Lecture Notes

Lecture 1: Introduction to 3.22/Introduction to Elasticity

Introduction
Overview, Admin.
Types of Mechanical Behavior

• Macroscopic Response
• Microscopic Response
• Applications

Material Selection
Elasticity
Ideal Linear Elasticity
Applications

• Continuum Mechanics
• Micro Mechanics

Hooke's Law
Data for E
Measurement of Modulus

• Static Methods
• Dynamic Methods

Lecture 2: Tensors, Stress Tensor

Tensors

• 3 Tensor Conventions
• 2 Tensor Operators

Stress

• Definition
• Static Equilibrium
• Traction
• Principal Stresses

Lecture 3: Stress, Strain Tensors, Tensor Transformations

Stress

• Invariants
• Special States of Stress

Strain

• 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

Rubbers

• 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

Introduction

• 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

Introduction

• 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

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

Limit Analysis: Examples

• Grooved Plate in Tension
• Sandwich Beam Indentation

Necking in Uniaxial Tension
Plasticity

Lecture 14: Dislocation Mechanics

Introduction

• 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

Introduction

• 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