Mechanical Behaviour of Engineering Materials

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.