Many physical systems require the description of mechanical interaction across interfaces if they are to be successfully analyzed. Examples in the engineered world range from the design of prosthetics in biomedical engi neering (e. g. , hip replacements); to characterization of the response and durability of head/disk interfaces in computer magnetic storage devices; to development of pneumatic tires with better handling characteristics and increased longevity in automotive engineering; to description of the adhe sion and/or relative slip between concrete and reinforcing steel in structural engineering. Such mechanical interactions, often called contact/impact in teractions, usually necessitate at minimum the determination of areas over which compressive pressures must act to prevent interpenetration of the mechanical entities involved. Depending on the application, frictional be havior, transient interaction of interfaces with their surroundings (e. g. , in termittent stick/slip), thermo-mechanical coupling, interaction with an in tervening lubricant and/or fluid layer, and damage of the interface (i. e. , wear) may also be featured. When taken together (or even separately!), these features have the effect of making the equations of mechanical evolu tion not only highly nonlinear, but highly nonsmooth as well. While many modern engineering simulation packages possess impressive capabilities in the general area of nonlinear mechanics, it can be contended that methodologies typically utilized for contact interactions are relatively immature in comparison to other components of a nonlinear finite element package, such as large deformation kinematics, inelastic material modeling, nonlinear equation solving, or linear solver technology.

This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields. These include civil engineering, car design, aeronautics, metal forming, or biomechanics. For this second edition, illustrative simplified examples and new discretisation schemes and adaptive procedures for coupled problems are added. This book is at the cutting edge of an area of significant and growing interest in computational mechanics.

The subject of Computational Contact Mechanics has many facets. Its main impact lies in the transfer of knowledge form theoretical research to applied sciences, and from there to industry. The application fields are literally countless, ranging from classical engineering to biomechanics and nano-sciences. The remarkable increase of computer power in recent years has been instrumental in enabling the development of simulation-based analysis in current design activity. This still involves tremendous effort in research, which focuses on, for example, multi-field and multi-scale problems, algorithmic robustness, and geometrical accuracy. Moreover, several aspects of Contact Mechanics, Debonding and Fracture Mechanics, have been combined to offer new enhanced possibilities to the computer simulation of complex phenomena. With these contributions of prominent scientists, this book offers a wide overview on the ongoing research at the highest level in the field.

Introduction to Computational Contact Mechanics: A GeometricalApproach covers the fundamentals of computational contactmechanics and focuses on its practical implementation. Part one ofthis textbook focuses on the underlying theory and covers essentialinformation about differential geometry and mathematical methodswhich are necessary to build the computational algorithmindependently from other courses in mechanics. The geometricallyexact theory for the computational contact mechanics is describedin step-by-step manner, using examples of strict derivation from amathematical point of view. The final goal of the theory is toconstruct in the independent approximation form /so-calledcovariant form, including application to high-order andisogeometric finite elements. The second part of a book is a practical guide for programming ofcontact elements and is written in such a way that makes it easyfor a programmer to implement using any programming language. Allprogramming examples are accompanied by a set of verificationexamples allowing the user to learn the research verificationtechnique, essential for the computational contact analysis. Key features: Covers the fundamentals of computational contact mechanics Covers practical programming, verification and analysis ofcontact problems Presents the geometrically exact theory for computationalcontact mechanics Describes algorithms used in well-known finite element softwarepackages Describes modeling of forces as an inverse contactalgorithm Includes practical exercises Contains unique verification examples such as the generalizedEuler formula for a rope on a surface, and the impact problem andverification of thå percussion center Accompanied by a website hosting software Introduction to Computational Contact Mechanics: A GeometricalApproach is an ideal textbook for graduates and seniorundergraduates, and is also a useful reference for researchers andpractitioners working in computational mechanics.

Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.

This book is intended to help the reader understand impact phenomena as a focused application of diverse topics such as rigid body dynamics, structural dynamics, contact and continuum mechanics, shock and vibration, wave propagation and material modelling. It emphasizes the need for a proper assessment of sophisticated experimental/computational tools promoted widely in contemporary design. A unique feature of the book is its presentation of several examples and exercises to aid further understanding of the physics and mathematics of impact process from first principles, in a way that is simple to follow.

This carefully edited book offers a state-of-the-art overview on formulation, mathematical analysis and numerical solution procedures of contact problems. The contributions collected in this volume summarize the lectures presented by leading scientists in the area of contact mechanics, during the 4th Contact Mechanics International Symposium (CMIS) held in Hannover, Germany, 2005.

This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation. The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and contains the associated numerical analysis as well as some new analytical results in contact mechanics.

Indispensable treatise on the mechanics of extreme dynamic events, including impact, shocks, penetration and high-rate material response.