Simulation of the Tractive Performance of Tire Treads on Granular Terrain by Means of Finite and Discrete Element Coupling

peer reviewedKurzfassung 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.XDE