This textbook provides an overview of the fundamental concepts in continuum mechanics for application in real material behavior analysis. The contents cover basic topics such as Kinematics—the motion of any material point representing a material body using the Lagrangian and Eulerian approaches; stress tensors—stress analysis of material bodies experiencing small deformations; mathematical modeling of material properties in continuum mechanics; balance principles—transfer of specific mechanical properties from a system to its environment or vice-versa through the system boundary. The textbook also contains pedagogical elements such as worked examples and end-of-chapter exercises which are derived from typical engineering problems, and the solution manual so that students can solve computational problems by running simulations on Matlab or Python on their own. This benefits engineering students understand the concept of continuum mechanics for future analysis using finite-element analysis, boundary element method or any other computational methods.
Author(s): Nik Abdullah Nik Mohamed
Publisher: Springer
Year: 2023
Language: English
Pages: 195
City: Singapore
Preface
Contents
About the Author
List of Symbols
Chapter 2
Chapter 3
Chapter 4
Chapter 5
1 Introduction
1.1 Description of Material Behaviour via Continuum Mechanics
1.2 Terminology and Notation
1.3 Understanding Some Basic Concepts
2 Kinematics
2.1 Lagrangian and Eulerian Approaches
2.1.1 Reference Versus Current Configuration. Deformation Gradient
2.1.2 Material and Spatial Description of Property
2.1.3 Examples and Problems
2.2 Lagrangian and Eulerian Displacement Gradient
2.2.1 Examples and Problems
2.3 Strain Tensor
2.3.1 Examples and Problems
2.4 Polar Decomposition Theorem
2.4.1 Examples and Problems
2.5 Principal Strains and Directions
2.5.1 Examples and Problems
2.6 Distortion and Dilatation
2.6.1 Examples and Problems
2.7 Deformation Velocity Tensor
2.7.1 Examples and Problems
2.8 Condition of Compatibility
2.8.1 Examples and Problems
2.9 Deformation Gradient of a Discretized Body
2.9.1 Examples and Problems
3 Stress
3.1 Force and Stress
3.2 Cauchy Stress Tensor
3.2.1 Examples and Problems
3.3 Principal Values and Directions
3.3.1 Examples and Problems
3.4 First and Second Piola–Kirchhoff Stress Tensor
3.4.1 Examples and Problems
3.5 State of Stress in a Damaged Continuum
3.5.1 Examples and Problems
4 Constitutive Relations
4.1 Elastic Materials
4.1.1 Elasticity Tensor
4.1.2 Elastic Potential
4.1.3 Linear Isotropic Elastic Material
4.1.4 Linear Orthotropic Elastic Material
4.1.5 Examples and Problems
4.2 Hyperelasticity
4.2.1 Mooney–Rivlin Materials
4.2.2 Ogden Materials
4.2.3 Superelastic Materials—Thamburaja and Nikabdullah Model
4.2.4 Examples and Problems
5 Balance Principles in Continuum Mechanics
5.1 General Mechanical Balance Equation
5.1.1 Balance Equation for Mass Transfer
5.1.2 Balance Equation for Linear Momentum
5.1.3 Balance Equation for Angular Momentum
5.1.4 Examples and Problems
6 Solutions to the Problems
6.1 Section 2.1
6.2 Section 2.2
6.3 Section 2.3
6.4 Section 2.4
6.5 Section 2.5
6.6 Section 2.6
6.7 Section 2.7
6.8 Section 2.8
6.9 Section 2.9
6.10 Section 3.2
6.11 Section 3.3
6.12 Section 3.4
6.13 Section 3.5
6.14 Section 4.1
6.15 Section 4.2
6.16 Section 5.1
Appendix Appendix
Appendix References
Index
