based methods. Simulation of the initiation and propagation of pressure-driven fractures in brittle rocks is presented in this study. By exploiting techniques commonly used in traditional continuum methods, we have developed an elasto-plastic SPH model, which is based on the Drucker-Prager yield criterion, and the Grady-Kipp damage model. The model is validated against Brazil test data. Results are also presented the Brazil test, uni-axial compressive fracture as well as initial results for intersection of dynamic fractures with intersecting joints.

Abstract

Roughly speaking, granular media exhibit three basic scales: the specimen scale, the contact scale, and an intermediate scale made up of a set of adjoining particles. In this lecture, we will discuss this latter scale, in a two dimensional context. More specifically, the granular assembly can be regarded as a two phases medium. Grain column like patterns (force chains) develop within the medium, participating actively to its mechanical strength. These columns are surrounded by grain loops, made up of 3, 4, 5, or 6 grains (larger grain loops are much less frequent). According to the number of constituting grains, the mechanical properties of grain loops are very different. In particular, 6 grains loops are prone to deform, contributing locally to a change in the void ratio. On the contrary, 3 grains loops deform just a little, but resist quite well to a deviatoric stress. According to the initial porosity of the assembly, and depending upon the loading path considered, the nature of grain loops surrounding force chains is versatile, with continuous transition mainly from 3 grains loops to 6 grains loops (or vice versa). This is a new route to investigate from a microstructural point of view why a granular assembly may be destabilized, leading to a localized or diffuse failure pattern. In addition, these ingredients are shown to give rise to a microstructural interpretation of the socalled critical state, according to the failure mode taking place.

Abstract

Numerical simulations of granular flows based on the Distinct Element Method (DEM) commonly use spherical particles for ease of contact mechanics calculations and for having fast contact searching algorithms. However, for irregularly shaped particles, rotation is not only affected by friction but also by mechanical interlocking (Cleary, 2010). Only tangential forces lead to the rotation of spherical particles, whereas for irregularly shaped particles, rotation can be as a result of both normal and tangential contact forces (Favier et al., 2001). Mechanical interlocking of irrregularly shaped particles can be simulated in DEM by (i) limiting the rolling friction of spherical particles (Morgan, 2004), (ii) using overlapping spheres (Favier et al., 2001), (iii) using polyhydra (Potapov and Campbell, 1997). The first two method have been critically evaluated for the flow of corn seeds and spray-dried powders. A comparison is made of the estimated solid fraction and the tangential and radial velocity distributions of the particles from DEM and those measured experimentally. The shapes of the corn seeds and spray-dried powders have been captured using X-Ray micro tomography, and ASG2013 software has been used to generate the coordinates of the overlapping spheres. It is shown that the approximation of particle shape is only critical for dense shearing flows. The use of polyhydra enables particle fracture to be simulated more realistically, but necessitates implementation of fracture mechanics to be predictive. In this paper the results of our evaluations are reported.

Abstract

Reproducing Kernel Particle Method (RKPM) has been applied to many large deformation problems. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties, but requires appropriate kernel support coverage of neighboring particles to ensure kernel stability. This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment-impact processes commonly exist in many extreme events. A new reproducing kernel formulation with “quasi-linear” reproducing conditions is introduced. In this approach, the first order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first completeness, nearly 2 nd order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this new quasi-linear RKPM formulation is demonstrated by modelling fragment-impact and penetration extreme events.

Abstract

Spatial coarse-graining techniques are powerful methods to overcome the computational limits of molecular dynamics. In order to extend atomistic simulations of crystalline materials to the micronscale and beyond, the quasicontinuum (QC) approximation reduces large crystalline atomistic ensembles to a significantly smaller number of representative atoms with suitable interpolation schemes to infer the motion of all particles. In contrast to most other concurrent multiscale techniques, this allows for the simulation of large systems solely based on interatomic potentials and thus without the need for (oftentimes phenomenological) continuum constitutive models. This promises superior accuracy for predictive simulations at the meso- and macroscales. Here, we will discuss one such coarse-graining scheme, viz. a fully-nonlocal energy-based QC technique which excels by minimal approximation errors and vanishing force artefacts (a common problem in concurrent scale-coupling methods). Our model is equipped with automatic adaptation techniques to effectively tie atomistic resolution to regions of interest while efficiently coarse-graining the remaining solid. We review both mesh-based and meshless formulations. The former adopts methods from finite elements (using an affine interpolation on a Delaunay triangulation), whereas the latter is based on local maximum-entropy interpolation schemes. In both cases, the result is a computational toolbox for coarse-grained atomistic simulations, whose computational challenges are quite similar to those of molecular dynamics. Finite temperature extensions as well as coarse-graining in time can be incorporated in the presented framework. We will review the underlying theory and give an overview of the state of the art, followed by a suite of numerical examples demonstrating the benefits and limitations of the nonlocal energy-based QC method. Examples range from nanoindentation and material failure to defect interactions and nanoscale mechanical size effects. 

