Lectures in course ME-331: Solid mechanics

Covers the basics of vectors in 3 dimensions, including representation, unit vectors, and basis transformations.

Covers forces, traction vectors, and stress principles in deformable bodies, emphasizing equilibrium and stress components.

Vectors and Tensors: Mathematical Preliminaries and Transformations

Explores mathematical preliminaries of tensors and their transformations under basis rotations.

Stress Analysis in Solid Mechanics

Covers stress analysis, traction vectors, coordinate transformations, and failure analysis in fiber composites.

Vectors and Tensors: Mathematical Preliminaries and Spectral Decomposition

Explores mathematical preliminaries, eigenvectors, eigenvalues, and tensor fields in solid mechanics.

Symmetric Stress Tensor

Explains principal stresses, spectral decomposition, simple states of stress, and the importance of a symmetric stress tensor.

Vectors and Tensors: Derivatives and Transformations

Explores gradient, divergence, and integral theorems in vector calculus.

Stress Power

Explains how forces do work on a body and manipulates power incorporation.

Kinematics: Deformation Mapping and Gradient Tensor

Covers kinematics, deformation mapping, rigid body translation, rotation, stretching, shearing, and the deformation gradient tensor.

Kinematics: Motion and Deformation of Bodies

Covers kinematics, focusing on motion and deformation of bodies independently of forces, including deformation gradient and stretch ratios.

Virtual Power and FEM: Derivation and Application

Covers the derivation and application of the principle of virtual power in the context of Finite Element Method (FEM).

Kinematics: Deformation and Expansion

Explores kinematics of deformation, focusing on radial and linear expansion, torsion, and rotation by an angle.

Stress Measures: Beyond Cauchy

Explores stress measures beyond Cauchy, focusing on 1st and 2nd Piola-Kirchhoff stress.

Deformation Analysis: Small Strain and Kinematics

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

Shape Change and Polar Decomposition

Explains shape change, polar decomposition, and strain tensor interpretation.

Linear Elasticity: Spherically-Symmetric Problems

Explores linear elasticity in spherically-symmetric problems and axially-symmetric cylindrical shells.

Linear Elasticity: Cylindrically-symmetric Problems

Covers linear elasticity, focusing on cylindrically-symmetric problems and the simplification of Hooke's Law for axially-symmetric cases.

Plasticity: Stress-Strain Behavior and Plastic Flow

Covers stress-strain behavior, plastic flow, work hardening, and dislocation motion.

Von-Mises Plasticity: Yield Criteria and Stress Invariants

Explores the Von-Mises plasticity theory, discussing yield criteria and stress invariants.

Plasticity in Plate with Hole

Covers the application of the plasticity condition in a plate with a hole and the estimation of the plastic zone region using the elastic stress field.