The book presents the principles of Damage Mechanics along with the latest research findings. Both isotropic and anisotropic damage mechanisms are presented. Various damage models are presented coupled with elastic and elasto-plastic behavior. The book includes two chapters that are solely dedicated to experimental investigations conducted by the authors. In its last chapter, the book presents experimental data for damage in composite materials that appear in the literature for the first time. · Systematic treatment of damage mechanics in composite materials · Includes special and advanced topics · Includes basic principles of damage mechanics · Includes new experimental data that appears in print for the first time · Covers both metals and metal matrix composite materials · Includes new chapters on fabric tensors · Second edition includes four new chapters

This book provides in a single and unified volume a clear and thorough presentation of the recent advances in continuum damage mechanics for metals and metal matrix composites. Emphasis is placed on the theoretical formulation of the different constitutive models in this area, but sections are added to demonstrate the applications of the theory. In addition, some sections contain new material that has not appeared before in the literature. The book is divided into three major parts: Part I deals with the scalar formulation and is limited to the analysis of isotropic damage in materials; Parts II and III deal with the tensor formulation and is applied to general states of deformation and damage. The material appearing in this text is limited to plastic deformation and damage in ductile materials (e.g. metals and metal matrix composites) but excludes many of the recent advances made in creep, brittle fracture, and temperature effects since the authors feel that these topics require a separate volume for this presentation. Furthermore, the applications presented in this book are the simplest possible ones and are mainly based on the uniaxial tension test.

The major goal of this book is to present the implementation of some damage models with finite elements. The damage models are based on the principles of continuum damage mechanics and the effective stress concept. Several books have appeared recently on damage mechanics but are mostly theoretical in nature. Alternatively, this book provides a complete finite element program that includes the effects of damage. The book consists of two parts. Part I includes two chapters mainly review ing topics from finite element analysis and continuum damage mechanics. The reader is cautioned that the material contained in this part is introductor- other references must be consulted for the theoretical aspects of these topics. For a complete theoretical treatment of the subject, the reader is referred to the book Advances in Damage Mechanics: Metals and Metal Matrix Composites by Voyiadjis and Kattan, published in 1999. In Part II the finite element program DNA is introduced in three chapters. DNA stands for "Da mage Nonlinear Analysis". The program can be used for the analysis of elasto plastic material behavior including the effects of damage within the frame work of damage mechanics. Two versions of DNA are presented - one for small strain analysis and one for finite strain analysis. The program makes extensive calls to a library of tensor operations developed by the authors. The tensor library is extensively outlined in the last chapter of the book.

Scalar Damage and Healing Mechanics outlines the latest cutting-edge research in the field of scalar damage and healing mechanics, providing step-by-step insight on how to use scalar damage variables in various modeling scenarios. Additionally, the book discusses the latest advances in healing mechanics, covering the evolution of healing and damage, small damage and small healing, healing processes in series and in parallel, super healing, and the thermodynamics of damage and healing. Coupled systems, in which damage triggers self-healing as well as a decoupled system where healing occurs after damage is identified by external detection, are also discussed. Readers are additionally introduced to fundamental concepts such as effective stress, damage evolution, plane stress damage decomposition, and other damage processes that form the basis for a better understanding of the more advanced chapters. Synthesizes the latest research in damage mechanics and the healing mechanics of materials, including thermodynamics, elasticity and plasticity Includes practical exercises and problems for readers to work with before performing their own modeling scenarios Covers various scalar damage variables and outlines different damage processes

"Continuum Damage Mechanics and Numerical Applications" presents a systematic development of the theory of Continuum Damage Mechanics and its numerical engineering applications using a unified form of the mathematical formulations in anisotropic and isotropic damage models. The theoretical framework is based on the thermodynamic theory of energy and material dissipation and is described by a set of fundamental formulations of constitutive equations of damaged materials, development equations of the damaged state, and evolution equations of micro-structures. According to concepts of damage-dissipation of the material state and effective evolution of material properties, all these advanced equations, which take nonsymmetrized effects of damage aspects into account, are developed and modified from the traditional general failure models so they are more easily applied and verified in a wide range of engineering practices by experimental testing. Dr. Wohua Zhang is a Professor at Engineering Mechanics Research Center in Zhejiang University of China. Dr. Yuanqiang Cai is a Professor at Department of Civil Engineering in Zhejiang University of China.

Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and analyze large and complex diffusion data such as High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging (DKI). A Part entitled Tensor Signal Processing presents new methods for processing tensor-valued data, including a novel perspective on performing voxel-wise morphometry of diffusion tensor data using kernel-based approach, explores the free-water diffusion model, and reviews proposed approaches for computing fabric tensors, emphasizing trabecular bone research. The last Part, Applications of Tensor Processing, discusses metric and curvature tensors, two of the most studied tensors in geometry processing. Also covered is a technique for diagnostic prediction of first-episode schizophrenia patients based on brain diffusion MRI data. The last chapter presents an interactive system integrating the visual analysis of diffusion MRI tractography with data from electroencephalography.