Peter Wriggers

Shahab Sahraee

The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.

With Solved Exercises

Tensor Calculus and Differential Geometry for Engineers

Ernst Stephan

The book includes different contributions that cover interdisciplinary research in the areas of · Error controlled numerical methods, efficient algorithms and software development · Elastic and in elastic deformation processes · Models with multiscales and multi-physics “High Performance” adaptive numerical methods using finite elements (FEM) and boundary elements (BEM) are described as well as efficient solvers for linear systems and corresponding software components for non-linear, coupled field equations of various branches of mechanics, electromagnetics, and geosciences.

Modelling, Simulation and Software Concepts for Scientific-Technological Problems

Udo Nackenhorst

This book contains the proceedings of the IUTAM Symposium held in Hanover, Germany, in November 2006. Coverage includes new mathematical techniques, new discretization techniques, advanced applications of unilateral contact to masonry structures, decohesion analysis and tractive rolling of tires. The book provides a good overview of modern techniques and state-of-the-art discretizations schemes applied in contact mechanics.

Proceedings of the IUTAM Symposium held in Hannover, Germany, November 5-8, 2006

IUTAM Symposium on Computational Methods in Contact Mechanics

Paolo de Mattos Pimenta

The main focus of the book is to convey modern techniques applied within the range of computational mechanics of beams, plates and shells. The topics of interest are wide ranging and include computational aspects of nonlinear theories of shells and beams including dynamics, advanced discretization methods for thin shells and membranes, shear-deformable shell finite elements for SMA composite devices, optimization and design of shells and membranes, fluid-structure interaction with thin-walled structures, contact mechanics with application to thin structures and edge effects in laminated shells.

New Trends in Thin Structures: Formulation, Optimization and Coupled Problems

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.

Computational Contact Mechanics

Ralf Müller

Dietmar Gross

Jörg Schröder

Wolfgang Ehlers

This book contains the most important formulas and more than 160 completely solved problems from Statics. It provides engineering students material to improve their skills and helps to gain experience in solving engineering problems. Particular emphasis is placed on finding the solution path and formulating the basic equations. Topics include: - Equilibrium - Center of Gravity, Center of Mass, Centroids - Support Reactions - Trusses - Beams, Frames, Arches - Cables - Work and Potential Energy - Static and Kinetic Friction - Moments of Inertia

Engineering Mechanics 1

Statics – Formulas and Problems

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.

Nonlinear Finite Element Methods

Jože Korelc

New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.

Automation of Finite Element Methods

Tarek I. Zohdi

In this, its second corrected printing, Zohdi and Wriggers’ illuminating text presents a comprehensive introduction to the subject. The authors include in their scope basic homogenization theory, microstructural optimization and multifield analysis of heterogeneous materials. This volume is ideal for researchers and engineers, and can be used in a first-year course for graduate students with an interest in the computational micromechanical analysis of new materials.

An Introduction to Computational Micromechanics

Thomas Lenarz

This book provides an overview of new mathematical models, computational simulations and experimental tests in the field of biomedical technology, and covers a wide range of current research and challenges. The first part focuses on the virtual environment used to study biological systems at different scales and under multiphysics conditions. In turn, the second part is devoted to modeling and computational approaches in the field of cardiovascular medicine, e.g. simulation of turbulence in cardiovascular flow, modeling of artificial textile-reinforced heart valves, and new strategies for reducing the computational cost in the fluid-structure interaction modeling of hemodynamics. The book’s last three parts address experimental observations, numerical tests, computational simulations, and multiscale modeling approaches to dentistry, orthopedics and otology. Written by leading experts, the book reflects the remarkable advances that have been made in the field of medicine, the life sciences, engineering and computational mechanics over the past decade, and summarizes essential tools and methods (such as virtual prototyping of medical devices, advances in medical imaging, high-performance computing and new experimental test devices) to enhance medical decision-making processes and refine implant design. The contents build upon the International Conference on Biomedical Technology 2015 (ICTB 2015), the second ECCOMAS thematic conference on Biomedical Engineering, held in Hannover, Germany in October 2015.

Modeling, Experiments and Simulation

Biomedical Technology

Jurica Sorić

Olivier Allix

This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.

Multiscale Modeling of Heterogeneous Structures

Alexander Popp

The book conveys modern techniques and the latest state-of-the-art with regard to the most fundamental aspects of computational contact mechanics. However, since contact can readily be interpreted as a special type of interface problem, it seems advisable not to isolate contact mechanics, but rather to address it in the context of a broader class of problems denoted as computational interface mechanics. The book gives a clear understanding of the underlying physics of interfaces, and a comprehensive insight into the current state-of-the-art and selected cutting-edge research directions in the computational treatment of interface effects. It focuses on the modeling of friction, wear, lubrication, cohesive interfaces, grain boundaries, phase boundaries, fracture, thermo-mechanics and particulate contact (e.g. granular media). Also the most important computational aspects are addressed, including discretization techniques for finite deformations, solution algorithms for single- and multi-processor computing environments, multi-scale approaches, discrete element models and multi-physics problems including contact and interface constraints. Among the computational techniques covered in this book are finite element (FEM) and boundary element (BEM) methods, atomistic models, molecular dynamics (MD), discrete element methods (DEM), coupling approaches for multi-scale simulations, and tools for an efficient automated FEM code generation.

Contact Modeling for Solids and Particles

Carsten Carstensen

Mixed finite element methods are a tool to solve complex engineering problems of different nature. This subject is treated in the volume from the engineering and the mathematical point. Different applications are considered which depict the value of mixed formulations in engineering on one side. On the other side the mathematical background is provided including proofs of convergence and stability of these methods and adequate solvers for mixed problems are discussed. This broad spectrum yields an indepth treatment of mixed methods from different perspectives.

Mixed Finite Element Technologies

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.

Peter Wriggers

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