Numerical Methods In Contact Mechanics

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.

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 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 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.

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.

Engineering fields such as fracture mechanics, fatigue, friction and wear, contact mechanics, and damage are closely related and responsible for the reliability and durability of mechanical systems. The importance of contact mechanics problems - complex, time dependent and highly non-linear problems due to changes in the geometry and friction over contact surfaces - has been established in recent years, while the development of modern computational methods means that it now possible to solve complex problems for which there are no analytical solutions.

This book presents recent advances in the field of computational coupling and contact mechanics with particular emphasis on numerical formulations and methodologies necessary to solve advanced engineering applications. Featuring contributions from leading experts and active researchers in these fields who provide a detailed overview of different modern numerical schemes that can be considered by main numerical methodologies to simulate interaction problems in continuum mechanics. A number of topics are addressed, including formulations based on the finite element method (FEM) and their variants (e.g. isogeometric analysis or standard and generalized high-order FEM: hp-FEM and GFEM, respectively), the boundary element method (BEM), the material point method (MPM) or the recently proposed finite block method (FBM), among many more. Written with PhD students in mind, Advances in Computational Coupling and Contact Mechanics also includes the most recent numerical techniques which could be served as reference material for researchers and practicing engineers. All chapters are self-contained and can be read independently, with numerical formulations accompanied by practical engineering applications. Contents: Frictional Mortar Formulation for Large Inelastic Deformation Problems (T Doca and F M A Pires)Standard and Generalized High-order Mortar-based Finite Elements in Computational Contact Mechanics (A P C Dias, S P B Proenca and M L Bittencourt)A Large Deformation Frictionless Contact Treatment In NURBS-based Isogeometric Analysis (J Kopačka, D Gabriel, R Kolman and J Plesek)Treatment of Non-matching Interfaces in Partitioned Fluid-Structure Interaction Problems (J A González and K C Park)An Eulerian-based Thermo-flexible Multi-body Approach for Simulating Rig Testing of Disc Brakes (N Strömberg)Nonlinear Analysis with Functionally Graded Materials by Finite Block Method (J Li, J Jin, J J Yang, T Huang and P H Wen)A Coupled Finite Element Material Point Method for Large Deformation Problems (Y Lian and X Zhang)Fracture and Contact in the Material Point Method: New Approaches and Applications (M A Homel and E B Herbold)A Cohesive-frictional Grain-boundary Technique for Microstructural Analysis of Polycrystalline Materials (I Benedetti)Piezoelectric and Magneto-electro-elastic Frictional Contact Modelling (L Rodríguez-Tembleque, F C Buroni, A Sáez and M H Ferri Aliabadi) Readership: PhD students in computational mechanics; researchers and practicing engineers. Keywords: Contact Mechanics;Friction;Cohesive-Frictional Contact;Coupling Non-Matching Interfaces;Mortar formulations;Localized Lagrange Multipliers;Isogeometric Contact Analysis;Thermomechanical Contact;Finite Element Method;Finite Block Method;Material Point Method;Multi-Body Approach;Boundary Element Method;Large Inelastic Deformation;Microstructural Analysis of Polycrystalline Materials;Impact Problems;Fragmentation and Comminution Processes;Fluid-Structure Interaction Problems;Disc Brakes Testing;Functionally Graded Materials;Piezoelectric and Magneto-Electro-Elastic MaterialsReview:0