1st Edition

# Mechanics of Finite Deformation and Fracture

290 Pages 52 B/W Illustrations

290 Pages 52 B/W Illustrations

290 Pages

Also available as eBook on:

This important work covers the fundamentals of finite deformation in solids and constitutive relations for different types of stresses in large deformation of solids. In addition, the book covers the fracture phenomena in brittle or quasi-brittle materials in which large deformation does not occur. The book provides a thorough understanding of fracture mechanics as well.

Since mathematical proof with full derivation is demonstrated throughout the book, readers will gain the skills to understand and drive the basic concepts on their own, enabling them to put forward new ideas and solutions.

Finite deformations in material can occur with change of geometry such that the deformed shape may not resemble the initial shape. Analyzing these types of deformations needs a particular mathematical tool that is always associated with tensor notations. In general the geometry may be non-orthogonal, and the use of covariant and contra-variant tensor concepts to express the finite deformations and the associated mechanical strains are needed. In addition, it is obvious that in large deformations, there are several definitions for stress, each depending on the frame of the stress definitions. The constitutive equations in material also depends on the type of stress that is introduced. In simulation of the material deformation, components of the deformation tensor will be transformed from one frame to another either in orthogonal or in non-orthogonal coordinate of geometry. This informative book covers all this in detail.

Preface

Part One: Mechanics of Finite Deformations

Nonlinear Geometry of Continuum Solids via Mathematical Tools

General Theory for Deformation and Strain in Solids

General Theory for Stress in Solids

General Form of the Constitutive Equations in Solids

Stress - Strain Relationship in Large Deformation of Solids

Part Two: Mechanics of Fracture

Application of Complex Variable Method in Linear Elasticity

Derivation of Fracture Mechanics From Linear Elasticity

Describing Three Modes of Fracture

Elastic-Plastic Fracture Mechanics (EPFM)

Stress Intensity Factor for Trough Thickness Flaws and J Integral

Index

### Biography

Majid Aleyaasin, PhD, is currently a researcher and lecturer in the School of Engineering at the University in Aberdeen in Aberdeen, Scotland. He was formerly a lecturer in mechanical engineering at Mashhad University, Iran, where he received a BEng. He received his PhD in mechanical engineering at Bradford University in the United Kingdom and subsequently worked a research fellow at the University of Manchester Institute of Science and Technology and University of Manchester, United Kingdom. Dr. Aleyaasin’s research interest lies in the field of applied dynamics of solids and structures, and he has published 30 papers in international journals and in conference proceedings.

"This book deals with the mathematical formulations of the physical problems of large deformation and fracture of solids. It is conveniently divided into two independent parts: mechanics of finite deformations and mechanics of fracture. Many engineers use these formulations in numerical analysis software for solving real-life structural design problems. However, it is required for the users and developers of such software to have a firm grasp of the physical principles involved and their mathematical treatment. This book skillfully provides that in sufficient detail.

It's a very useful book for researchers, academics, numerical analysis software developers, and users of commercially available and in-house-developed industrial and research programs for large deformation analysis of solids and linear-elastic and elastic-plastic fracture analyses of materials and structures. Graduate students attending advanced courses on mechanics of deformable solids and fracture mechanics will also find this book useful for understanding the underlying concepts and their mathematical treatment."
—Dr. M. A. Sheikh, School of Mechanical, Aerospace & Civil Engineering, The University of Manchester, Manchester, UK