Lectures related to Shape Change and Polar Decomposition

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Deformation Analysis: Small Strain and Kinematics

Explores small strain theory, kinematics, and compatibility conditions in solid mechanics.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Review: 3D Linear Elasticity & Beams

Covers the review of 3D Linear Elasticity and beams, focusing on mechanics of slender structures.

Eshelby Inclusion Mechanics

Explores the Eshelby method for ellipsoidal inclusions and the mechanics of particles undergoing shape changes due to eigenstrains.

Continuum Mechanics: Kinematics and Deformation Analysis

Covers kinematics and deformation in continuum mechanics, focusing on displacement vectors and the deformation gradient tensor.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Eshelby Inclusion: Mechanics and Eigenstrains

Explores the Eshelby method for mechanics of inclusions and eigenstrains, focusing on stress and strain fields inside inclusions.

Spectral Clustering: Theory and Applications

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

3D Linear Elasticity & Beams

Covers 3D linear elasticity, stress, strain, beams' behavior under loads, and torsion.

Mechanics of Slender Structures: Final Review and Overview

Covers the main learning objectives of ME-411, focusing on dimensional analysis, scalings, and mechanical elements.

Mechanics of Slender Structures: Elasticity & Buckling

Explores 3D elasticity, beam bending, and buckling phenomena in slender structures.

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Finite & Infinite Deformation: Key Distinction

Explains the geometric interpretation of eigen vectors and values in material deformation.

Polar Decomposition Theorem

Explores the Polar Decomposition Theorem, decomposing deformations into stretches and rotations, discussing uniqueness and implications in continuum mechanics.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Continuum Mechanics: Forces and Deformation

Covers the basics of continuum mechanics, including forces transmission, energy conservation, and body motion geometry.

Transformation Laws: Diagonalization of Symmetric Tensors

Discusses tensor transformations and diagonalization of symmetric tensors, focusing on stress analysis and the significance of principal stresses.

Spectral Decomposition and SVD

Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.