An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics (2011

An adaptive granular representative volume element model with an evolutionary periodic boundary for hierarchical multiscale analysis

The hierarchical multiscale analysis normally utilises a microscopic representative volume element (RVE) model to capture path/history‐dependent macroscopic responses instead of using phenomenological constitutive models. However, for problems involving large deformation, the current RVE model used in geomechanics may lose representative properties due to the progressive distortion of the RVE box, unless a proper reinitialization is applied. This work develops an adaptive RVE model in conjunction with an evolutionary periodic boundary (EPB) algorithm for hierarchical multiscale analysis of granular materials undergoing large deformation based on a recent RVE model proposed for coupling molecular dynamics and the material point method. The proposed adaptive RVE model avoids the reinitialization of the RVE box that even undergoes extremely large shear deformation; meanwhile, it accounts for the deformation history of the RVE model and treats the interaction between boundary particles and other image particles in a more efficient way. Numerical examples with extremely large deformation are used to illustrate the adaptive granular RVE model enhanced by the proposed EPB algorithm. Furthermore, some key features of this new methodology are further discussed for clarification

Parallel Multiscale Contact Dynamics for Rigid Non-spherical Bodies

The simulation of large numbers of rigid bodies of non-analytical shapes or vastly varying sizes which collide with each other is computationally challenging. The fundamental problem is the identification of all contact points between all particles at every time step. In the Discrete Element Method (DEM), this is particularly difficult for particles of arbitrary geometry that exhibit sharp features (e.g. rock granulates). While most codes avoid non-spherical or non-analytical shapes due to the computational complexity, we introduce an iterative-based contact detection method for triangulated geometries. The new method is an improvement over a naive brute force approach which checks all possible geometric constellations of contact and thus exhibits a lot of execution branching. Our iterative approach has limited branching and high floating point operations per processed byte. It thus is suitable for modern Single Instruction Multiple Data (SIMD) CPU hardware. As only the naive brute force approach is robust and always yields a correct solution, we propose a hybrid solution that combines the best of the two worlds to produce fast and robust contacts. In terms of the DEM workflow, we furthermore propose a multilevel tree-based data structure strategy that holds all particles in the domain on multiple scales in grids. Grids reduce the total computational complexity of the simulation. The data structure is combined with the DEM phases to form a single touch tree-based traversal that identifies both contact points between particle pairs and introduces concurrency to the system during particle comparisons in one multiscale grid sweep. Finally, a reluctant adaptivity variant is introduced which enables us to realise an improved time stepping scheme with larger time steps than standard adaptivity while we still minimise the grid administration overhead. Four different parallelisation strategies that exploit multicore architectures are discussed for the triad of methodological ingredients. Each parallelisation scheme exhibits unique behaviour depending on the grid and particle geometry at hand. The fusion of them into a task-based parallelisation workflow yields promising speedups. Our work shows that new computer architecture can push the boundary of DEM computability but this is only possible if the right data structures and algorithms are chosen

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Shear Bands in Granular Materials: Formation and Persistence at Smooth Walls

