| Lecture 1 |
Introduction to Fourier Transform, Fourier Transfom of Dirac Delta Function |
| Lecture 2 |
Convolution Theorem, Green's Function, Construction of Green's Function |
| Lecture 3 |
Physical Interpratation of Green's Function, Betti's Theorem |
| Lecture 4 |
Green's Function for 2D and 3D Poisson's Equation |
| Lecture 5 |
Integral Representation of Elasticity Solutions - I (Unbounded Domain) |
| Lecture 6 |
Integral Representation of Elasticity Solutions - II (Unbounded Domain) |
| Lecture 7 |
Integral Representation of Elasticity Solutions - III (Bounded Domain) |
| Lecture 8 |
Eigenstrains, General Solution of Eigen Strain Problem |
| Lecture 9 |
Inclusions & Inhomogeneities - I (Ellipsoidal Inclusion with Uniform Eigenstrain - Eshelby Solution) |
| Lecture 10 |
Inclusions & Inhomogeneities - II (Ellipsoidal Inhomogeneities) |
| Lecture 11 |
Inclusions & Inhomogeneities - III (Inhomogeneous Inhomogeneities) |
Quiz-1 |
Spring 2023
|
| Lecture 12 |
Heterogeneity & Length Scales, Representative Volume Element, Random Media: Ergodic Hypothesis & Concepts |
| Lecture 13 |
Macroscopic Averages: Average Stress Theorem, Average Strain Theorem |
| Lecture 14 |
Hill's Lemma, Effective Modulus of Heterogeneous Media |
| Lecture 15 |
Concentration/Influence Tensors & Effective Properties |
| Lecture 16 |
Bounds for Effective Modulii - I (Variational Theorems in Linear Elasticity: Min. Potential Energy & Min. Complementary Energy) |
| Lecture 17 |
Bounds for Effective Modulii - II (Voigt and Reuss Bounds) |
| Lecture 18 |
Bounds for Effective Modulii - III (Use of Classical Variational Principles - I) |
| Lecture 19 |
Bounds for Effective Modulii - IV (Use of Classical Variational Principles - II) |
| Lecture 20 |
Bounds for Effective Modulii - IV (Hashin Shtrikman Bounds) |
Mid-Term Exam |
Spring 2023
|
| Lecture 21 |
Determination of Effective Modulii |
| Lecture 22 |
Eshelby Method |
| Lecture 23 |
Mori-Tanaka Method, Self Consisten Methods (SCM) |
| Lecture 24 |
Example: Ellective Mudulii of Isotropic Material (Eshelby, Mori-Tanaka, Self Consisten Method) |
| Lecture 25 |
Differential Scheme |
| Lecture 26 |
Comparison of Methods (Dilute & High Concentration, Rigid Particles) |
| Lecture 27 |
Transformation Field/Strain: Local Transformtion Fields |
| Lecture 28 |
Relation between Mechanical & Influence Functions for Two Phase System, Overall Response |
| Lecture 29 |
Clapeyron Theorem, The Levin Formula |
| Lecture 30 |
Generalized Levin's Theorem |
| Lecture 31 |
Transformed Homogeneous Inclusion, Local Fields in Ellipsoidal Inclusions, Transformed Inhomogeneities (Method of Uniform Fields - I) |
| Lecture 32 |
Transformed Homogeneous Inclusion, Local Fields in Ellipsoidal Inclusions, Transformed Inhomogeneities (Method of Uniform Fields - I) |
Quiz-2 |
Spring 2023
|
| Lecture 33 |
Transformed Inhomogeneities (Method of Uniform Fields - II) |
| Lecture 34 |
Transformed Inhomogeneities (Equivalent Inclusion Method) |
| Lecture 35 |
Transformation Influence Functions & Concentration Factors: Local & Overall Residual Fields |
| Lecture 36 |
Multiphase Systems: Overall Strain & Phase Eigen Strains prescribed, Overall Stress & Phase Eigen Stress applied |
| Lecture 37 |
Properties of Transformation Influence Tensors |
End-Term Exam |
Spring 2023
|