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2-2d: Plasticity in a 1-D Bar (Isotropic Hardening-Part I)
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Classroom Contents
Plasticity and Viscoelasticity
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- 1 Vector Notation and Conventions
- 2 Tensor Review (Definitions)
- 3 Tensor Review (Coordinate Transformation)
- 4 1-2a: Continuum Kinematics (Reference Frames and Deformation)
- 5 1-2b: Continuum Kinematics (Lagrange Finite Strain Tensor)
- 6 1-2c: Continuum Kinematics (Meaning of the Lagrange Finite Strain Tensor)
- 7 1-2d: Continuum Kinematics (Displacement-Based Strain Formulation)
- 8 1-2e: Continuum Kinematics (Shear Strain)
- 9 Continuum Stresses (Cauchy Stress Formula)
- 10 Continuum Stresses (Principal Stresses)
- 11 Continuum Stresses (Stress Invariants)
- 12 Continuum Stresses (Hydrostatic and Deviatoric Stresses)
- 13 1-4: Equations of Motion and Equlibrium
- 14 1-5: Constitutive Law (Hooke's Law)
- 15 1-6: Linking Linear Elastic Mechanics with Plasticity
- 16 2-1a: Plasticity Mechanisms (Plastic Deformation in Metals)
- 17 2-1b: Plasticity Mechanisms (Plastic Deformation in Other Materials)
- 18 2-2a: Plasticity in a 1-D Bar (Deformation Measures)
- 19 2-2b: Plasticity in a 1-D Bar (Deformation Decomposition)
- 20 2-2c: Plasticity in a 1-D Bar (Elastic-Perfectly Plastic)
- 21 2-2d: Plasticity in a 1-D Bar (Isotropic Hardening-Part I)
- 22 2-2e: Plasticity in a 1-D Bar (Isotropic Hardening-Part II)
- 23 2-2f: Plasticity in a 1-D Bar (Kinematic Hardening)
- 24 2-3a: General (3-D) Framework for Plasticity (Yield Function)
- 25 2-3b: General (3-D) Framework for Plasticity (Consistency Condition)
- 26 2-3c: General (3-D) Framework for Plasticity (Flow Rule)
- 27 2-4a: Uniqueness and Stability (Net Stress Work and Net Complementary Stress Work)
- 28 2-4b: Uniqueness and Stability (Stress Cycle)
- 29 2-5a: Properties of Yield Surfaces (Maximum Dissipation Postulate)
- 30 2-5b: Properties of Yield Surfaces (Convexity of Surface and Normality of Plastic Strain Increment)
- 31 2-5c: Properties of Yield Surfaces (Consequences of the Normality Rule)
- 32 2-6a: Initial Yield Surfaces (Octahedral Plane)
- 33 2-6b: Initial Yield Surfaces (von Mises Yield Criterion)
- 34 2-6c: Initial Yield Surfaces (Tresca Yield Criterion)
- 35 2-6d: Initial Yield Surfaces (Yield Criteria with Hydrostatic Effects)
- 36 2-7: Subsequent Yield Surfaces
- 37 2-8a: 3D Incremental Plasticity (von Mises with Isotropic Hardening)
- 38 2-8b: 3D Incremental Plasticity (Scalar Hardening Function)
- 39 2-9: Path Dependence of Plastic Strains
- 40 2-10: Combined Isotropic and Kinematic Hardening
- 41 3-1a: Viscoelasticity Introduction (Basics)
- 42 3-1b: Viscoelasticity Introduction (Physical Mechanisms)
- 43 3-2a: Simple Viscoelastic Models (Maxwell and Kelvin-Voight Materials)
- 44 3-2b: Simple Viscoelastic Models (Creep Compliance)
- 45 3-2c: Simple Viscoelastic Models (Relaxation Modulus)
- 46 3-3a: Laplace Transform (Overview)
- 47 3-3b: Laplace Transform (Creep Compliance Example)
- 48 3-4a: Generalized Viscoelastic Models (Generalized Maxwell Model - Part I)
- 49 3-4b: Generalized Viscoelastic Models (Generalized Maxwell Model - Part II)
- 50 3-4c: Generalized Viscoelastic Models (Generalized Kelvin-Voight Model)
- 51 3-4d: Generalized Viscoelastic Models (Creep Compliance - Part I)
- 52 3-4e: Generalized Viscoelastic Models (Creep Compliance - Part II)
- 53 3-5a: Hereditary Integrals (Creep Compliance)
- 54 3-5b: Hereditary Integrals (Relaxation Modulus)
- 55 3-5c: Hereditary Integrals (Alternate Forms)
- 56 3-6a: Correspondence Principle
- 57 3-6b: Correspondence Principle (Beam Example)
- 58 3-7: Viscoelasticity in Three Dimensions
- 59 3-8: Time-Temperature Superposition
- 60 3-9a: Oscillatory Loading (Storage and Loss Moduli)
- 61 3-9b: Oscillatory Loading (Loss Tangent)
- 62 3-9c: Oscillatory Loading (Relationships between Complex Quantities)
- 63 3-10: Energy Dissipation in Viscoelastic Materials