This thesis contains numerical studies of rheology and shear characteristics of dense assemblies of granular materials. Beside the various experimental and theoretical studies, which deal with these materials, there is also a wide variety of simulation methods, which are used to study the flow behavior, compaction and other characteristics of granular materials. In this work, the contact dynamics method (CD) has been used to study two-dimensional systems of hard, dry disks. The particles interact by Coulomb friction forces parallel to, and volume exclusion forces normal to the contact surfaces, with collisions being fully inelastic. The shear flow is confined between two parallel, smooth, frictional walls, moving with opposite prescribed velocities. Discrete element simulations, carried out in samples with prescribed normal stress reveal that, unlike rough walls made of strands of particles, absolutely smooth but frictional ones can lead to inhomogeneous shear rate and shear strain localization in boundary layers. These are both caused by slip at smooth walls. Three shear regimes associated with different shear velocity intervals are identified and studied in this work. The transitions between these regimes are essentially independent of system size and occur for specific values of shear velocity. Applying constitutive laws deduced both for the bulk material and the boundary regions supplemented by an elementary stability analysis, the occurrence of both transitions, as well as the characteristic transient times are predicted. Investigating the role of the rotational degrees of freedom of round frictional particles and their microscopic contact properties at smooth walls, a critical microscopic friction coefficient at the walls is identified, below which the walls are unable to shear the system. New distinctive features are observed at this critical point. To perform a finite-size-analysis, simulations with very large systems have been frequently necessary during this thesis. To afford large scale simulations with CD, which are more comparable to real granular systems, within a conceivable time, a fully parallel version of CD is presented in this work. For large enough systems, 100% efficiency is achieved for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. Compared to the sequential implementation, no influence of the parallelization on simulation results is found.Scherbänder in granularer Materie: Entstehung und Stabilität an glatten Wänden Diese Arbeit behandelt die numerische Untersuchung der Rheologie und Schereigenschaften granularer Materie aus runden Teilchen. Neben den vielfältigen experimentellen und theoretischen Arbeiten, die sich mit dieser Materie beschäftigen, gibt es unterschiedliche Simulationsmethoden mit denen das Fließverhalten, die Kompaktierung und andere Eigenschaften granularer Materie untersucht werden. In dieser Arbeit wurde die Kontakt-Dynamik-Methode (CD) zur Untersuchung eines zweidimensionalen Systems aus granularer Materie angewandt. Die Teilchen sind starre Scheiben und die einzigen Kontaktkräfte zwischen diesen sind die Coulombsche Reibungskraft parallel und Volumenausschluss-Kräfte senkrecht zur Kontaktfläche. Die Teilchen befinden sich in einem System mit planarer Geometrie, das von oben und unten durch zwei parallele Wände begrenzt ist. Der Druck und die Schergeschwindigkeit sind in jeder Simulation fest vorgegeben und bleiben während der gesamten Simulation konstant. In dieser Arbeit werden, im Gegensatz zu vielen aktuellen Untersuchungen, absolut glatte, mit Reibung versehene Wände zur Scherung benutzt. Diese führen zu sehr inhomogenen Scherraten im System mit deutlicher Scherlokalisierung an den Wänden, die durch den Schlupf an diesen verursacht wird. Drei unterschiedliche Scherregime werden hierbei beobachtet. Jedes dieser Regime gehört zu einem wohldefinierten Intervall der Schergeschwindigkeit, das hauptsächlich von der Systemgröße unabhängig ist. Sowohl die Eigenschaften dieser drei Regime als auch die beiden Übergänge zwischen Ihnen werden detailliert in Kapitel 6 behandelt. In Kapitel 7 werden die konstitutiven Gesetze separat im Bulk und in den Grenzgebieten zu den Wänden hergeleitet. Anhand dieser konstitutiven Gesetze und ergänzender elementarer Stabilitätsanalysen wird das Vorkommen beider Übergänge, sowie charakteristische Transientenzeiten vorausberechnet. In Kapitel 8 wird eine kritische Mindestgröße des Reibungskoeffizienten an glatten Wänden festgestellt, die das Scheren ermöglicht. Bei diesem kritischen Reibungskoeffizienten wird ein besonderes Verhalten des Systems im quasistatischen Regime beobachtet, über welches zuvor noch nicht in der Literatur berichtet worden ist. In Kapitel 9 wird über eine erfolgreiche Parallelisierung der CD berichtet. Diese ermöglicht Simulationen in größeren Systemen, eher vergleichbar zur realen Systemen, die ebenso für die ``Finite-Size-Analyse'' notwendig sind

Multi-scale modeling of complex fluids and deformable fibrous media for liquid composite molding

In the last few years, the interest of the aerial and terrestrial transport industry in the fabrication of textile-reinforced composite materials has sensibly grown. This is basically due to the remarkable properties of these materials, which combine high mechanical strength with reduced weight. The manufacturing techniques that provide better control on the final quality of the components rely on autoclave curing: heat and pressure are applied on vacuum bags to achieve high volume fractions of the reinforcement and low number of defects due to the presence of voids. Nevertheless, autoclave curing implies high costs for the acquisition of the vessel and the process is energy and time consuming. To reduce the production costs, the industry has increased its interest in out-of-autoclave processing technologies, that is, liquid composite molding (LCM) techniques. In its most basic version, the technique consists in the injection of a catalyzed resin into a closed cavity, where a pre-placed fiber stack lies. When the resin has completely permeated the preform, the mold is subject to high temperatures to induce the curing of the resin to obtain the composite. The current challenge for this technology is to achieve the same quality standards for the final component as those achievable with in-autoclave processing. In LCM processes, the final quality of the component depends on several factors, such as: the structure of the textile, the arrangement of the layers, the adaption to the mold, the compaction process, the operating conditions, the geometry of the component, the configuration of the injection points for the resin, the physical and chemical interactions between the resin and the textile. All these factors affect the correct saturation of the reinforcement, and therefore process parameters must be adequately controlled in order to guarantee the required quality standards for the composite. In this sense, mold filling simulation software is a valuable tool for the process optimization; however the permeability of the reinforcement is required as an input parameter. An accurate evaluation of the permeability of the reinforcement however, represents a challenging task. Fibrous preforms for LCM generally present a hierarchical structure: the fibers are bunched in yarns, which in turn are bundled in a fabric. This structure, undergoes complex deformations during the production process: 1) during the compaction in the mold and 2) during the injection of the resin. This issue remarkably complicates an accurate evaluation of the permeability of the reinforcement and may be at the origin of the scatter observed in the experimental measurements. From a modeling point of view, the different length scales to be taken into account (typically ranging between one and three orders of magnitude) hinders a proper simulation of the deformation of the textile. The typical diameter of the fibers ranges indeed in few micrometers, while the characteristic dimension of the yarns is in the order of the millimeter. This issue represents a constraint for standard numerical approaches due to computational limits. In order to account for the effect on the permeability of the deformation of the hierarchical structure of the preform, multi-scale modeling techniques must be adopted. The objective of the thesis is the development of novel theoretical and numerical frameworks to account for the effect on the permeability of the multi-scale deformations that the textile undergoes during the two aforementioned stages of the process. The development focuses on the fiber-yarn level in 2D, where the yarn is always modeled as suspension of fibers by analogy with a complex fluid. The numerical implementations use computational fluid dynamic (CFD) tools. In order to address the problem, the permeability of a textile preform for LCM is first analyzed by experimental means. A standard CFD approach is then adopted for the simulation of a representative elementary volume of the textile; it is shown that, by means of this approach, the experimental permeability cannot be recovered over the full range of porosities. An X-ray computed microtomography of the textile is then performed. The obtained data are used for the virtual reconstruction of the exact geometry of the textile after its use for LCM. The simulations with this latter geometry provide better results; however the uncertainties on permeability still hold, and the permeability is always overestimated. These uncertainties are discussed in detail and motivate the work described hereafter. The first modeling block of the thesis concerns the analysis of the deformation that the textiles undergo during the compaction in the mold. A continuum model is first developed and validated for the squeeze flow of epoxy-based materials, the rheology of which is given by a viscoplastic constitutive law. The model is then applied to the compaction of yarns, where a viscoplastic behavior for the fiber bundle is assumed in the quasi-static regime of compression and by an analogy with flowing granular media. The rheological parameters are obtained from experimental data by a simplified analytical model for the deformation of the yarns under compaction. The commercial CFD code ANSYS Fluent is adopted for the numerical solution. The model yields information about the evolution of the fiber volume fraction during the compaction and is found to correctly recover the experimental force for high compression ratios. The second modeling block of the thesis concerns the analysis of the deformation that the textiles undergo during the injection of the resin. A numerical framework is first developed and validated for the direct numerical simulation of dilute colloidal suspensions of polymeric molecules. The numerical method consists in a coupled finite-volume/lattice-Boltzmann solution: finite volume method for hydrodynamics and lattice Boltzmann method for the sub-grid-scale physics. For computational efficiency, the lattice Boltzmann solution is accelerated on a graphic processing unit (GPGPU) with a tailored implementation and efficiently coupled with the macroscopic solver (ANSYS Fluent). The numerical method is then exploited for the solution of a mesoscopic model for the flow-induced fiber dynamics during the injection. A statistical model for the fiber dynamics is derived, based on analogy of the yarn with a non-Brownian suspension of particles with confining potentials. The fiber topology during the injection is recovered by a topological invariant and yields information about the change in permeability due to the clustering of fibers in steady-state, fully-saturated conditions. The results are presented in the form of phase diagrams, which show that in the deformable case the permeability can be up to one order of magnitude lower than in the rigid case. On the basis of the results obtained, the following main conclusions can be drawn: 1. The model developed for the compaction in the mold showed to be appropriate for a phenomenological analysis of the deformation of the yarns under compression. The model allows to analyze quantitatively the evolution of the fiber volume fraction, which yields useful information for a better understanding of the distribution of the fibers before the injection. 2. The model developed for the fiber dynamics during the injection, allows to analyze their topology induced by the fluid flow. The clustering of fibers significantly reduces the permeability at the fiber level, which could explain the overestimation obtained with simplified numerical approaches. The phase diagrams obtained for the permeability, both at the yarn and fiber level, allow to identify the best operating conditions for the infiltration of the resin. The proposed models have been developed using fluid dynamic techniques, which opens the possibility for a unified framework for the analysis, and ultimately, for a more precise estimation of the permeability. This work aims to represent a first tentative in this direction

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

GPUs Based Material Point Method for Compressible Flows

Particle-In-Cell (PIC) methods such as the Material Point Method (MPM) can be cast in formulations suitable to the requirements of data locality and fine-grained parallelism of modern hardware accelerators such as Graphics Processing Units (GPUs). While continuum mechanics simulations have already shown the capabilities of MPM on a wide range of phenomena, the use of the method in compressible gas dynamics is less frequent. This contribution aims to show the potential of a GPU-based MPM parallel implementation for compressible fluid dynamics, as well as to assess the reliability of this approach in reproducing supersonic gas flows against solid obstacles. The results in the paper represent a stepping stone towards a highly parallel, Multi-GPU, MPM-base solver for M ach > 1 Fluid-Structure Interaction problems