Plasticity and Viscoelasticity

Plasticity and Viscoelasticity

Fertig Research Group: Multiscale Failure of Materials via YouTube Direct link

Vector Notation and Conventions

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Vector Notation and Conventions

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Plasticity and Viscoelasticity

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

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