Abstract

When we think of materials “by design”, we are envisioning a process that gets us from a design target, namely certain desired overall materials properties, to requirements for the constituent components. This is challenging because it requires us to invert the typical modeling approach in physics and material science, which starts from microscale components in order to predict macroscale behavior. How can one tackle this inverse problem for granular materials that are inherently disordered and far from equilibrium, and for which the target is not a thermodynamically favored ‘ground state’? I will discuss how concepts from artificial evolution make it possible to find with high efficiency particle-scale parameters best adapted to given target properties. In particular, I will show how one can find particle shapes that are optimized for specific desired outcomes, such as low aggregate porosity or high stiffness under compression. This approach uses large numbers of parallel molecular dynamics simulations together with optimization techniques based on artificial evolution. Optimized shapes are then validated by physical measurements that test large aggregates of 3D-printed versions of the particles. This approach has general applicability and opens up new opportunities for granular materials design as well as discovery.

Abstract

The main idea of the Particle Finite Element Method in both versions: with moving mesh or with fixed mesh, are to have a set of particles that move in a Lagrangian frame convecting all the physical and mathematical variables (for instance, the density, the viscosity or the conductivity, but also the velocity, the pressure or/and the temperature). These physical and mathematical values are projected at the end of each time-step on a moving mesh or on a fixed mesh. The second possibility has been named PFEM-Second Generation or simply PFEM-2. One of the main drawback of the time integrations using Eulerian formulations are the restricted time-step size that is necessary to use due to the lack of accuracy of the convective terms. Both time integrations, explicit or implicit are, in most cases, limited to small CFL numbers. The cases in which the problem to be solved include free-surfaces or moving internal interfaces, like multi-fluids of fluid-structure interactions this time-step limitation is even worse. The objective of this presentation is to make an overview of recent examples solved using PFEM-2 and to demonstrate why this method based on particles that move in a Lagrangian frame projecting the results on a fixed mesh is faster than a classical Eulerian Finite Element Method. The authors claim that nowadays, the best way to improve the efficiency of the majority of the CFD problems is the use of a particle-based method like PFEM-2.

Abstract

In many situations ranging from geophysics to chemical engineering, turbulent drag moves particle clouds. I will present and compare various numerical approaches. On the one hand the mean velocity profile above ground is systematically constructed subtracting momentum loss; on the other hand the intrinsic spatio-temporal fluctuations are imposed from empirical distributions on point-like fluid particles. Various applications are explored. One is saltation, i.e. Aeolian transport of sand, discovering that the onset of particles flux exhibits a first order transition with hysteresis. The inclusion of mid-air grain collisions is found to increase the flux considerably due to the formation of a floating “soft bed” that screens energy-rich grains (saltons) from hitting the ground. Solving the fluid motion with the Lattice Boltzmann Method the effect of particle-particle collisions on preferential concentration is also investigated. Another application is powder mixing in a channel due to turbulent fluctuations. Following A.M. Reynolds (2003), a stochastic differential equation is solved for the motion of fluid particles that are attached to real particles. The dependence of the observed diffusive behaviour on Reynolds and Stokes number is monitored. Finally, also spatial correlations in the velocity field are imposed by a Heisenberg-type Hamiltonian. 

Abstract

Particles are used to simulate phenomena spanning twenty orders of magnitude, from the folding of proteins to the formation of our universe. I distinguish particle methods for the discretisation of continuum conservation laws and particle models of complex systems. In this talk, I will emphasize the need for controlling the accuracy of continuum particle methods and demonstrate how particle remeshing allows for a seamless integration of grids and particles. I will also discuss the need for data driven, uncertainty quantification of particle models. I will provide examples from the capabilities and challenges for particle methods through flow simulations in massively parallel computing architectures, ranging from fish swimming and cavitation to cell sorting in microfluidic channels.

Abstract

A first-principles model for the simulation of pedestrian flows and crowd dynamics capable of computing the movement of millions of pedestrians in real time has been developed. The pedestrians are treated as `intelligent' particles subjected to a series of forces, such as: will forces (the desire to reach a place at a certain time), pedestrian collision avoidance forces, obstacle/wall avoidance forces; pedestrian contact forces, and obstacle/wall contact forces. In order to allow for general geometries a so-called background triangulation is used to carry all geographic information. At any given time the location of any given pedestrian is updated on this mesh. The code has been ported to shared and distributed memory parallel machines. The results obtained show that the stated aim of computing the movement of millions pedestrians in real time has been achieved. This is an important milestone, as it enables faster-than-real-time simulations of large crowds (stadiums, airports, train and bus stations, concerts) as well as evacuation simulations for whole cities. This may enable the use of validated, micro-model-based pedestrian simulation for design, operation and training within the context of large crowds. 

Abstract

The numerical simulation of complex dynamical systems is an important way for studying phenomena that are difficult to investigate experimentally. We could then speak about numerical granular media as a specific scientific field similarly to the numerical fluids twenty years ago. The numerical investigation progresses so quickly with respect with the experiments that the comparison between simulations and experiments is often rather coarse. Moreover the numerical tools may be used beyond their limits of validity. We propose to analyse the contributions, but also the limits of the NonSmooth Contact Dynamics (NSCD), developed by J.J. Moreau, applied to the granular systems starting from some experiences and from the numerous remarks given by Moreau himself in his papers. The NSCD method has been developed for dealing with large collections of packed bodies and then for simulating the behaviour of granular materials. The Nonlinear Gauss-Seidel (NLGS) algorithm is the generic solver applied to the NSCD formulation. This combination allows simulation of the behaviour of a collection of (especially rigid) bodies involving different and mixed regimes: static, slow dynamics (solid), fast dynamics (fluid). Some examples illustrate the ability of the Moreau’s approach for dealing with a large range of granular problems. For illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law. The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework?