A Discrete Approach to Describe the Kinematics between Snow and a Tire Tread

Doctoral thesis (2014)

The objective of this study is to develop a simulation technique that enables to describe the interactions between snow and a moving surface. The develop- ments of this study are focused on the ... [more ▼]

The objective of this study is to develop a simulation technique that enables to describe the interactions between snow and a moving surface. The develop- ments of this study are focused on the application of the interactions between a tire tread and a snow-covered road. Contrary to a continuum mechanics approach snow is considered to exist of discrete grains which are allowed to bond and collide with each other. There- fore, a discrete approach based on the extended Discrete Element Method is applied to the snow. Micro-mechanical models are developed to describe the deformational behaviour of snow. The micro-mechanical models describe the deformation and growth of the bonds between grains as well as the contact behaviour of snow grains on the grain-scale. Further, the age of a snow sample, the temperature and deformation rate applied are taken into account by the de- veloped models. The deformational behaviour of snow under brittle and ductile loading rates is validated with experimental data of common measurements in the field of snow mechanics. The simulation results successfully recapture the macro- and micro-scale deformation behaviour of snow and enable to identify the primary deformation mechanism in charge at the different loading rates, densities and temperatures. However, this approach allows treating individual snow grains during loading due to a rolling tire and predicting both position and orientation of grains. The micro-mechanical response of each snow grain in contact with the structure of the tire surface generates a global impact that defines the interaction forces be- tween the snow and the tire surface, which simultaneously indicate the strength of traction. In order to predict the elastic deformation of the tire surface the Finite Element Method is employed. A coupling method is developed between the discrete approach to characterise snow and the finite element description of the tire tread. The coupling method compensates quite naturally the shortages of both numerical methods. Further, a fast contact detection algorithm has been developed to spare valuable com- putation time. The coupling approach was successfully tested and validated with a small scale application but also with the large scale application of tire - soil interaction. The large-scale simulation results of tire - soil interactions showed to be accurate in comparison to similar traction measurements. Finally, the interaction of snow with rigid and deformable tread parts has been studied in accordance to friction measurements of the field of tire mechanics. The results show the ability of the simulation technique to describe the targeted interactions and give valuable insight into the underlying mechanisms. [less ▲]

Beschreibung des Transportes von Schwimmkörpern bei Flutwasser über eine Euler-Lagrange Kopplung

in Dresdner Wasserbauliche Mitteilungen (2014)

XDEM - FEM Coupling Simulations of the Interactions between a Tire Tread and Granular Terrain

E-print/Working paper (2014)

This study proposes an efficient combination of the Discrete Element Method (DEM) and the Finite Element Method (FEM) to study the tractive performance of a rubber tire in interaction with granular ... [more ▼]

This study proposes an efficient combination of the Discrete Element Method (DEM) and the Finite Element Method (FEM) to study the tractive performance of a rubber tire in interaction with granular terrain. The presented approach is relevant to all engineering devices interacting with granular matter which causes response forces. Herein, the extended discrete element method (XDEM) is used to describe the dynamics of the granular assembly. On the one hand, the discrete approach accounts for the motion and forces of each grain individually. On the other hand, the finite element method accurately predicts the deformations and stresses acting within the tire tread. Hence, the simulation domain occupied by the tire tread is efficiently described as a continuous entity. The coupling of both methods is based on the interface shared by the two spatially separated domains. Contact forces develop at the interface and propagate into each domain. The coupling method enables to capture both responses simultaneously and allows to sufficiently resolve the different length scales. Each grain in contact with the surface of the tire tread generates a contact force which it reacts on repulsively. The contact forces sum up over the tread surface and cause the tire tread to deform. The coupling method compensates quite naturally the shortages of both numerical methods. It further employs a fast contact detection algorithm to save valuable computation time. The proposed DEM-FEM Coupling technique was employed to study the tractive performance of a rubber tire with lug tread patterns in a soil bed. The contact forces at the tread surface are captured by 3D simulations for a tire slip of 5%. The simulations showed to accurately recapture the gross tractive effort, running resistance and drawbar pull of the tire tread in comparison to related measurements. Further, the traction mechanisms between the tire tread and the granular ground are studied by analysing the motion of the soil grains and the deformation of the tread. [less ▲]

An Efficient 3D FEM - DEM Coupling for Granular Matter Applications

in Coupled MBS-FE Applications: A New Trend in Simulation (2013, November)

The presented approach is relevant to almost all engineering applications that deal with granular matter such as off-road tire performance, transport on conveyor belts or displacement of granular material ... [more ▼]

The presented approach is relevant to almost all engineering applications that deal with granular matter such as off-road tire performance, transport on conveyor belts or displacement of granular material as in mixers or excavation of soil. For all these applications an engineering device is in contact with granular matter which causes responses due to the interaction forces. The proposed Extended Discrete Element Method (XDEM) as a combination of the Discrete Element Method (DEM) and the Finite Element Method (FEM) allows to sufficiently resolve the different domains involved in these engineering applications. Herein the motion of each grain is accounted for individually. Simultaneously, the finite element method accurately predicts the deformations experienced by the engineering device. Thus, the simulation domain occupied by the device is efficiently described as a continuous entity. The coupling of both methods is based on the interface shared by the two spatially separated domains. The interface coupling enables to apply a contact model suited to the particular contact behaviour between the grains and the surface material if the engineering device. In contact, forces develop at the interface and generate an responce in each domain. The coupling method enables to capture both responses simultaneously. Each grain in contact with the device surface generates a contact force to which it reacts repulsively. The contact forces sum up over the surface and cause deformations of device body. It further employs a fast contact detection algorithm to save valuable computation time. This concept is supported by the software tools of the Discrete Particle Method (DPM) and Diffpack. To exemplify the presented method, the tractive performance of different tire treads has been studied on a soil layer of the stony terrian. The simulation results are used to analyse the gross tractive effort, running resistance and drawbar pull of the different tread patterns. [less ▲]

Simulation des Traktionsverhaltens von Reifen auf granularem Untergrund durch eine Kopplung zwischen der Finiten (FEM) und der Diskreten Element Methode (DEM)

in VDI-Berichte "Reifen-Fahrwerk-Fahrbahn" (2013, October)

Kurzfassung Innerhalb dieses Beitrags wird die numerische Simulationsmethode der Extended Discrete Element Methode (XDEM) vorgestellt, mit der die Wechselwirkung zwischen Reifen und steinigem Untergrund ... [more ▼]

Kurzfassung Innerhalb dieses Beitrags wird die numerische Simulationsmethode der Extended Discrete Element Methode (XDEM) vorgestellt, mit der die Wechselwirkung zwischen Reifen und steinigem Untergrund detailliert beschrieben werden kann. Dabei wird der Reifen als ein Kontinuum betrachtet, das mit der Finiten Element Methode (FEM) abgebildet wird. Der grobkörnige Untergrund, wie beispielsweise Sand oder Kies, wird als granulares Medium betrachtet. Dieses kann sehr vorteilhaft mit der Diskreten Element Methode (DEM) behandelt werden, die eine Betrachtung der individuellen Partikel zulässt. Basierend auf den Gesetzen von Newton werden Position und Orientierung aller Partikel berechnet, wobei Kräfte zwischen den Partikeln und dem Reifen berücksichtigt werden. Kräfte zwischen Partikeln und Reifen treten als Randbedingungen in der FEM Struktur des Reifens auf, und führen damit zur Deformation und somit zu Spannungverteilung in der Reifenstrucktur. Eine Integration in der Zeit bestimmt sowohl den Zustand des Untergrunds als auch die Reaktion des Reifens. Dies wird durch eine innovative Kopplung zwischen der Discrete Particle Method (DPM) zur Beschreibung des granularen Mediums und dem Finite Element Löser DiffPACK erreicht und deshalb als Extended Discrete Element Methode bezeichnet wird. Beides sind objekt- orientierte Software-Werkzeuge, die über eine Schnittstelle die notwendigen Daten austauschen, so dass der Anwender sein Augenmerk auf die Problemlösung richten kann als sich mit Datenaustausch und Algorithmen zu befassen. Damit wurde ein vielseitiges und flexibles Werkzeug zur Lösung vielfältiger Probleme wie auch die Bewegung eines Reifens im Schnee geschaffen. Das neuartige Konzept ist sowohl auf Windows als auch auf UNIX basierenden Betriebssystemen verfügbar. Abstract The objective of this contribution is to resolve different length scales in structure analysis by an interface coupling the Discrete Element Method (DEM) with the Finite Element Method (FEM) and therefore, is labelled Extended Discrete Element Methode (XDEM). This approach distinguishes itself from other methods in so far that no overlapping domains between Finite and Discrete Elements exist. Both domains are separated in physical space and numerical simulation domain. The proposed approach is relevant to almost all engineering applications that deal with granular matter such as storage in hoppers, transport on conveyor belts or displacement of granular material as in mixers or excavation of soil. For these applications an engineering device such as mixer blades or cutting tools are in contact with granular matter. Contacts with individual particles generate contact forces that act on both the engineering device and the granular material. The latter experiences a displacement of individual particles whereby the engineering structure responds with deformation and stresses. In order to predict and optimize both the behaviour and motion of granular material and the structures in contact, numerical simulation tools are increasingly employed [1]. Simulations are popular especially because experiments which are often expensive, time- consuming and sometimes even dangerous [2]. The continuous increase in computing power is now enabling researchers to implement numerical methods that do not focus on the granular assembly as an entity, but rather deduce its global characteristics from observing the individual behaviour of each grain. An interaction between granular media and a structure relies on a transfer of forces between them. Granular media consists of an ensemble of particles of which a number of particles may be in contact with a surface e.g. walls as surfaces of solid structures. The contact is resolved similar to inter-particle contacts by a representative overlap. It defines the position of impact as well as the force acting on the particle at this position. The same force, however, into the opposite direction defines a mechanical load for the structure. In order to determine the effect of forces on the solid structure, it is discretised by finite elements. The impact of the force is transferred to the nodes of the respective surface element and appears as a load for the finite element system. Hence, integrating particle dynamics and the response of the solid structure due to particle impacts advances both new position of particles and corresponding deformation and stress of the solid structure in time. Developing flexible software which is capable of performing simulation in different applications will enable the engineers to focus entirely on their specific problem and hence save them valuable time. This concept is supported by the software tools of the Discrete Particle Method (DPM) and Diffpack. Hence, the solid structure is analysed by the Finite Element Method under load due to the impact of individual particles that changes both in time and space. For this purpose traditional formulations of the Finite Element Method are employed that are available by the commercial multi-physics software package Diffpack. It represents object-oriented hierarchy of classes that provide an excellent interface to introduce external loads from particle impact onto the finite element structure. Diffpack is an object-oriented development environment, which comes as a rich set of C++ classes, for the numerical modelling and solution of arbitrary differential equations. User applications cover a wider range of engineering areas and span from simple educational applications to major product development projects. The behaviour of granular material is represented by the advanced software package of the Discrete Particle Method (DPM), which is based on the Discrete Element Method. It is designed to relieve users from underlying mathematics and software design and allows them to focus on physics and their applications. The software uses object oriented techniques that support objects representing three-dimensional particles of various shapes such as cylinders, discs or tetrahedrons for example, size and material properties. This makes it a highly versatile tool dealing with a large variety of different applications of granular matter arising in the automotive industry, such as road tire interaction. Various force models for the inter- particle and particle-wall contacts are also available. A minimal user interface easily allows extending the software further by adding user-defined impact models or material properties to an already available selection of materials and properties. Thus, the user is relieved of the underlying mathematics or software design, and therefore, is able to direct his focus entirely onto the application. The Discrete Particle Method is written in C++ programming language and works both in Linux and Windows environments. [less ▲]

Discrete Modeling of Inter-Granular Bonds between Snow Grains

Presentation (2013, April 23)

Discrete Element Modeling of Inter-Granular Bonds between Snow Grains

in PARTEC - International Congress on Particle Technology (2013, April)

The mechanical behaviour of snow was long studied to help predict natural hazards, like avalanches. For those predictions the behaviour of snow deforming at low strain rates is of importance. On the other ... [more ▼]

The mechanical behaviour of snow was long studied to help predict natural hazards, like avalanches. For those predictions the behaviour of snow deforming at low strain rates is of importance. On the other hand, a large group of industrial applications concerning trafficability and transportation safety also benefit from the understanding of snow physics. These applications requiring an understanding of the high strain rate behaviour of snow. The material behaviour of snow is based on its micro-structure. The micro-structure consists of ice grains connected by ice bonds building up an open-foam like structure. The macroscopic response of a snow pack to loading is determined by the deformation and failure of its bonds and the inter-granular friction whiles rearrangement of the grains. The work reported here proposes an inter-granular snow model developed and deployed using a discrete element technique. The goal is to understand the material behaviour of dry snow at high strain rates, from 0.01s^-1 up to 100s^-1. The developed algorithm predicts the displacement of the individual grains due to inter-granular contact and bond forces. The micro-structure of a snow pack is represented by generating an ensemble of explicit geometrical shapes describing the individual ice grains and bonds. The distributions of grain size and position are generated by gravitational deposition and by applying a fractal algorithm. Snow structures of densities from 200 kg/m^3 up to 600 kg/m^3 are generated. The developed inter-granular bond models assume a cylindrical neck between adjoining ice grains. Material properties and constitutive models of the hexagonal single- and poly-crystal Ih ice are used to describe the material behaviour of each individual bond. Simulations of tensile and compression tests have been conducted using samples of 10^3 up to 10^5 grains. Here, results of different parametric studies are reported. Assessed are the dependences of the macroscopic snow behaviour on microstructural properties and mechanical properties on grain-scale. These results are compared to experimental measurements and corresponding finite element simulations. The calculation results enable to identify primary deformation mechanism at the given strain rates. [less ▲]

Unified Design for Parallel Execution of Coupled Simulations using the Discrete Particle Method

in Proceedings of the Third International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering (2013)

This paper presents the enhanced design of the Discrete Particle Method (DPM), a simulation tool which provides high quality and fast simulations to solve a broad range industrial processes involving ... [more ▼]

This paper presents the enhanced design of the Discrete Particle Method (DPM), a simulation tool which provides high quality and fast simulations to solve a broad range industrial processes involving granular materials. It enables to resolve mechanical and thermodynamics problems through different simulation modules (motions, chemical conversion). This new design allows to transparently couple the simulation modules in parallel execution. It relies on a unified interface and timebase of the simulation modules and a flexible decomposition in cells of the simulation space. Experimental results study the behavior of the Orthogonal Recursive Bisection (ORB) partitioning algorithm. A good scalability is achieved as the parallel execution on a distributed platform provides a 17-times speedup using 64 processes. [less ▲]

Application of the Extended Discrete Element Method (XDEM) in Computer-Aided Process Engineering

Scientific Conference (2013)

Resolution of Different Length Scales by an Efficient Combination of the Finite Element Method and the Discrete Element Method

in Topping, B.H.V. (Ed.) Proceedings of the Eleventh International Conference on Computational Structures Technology (2012)

The combination of the discrete element method and the finite element method is shown to be a suitable technique to resolve different length scales within almost all engineering problems dealing with ... [more ▼]

The combination of the discrete element method and the finite element method is shown to be a suitable technique to resolve different length scales within almost all engineering problems dealing with granular assemblies, which are also in contact with a deformable body of an engineering device. The extended discrete element method (XDEM) describes the motion and forces of each individual grain within the granular assembly. Hence, the XDEM as a discrete approach accounts for each grain individually rather than describing the granular assembly as a continuous entity. On the other hand, the finite element method predicts accurately the deformations and the responding stress of the engineering device. Thus, this part of the simulation domain is efficiently approximated by a continuum approach. The two domains share an interface which enables the employment of contact models fitting the particular behaviour of the contact problem between each grain and the surface of the device. At the interface impact forces develop which then propagate into the different length scales. Thus, the combined discrete and continuum approach now enables the tracking of both responses by the appropriate resolution. Each grain of the assembly in contact with the solid body generates a contact force and experiences a repulsive force which it reacts on individually. The contact forces sum up on the interface and cause the solid body to deform. This results in stresses which again the assembly recognise as a repulsive response. The coupling method utilises quite naturally the advantages of both the continuum and the discrete approach and thereby compensating the shortages of each method. The coupling method not only resolves the different scales it further contributes to the efficiency of the computations. The method employs a fast contact detection algorithm, which spares valuable computation time by a fast separation of the important pairs of particles and surface element for the contact force prediction. The discrete element method - finite element method (DEM-FEM) simulation technique is introduced with two engineering application of entirely different fields. However, both applications inherit similar physical problems of different length scales. In both cases individual particles are in contact with a widely used engineering device that is in contact with the granular material. Thus, the DEM-FEM coupling is shown to resolve the different scale responses within each domain separately. [less ▲]