NPTEL : NOC:Computational Continuum Mechanics (Mechanical Engineering)

Co-ordinators : Prof. Sachin Singh Gautam


Lecture 1 - Origin of nonlinearities - 1

Lecture 2 - Origin of nonlinearities - 2

Lecture 3 - Tensor and Tensor Algebra - 1

Lecture 4 - Tensor and Tensor Algebra - 2

Lecture 5 - Tensor and Tensor Algebra - 3

Lecture 6 - Tensor and Tensor Algebra - 4

Lecture 7 - Linearization and directional derivative, Tensor analysis - 1

Lecture 8 - Linearization and directional derivative, Tensor analysis - 2

Lecture 9 - Worked Examples - 1

Lecture 10 - Worked Examples - 2

Lecture 11 - Idea of Motion, Material and Spatial Descriptions, Deformation Gradient Tensor

Lecture 12 - Strain, Polar Decomposition - 1

Lecture 13 - Polar Decomposition - 2, Volume and Area Change

Lecture 14 - Worked Examples, Linearized Kinematics

Lecture 15 - Velocity, Acceleration, Material Time Derivative

Lecture 16 - Velocity Gradient, Rate of Deformation tensor, Area and Volume Rate, Reynolds Transport Theorem

Lecture 17 - Solved Examples

Lecture 18 - Conservation of Mass, Balance of Linear Momentum, Cauchy's Stress Principle - 1

Lecture 19 - Cauchy's Stress Principle - 2, Cauchy Stress Tensor

Lecture 20 - Objectivity, Stress Objectivity, Equilibrium Equations - 1

Lecture 21 - Equilibrium Equations - 2, Principle of Virtual Work

Lecture 22 - Work Conjugacy, First Piola-Kirchhoff Stress Tensor

Lecture 23 - Second Piola-Kirchhoff Stress Tensor, Decomposition of Stress - 1

Lecture 24 - Decomposition of Stress - 2, Objective Stress Measures

Lecture 25 - Solved Examples

Lecture 26 - Constitutive relations and constraints, Hyperelasticity, Material elasticity tensor

Lecture 27 - Spatial Elasticity Tensor, Solved Example

Lecture 28 - Isotropic hyperelasticity - material and spatial description, Hyperelastic models

Lecture 29 - Isotropic Hyperelasticity, Neo-Hookean Material Model, Solved Examples

Lecture 30 - Introduction, Linearization Process Overview

Lecture 31 - Linearization of Internal Virtual Work and External Virtual Work

Lecture 32 - Discretization of Kinematic Quantities, Equilibrium Equations

Lecture 33 - Discretization of Linearized Equilibrium Equations

Lecture 34 - Newton Raphson Method

Lecture 35 - Line Search Method

Lecture 36 - Arc Length Method, Solved Examples

Lecture 37 - FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Introduction

Lecture 38 - FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Formulation

Lecture 39 - FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - FEM

Lecture 40 - FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Results