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Lecture 1: Introduction to 3.22/Introduction to Elasticity

Overview, Admin.
Types of Mechanical Behavior

  • Macroscopic Response
  • Microscopic Response
  • Applications

Material Selection
Ideal Linear Elasticity

  • Continuum Mechanics
  • Micro Mechanics

Hooke's Law
Data for E
Measurement of Modulus

  • Static Methods
  • Dynamic Methods

Lecture 2: Tensors, Stress Tensor


  • 3 Tensor Conventions
  • 2 Tensor Operators


  • Definition
  • Static Equilibrium
  • Traction
  • Principal Stresses

Lecture 3: Stress, Strain Tensors, Tensor Transformations


  • Invariants
  • Special States of Stress


  • Deformation Tensor
  • Rotation Tensor
  • Strain Tensor
  • Relation between Straw Tensor & Engineering Strain
  • Principal Strains
  • Invariants

Tensor Transformations

Lecture 4: Generalized Hooke's Law

Stiffness and Compliance Tensors

  • Number Independent Eastic Constants
  • Matrix Notation
  • Material Symmetry
  • Relations between Compliance Tensor & Eng. Moduli
  • Relationships between El. Constants for Isotropic Materials

Elastic Strain Energy

Lecture 5: Physical Origin of Elastic Moduli

Crystalline Materials, Glasses

  • Energy - Separation Diagram


  • Entropy; Random Walk Theory

Lecture 6: Composites

Upper and Lower Bounds

  • Isostrain
  • Isostress
  • Hashin-Shtrikman

Laminates/Thin Films

  • Thermoelastic Analysis
  • Curvature
  • Maximum Stress
  • Stoney Formula

Lecture 7: Cellular Solids

Microstructure, Properties, Applications
Elastic Moduli
Trabecular Bone

  • Stress Shielding

Lecture 8: Introduction to Viscoelasticity


  • Viscous Fluid
  • Elastic Solid
  • Creep Test, Creep Compliance
  • Stress Relaxation Test, Relaxation Modulus

Linear Viscoelasticity in Amorphous and Crystalline Polymers

  • Modulus Variation with Temperature

Boltzmann Superposition Principle

Lecture 9: Spring-Dashpot Models

Spring-Dashpot Models

  • Maxwell Element
  • Voigt Element
  • Standard Linear Solid
  • Equivalent Models

Dynamic Mechanical Measurements

  • Storage and Loss Moduli
  • tan d

Time-Temperature Equivalence for Amorphous Polymers

  • Shift Factor, WLF Equation

Lecture 10: Role of Diffusion; Biomaterials

Mechanism of Time-Dependent Deformation: Diffusion
Viscoelasticity in Biomaterials

  • Collagen: Cartilage, Tendon, Bone, Uterine Cervix
  • Cellulose: Wood, Plant Cell Wall

Lecture 11: Continuum Plasticity


  • Plastic Behaviour
  • Applications
  • Measurement of Yield Strength
  • Data for Yield Strength

Continuum Plasticity

  • Idealizations
  • Assumptions
  • Yield Criteria: Tresca, Von Mises
  • 3D Stress Space; Yield Surface, p-plane

Lecture 12: Continuum Plasticity (cont.)

Continuum Plasticity

  • Equivalent Plastic Strain Increment
  • Plastic Stress-Strain Relationship; Levy-Mises
  • Yield Criteria for Porous Solids

Limit Analysis

  • Upper and Lower Bound Theorems

Lecture 13: Continuum Plasticity (cont.)

Limit Analysis: Examples

  • Grooved Plate in Tension
  • Sandwich Beam Indentation

Necking in Uniaxial Tension

Lecture 14: Dislocation Mechanics


  • Microscopic Aspects of Plasticity
  • Applications
  • Theoretical Shear Strength of Materials

Dislocations - Geometrical Aspects

  • Edge Dislocation
  • Screw Dislocation
  • Dislocation Motion: Glide and Climb
  • Plastic Shear Strain; Orowan's Equation
  • Elastic Stress Field Around a Dislocation
  • Elastic Strain Energy of a Dislocation
  • Line Tension
  • Glide Force on a Dislocation

Lecture 15: Mechanism of Low Temperature Plasticity

Lattice Resistance (Peierls Stress)
Temperature Dependence of Yield Strength

  • Effect of Diffusion
  • Rate and Temperature Dependence of Yield Strength

Microstructural Strengthening Mechanisms in Metals

  • Solid Solution Hardening
  • Precipitation Hardening
  • Dispersion Hardening
  • Work Hardening
  • Grain Boundary Strengthening; Hall-Petch Equation
  • High Temperature Creep of Metals and Ceramics

Lecture 16: Continuum Creep Response


  • High Temperature Time Dependent Deformation
  • Types of Creep
  • Multiaxial Stress States
  • Measurement of Creep Parameters
  • Diffusion Coefficients

Lecture 17: Mechanisms of Creep Deformation

Diffusional flow

  • Bulk Iffusion: Interstitial and Vacancy Diffusion
  • Grain Boundary Diffusion
  • Dislocation Core Diffusion
  • Relationship between Creep Strain-Rate and Diffusion

Power Law Creep

  • Dislocation Climb
  • Development of Power Law for Creep

Deformation Mechanism Maps

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