Shape Change and Polar Decomposition

Related lectures (31)

Page 1 of 4

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

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

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

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

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

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

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

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

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

Explores spectral and singular value decompositions of matrices.