Mechanical Behaviour of Engineering Materials

Inhaltsverzeichnis

• 1 Cartesian Tensors.
• 1.1 Introduction.
• 1.2 Indicial Notation.
• 1.3 Coordinate Transformation.
• 1.4 Tensor Algebra.
• 1.5 Special Tensors.
• 1.6 Some Applications of Cartesian Tensors.
• Example & quiz problems.
• 1.7 Principle Values and Principal Directions of Symmetric Second-Order Tensors.
• 1.8 Tensor Fields.
• 1.9 Divergence and Gradient Operations.
• 1.10 Common Tensor Operations.
• 1.11 Problems.
• 1.12 References.
• 1.13 Further Reading.
• 2 Analysis of Stress.
• 2.1 Introduction.
• 2.2 The “Continuous” Medium.
• 2.3 Fundamental Principles of Continuum Mechanics.
• 2.4 Analysis of Stress.
• 2.5 Stress Boundary Conditions.
• 2.6 Principal Axes of Stress, Principal Planes and Principal Stresses.
• 2.7 Piola-Kirchhoff s Stress Tensor.
• 2.8 Problems.
• 2.9 Remarks on the Actual Three-Dimensional Stresses in Materials.
• 2.10 eferences.
• 2.11 Further Reading.
• 3 Deformation and Strain Analysis of Motion.
• 3.1 Introduction.
• 3.2 Deformation Kinematics and Measures of Strain.
• 3.3 Problems.
• 3.4 Analysis of Motion.
• 3.5 Objective Tensors.
• 3.6 Problems.
• 3.7 Further Reading.
• 4 Thermomechanical Continua.
• 4.1 Introduction.
• 4.2 The Laws of Thermodynamics.
• 4.3 Thermodynamics of Continuous Media.
• 4.4 Thermodynamics of the Deformation Process.
• 4.5 Problems.
• 4.6 References.
• 4.7 Further Reading.
• 5 Transition to the Response Behaviour of Engineering Materials.
• 5.1 Introduction.
• 5.2 The Constitutive Equation.
• 5.3 Pertinent Notions of Analytical (Phenomenological) Mechanics.
• 5.4 Problems.
• 5.5 References.
• 5.6 Further Reading.
• 6 Elastic Response Behaviour.
• 6.1 Introduction.
• 6.2 Nonlinear Elasticity.
• 6.3 Linear Elasticity.
• 6.4 Problems.
• 6.5 The Elastic Boundary Value Problem.
• 6.6 Solved Problems in Linear Elasticity.
• 6.7 References.
• 6.8 Further Reading.
• 7 Elastic-PlasticBehaviour.
• 7.1 Introduction.
• 7.2 Elastic-Plastic Behaviour under Static Loading.
• 7.3 Yield Surfaces.
• 7.4 Post-Yield Behaviour Changes in the Yield Surface.
• 7.5 Constitutive Relations.
• 7.6 The Boundary Value Problem in Plasticity.
• 7.7 Derivation of the “Plane Problem” from the “Three-Dimensional Problem” Quadratic yield condition.
• 7.8 The Three-Dimensional Problem under General Yield Function.
• 7.9 The “Plane Problem” under General Yield Condition.
• 7.10 Problems.
• 7.11 Review Problems.
• 7.12 Transition to the Creep of Metals and Alloys.
• 7.13 Transition to Stress-Relaxation of Metals and Alloys.
• 7.14 Problems.
• 7.15 References.
• 7.16 Further Reading.
• 8 Viscoelastic Behaviour.
• 8.1 Introduction.
• 8.2 Linear Viscoelastic Behaviour.
• 8.2.2 Description in the “Fourier-spectrum” domain.
• 8.3 Inverse-relations between “Fourier-Spectrum” and “Creep and Relaxation Functions”.
• 8.4 Inter-relations between “Retardation-time” and”Relaxation-time” Spectra.
• 8.5 Inter-relations between “Fourier”, “Retardation-time” and “Relaxation-time” Spectra.
• 8.6 Inverse-relations between “Fourier”, “Retardation-time” and “Relaxation-time” Spectra.
• 8.7 Applications.
• 8.8 Problems.
• 8.9 Transition to Thermoviscoelasticity.
• 8.10 Problems.
• 8.11 References.
• 8.12 Further Reading.
• Appendix A Curvilinear Tensors.
• A.1 Introduction.
• A 2 Preliminary Material.
• A 3 Differential Geometry.
• A 4 Physical Components.
• A 5 Tensor Calculus.
• A.6 Problems.
• A.7 Further Reading.
• Appendix B Delta and Step Functions.
• B.1 The Delta Function 8(t).
• B.2 The Step “Heaviside” Function H(t).
• B 3 References.
• Appendix C Integral Transforms.
• C.1 Introduction.
• C.2 Laplace Transform.
• C.3 Problems.
• C.4 Fourier Transform.
• C.5 Problems.
• C.6References.
• C.7 Further Reading.
• Cumulative Subject Index.