3rd Edition

Theory, Applications, and Numerics

Authors: Martin Sadd
Hardcover ISBN: 9780124081369
eBook ISBN: 9780124104327
Imprint: Academic Press
Published Date: 7th February 2014
Page Count: 600
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Elasticity: Theory, Applications, and Numerics, Third Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods.

Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples and exercises, and new or expanded coverage of areas such as spherical anisotropy, stress contours, isochromatics, isoclinics, and stress trajectories. Using MATLAB software, numerical activities in the text are integrated with analytical problem solutions. These numerics aid in particular calculations, graphically present stress and displacement solutions to problems of interest, and conduct simple finite element calculations, enabling comparisons with previously studied analytical solutions. Online ancillary support materials for instructors include a solutions manual, image bank, and a set of PowerPoint lecture slides.

Key Features

  • Thorough yet concise introduction to linear elasticity theory and applications
  • Only text providing detailed solutions to problems of nonhomogeneous/graded materials
  • New material on stress contours/lines, contact stresses, curvilinear anisotropy applications
  • Further and new integration of MATLAB software
  • Addition of many new exercises
  • Comparison of elasticity solutions with elementary theory, experimental data, and numerical simulations
  • Online solutions manual and downloadable MATLAB code


Graduate students in Mechanical, Civil, Aerospace and Materials Engineering; R&D engineers in structural and mechanical design

Table of Contents



About the Author

PART 1 Foundations and Elementary Applications

Chapter 1. Mathematical Preliminaries

1.1 Scalar, vector, matrix, and tensor definitions

1.2 Index notation

1.3 Kronecker delta and alternating symbol

1.4 Coordinate transformations

1.5 Cartesian tensors

1.6 Principal values and directions for symmetric second-order tensors

1.7 Vector, matrix, and tensor algebra

1.8 Calculus of Cartesian tensors

1.9 Orthogonal curvilinear coordinates

Chapter 2. Deformation

2.1 General deformations

2.2 Geometric construction of small deformation theory

2.3 Strain transformation

2.4 Principal strains

2.5 Spherical and deviatoric strains

2.6 Strain compatibility

2.7 Curvilinear cylindrical and spherical coordinates

Chapter 3. Stress and Equilibrium

3.1 Body and surface forces

3.2 Traction vector and stress tensor

3.3 Stress transformation

3.4 Principal stresses

3.5 Spherical, deviatoric, octahedral, and von mises stresses

3.6 Stress distributions and contour lines

3.7 Equilibrium equations

3.8 Relations in curvilinear cylindrical and spherical coordinates

Chapter 4. Material Behavior—Linear Elastic Solids

4.1 Material characterization

4.2 Linear elastic materials—Hooke’s law

4.3 Physical meaning of elastic moduli

4.4 Thermoelastic constitutive relations

Chapter 5. Formulation and Solution Strategies

5.1 Review of field equations

5.2 Boundary conditions and fundamental problem classifications

5.3 Stress formulation

5.4 Displacement formulation

5.5 Principle of superposition

5.6 Saint-Venant’s principle

5.7 General solution strategies

Chapter 6. Strain Energy and Related Principles

6.1 Strain en


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About the Author

Martin Sadd

Martin H. Sadd is Emeritus Professor of Mechanical Engineering and Applied Mechanics at the University of Rhode Island. He received his Ph.D. in mechanics from the Illinois Institute of Technology and began his academic career at Mississippi State University. In 1979 he joined the faculty at Rhode Island and served as department chair from 1991 to 2000. Professor Sadd’s teaching background is in the area of solid mechanics with emphasis in elasticity, continuum mechanics, wave propagation, and computational methods. He has taught elasticity at two academic institutions, in several industries, and at a government laboratory. Professor Sadd’s research has been in the area of computational modeling of materials under static and dynamic loading conditions using finite, boundary, and discrete element methods. Much of his work has involved micromechanical modeling of geomaterials including granular soil, rock, and concretes. He has authored more than 70 publications and has given numerous presentations at national and international meetings.

Affiliations and Expertise

Mechanical Engineering & Applied Mechanics Department, University of Rhode Island, USA