Mechanics provides the link between mathematics and practical engineering app- cations. It is one of the oldest sciences, and many famous scientists have left and will leave their mark in this fascinating ?eld of research. Perhaps one of the most prominentscientists in mechanics was Sir Isaac Newton, who with his “laws of - tion” initiated the description of mechanical systems by differential equations. And still today, more than 300 years after Newton, this mathematical concept is more actual than ever. The rising computer power and the development of numerical solvers for diff- ential equations allowed engineersall over the world to predict the behavior of their physical systems fast and easy in an numerical way. And the trend to computational simulation methods is still further increasing, not only in mechanics, but practically in all branches of science. Numerical simulation will probablynot solve the world’s engineering problems, but it will help for a better understanding of the mechanisms of our models.

The papers in this volume present rules for mechanical models in a general systematic way, always in combination with small and large examples, many from industry, illustrating the most important features of modeling. The best way to reach a good solution is discussed. The papers address researchers and engineers from academia and from industry, doctoral students and postdocs, working in the fields of mechanical, civil and electrical engineering as well as in fields like applied physics or applied mathematics.

Nearly all solids are compised of grains. However most studies treat materials as a continious solid. The book applies analysis used on loose granular materials to dense grainular materials. This title’s main focus is devoted to static or dynamic loadings applied to dense materials, although rapid flows and widely dispersed media are also mentioned briefly. Three essential areas are covered: Local variable analysis: Contact forces, displacements and rotations, orientation of contacting particles and fabric tensors are all examples of local variables. Their statistical distributions, such as spatial distribution and possible localization, are analyzed, taking into account experimental results or numerical simulations. Change of scales procedures: Also known as “homogenization techniques”, these procedures make it possible to construct continuum laws to be used in a continuum mechanics approach or performing smaller scale analyses. Numerical modeling: Several methods designed to calculate approximate solutions of dynamical equations together with unilateral contact and frictional laws are presented, including molecular dynamics, the distinct element method and non-smooth contact dynamics. Numerical examples are given and the quality of numerical approximations is discussed.

By having its origin in analytical and continuum mechanics, as well as in computer science and applied mathematics, multibody dynamics provides a basis for analysis and virtual prototyping of innovative applications in many fields of contemporary engineering. With the utilization of computational models and algorithms that classically belonged to different fields of applied science, multibody dynamics delivers reliable simulation platforms for diverse highly-developed industrial products such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, smart structures, biomechanical applications and nano-technologies. The chapters of this volume are based on the revised and extended versions of the selected scientific papers from amongst 255 original contributions that have been accepted to be presented within the program of the distinguished international ECCOMAS conference. It reflects state-of-the-art in the advances of multibody dynamics, providing excellent insight in the recent scientific developments in this prominent field of computational mechanics and contemporary engineering.

Multibody dynamics started with the ideas of Jacob and Daniel Bernoul li and later on with d'Alembert's principle. In establishing a solution for the problem of the center of oscillation for a two-mass-pendulum Jacob Ber noulli spoke about balancing the profit-and-Ioss account with respect to the motion of the two masses. Daniel Bernoulli extended these ideas to a chain pendulum and called forces not contributing to the motion "lost forces", thus being already very close to d'Alembert's principle. D'Alembert considered a "system of bodies, which are interconnected in some arbitrary way. " He suggested separating the motion into two parts, one moving, the other being at rest. In modern terms, or at least in terms being applied in engineering mechanics, this means that the forces acting on a system of bodies are split into active and passive forces. Active forces generate motion, passive forces do not; they are a result of constraints. This interpretation of d'Alembert's principle is due to Lagrange and up to now has been the basis of multi body dynamics (D' Alembert, Traite de Dynamique, 1743; Lagrange, Mecanique Analytique, 1811). Thus, multibody dynamics started in France. During the nineteenth century there were few activities in the multi body field even though industry offered plenty of possible applications and famous re presentatives of mechanics were aware of the problems related to multibody dynamics. Poisson in his "Traite de Mecanique" (Paris 1833) gave an im pressive description of these problems, including impacts and friction.