Computational Continuum Mechanics (English)

   Friday, March 29, 2024   

Starting a new Lecture Notes Series on Computational Continuum Mechanics

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Lecture 1: Computational Continuum Mechanics

Lecture 2: Lec 1: Origin of nonlinearities - 1

Lecture 3: Lec 2: Origin of nonlinearities - 2

Lecture 4: Lec 3: Tensor and Tensor Algebra - 1

Lecture 5: Lec 4: Tensor and Tensor Algebra - 2

Lecture 6: Lec 5: Tensor and Tensor Algebra - 3

Lecture 7: Lec 6: Tensor and Tensor Algebra - 4

Lecture 8: Lec 7: Linearization and directional derivative, Tensor analysis - 1

Lecture 9: Lec 8: Linearization and directional derivative, Tensor analysis - 2

Lecture 10: Lec 9: Worked Examples - 1

Lecture 11: Lec 10: Worked Examples - 2

Lecture 12: Lec 11: Idea of Motion, Material and Spatial Descriptions, Deformation Gradient Tensor

Lecture 13: Lec 12: Strain, Polar Decomposition - 1

Lecture 14: Lec 13: Polar Decomposition - 2, Volume and Area Change

Lecture 15: Lec 14: Worked Examples, Linearized Kinematics

Lecture 16: Lec 15: Velocity, Acceleration, Material Time Derivative

Lecture 17: Lec 16:Velocity Gradient, Rate of Deformation tensor, Area & Volume Rate, Reynolds Transport Theorem

Lecture 18: Lec 17: Solved Examples

Lecture 19: Lec 18: Conservation of Mass, Balance of Linear Momentum, Cauchy's Stress Lec 18: Principle - 1

Lecture 20: Lec 19: Cauchy's Stress Principle - 2, Cauchy Stress Tensor

Lecture 21: Lec 20: Objectivity, Stress Objectivity, Equilibrium Equations - 1

Lecture 22: Lec 21: Equilibrium Equations - 2, Principle of Virtual Work

Lecture 23: Lec 22: Work Conjugacy, First Piola-Kirchhoff Stress Tensor

Lecture 24: Lec 23: Second Piola-Kirchhoff Stress Tensor, Decomposition of Stress - 1

Lecture 25: Lec 24: Decomposition of Stress - 2, Objective Stress Measures

Lecture 26: Lec 25: Solved Examples

Lecture 27: Lec 26: Constitutive relations and constraints, Hyperelasticity, Material elasticity tensor

Lecture 28: Lec 27: Spatial Elasticity Tensor, Solved Example

Lecture 29: Lec 28: Isotropic hyperelasticity - material and spatial description, Hyperelastic models

Lecture 30: Lec 29: Isotropic Hyperelasticity, Neo-Hookean Material Model, Solved Examples

Lecture 31: Lec 30: Introduction, Linearization Process Overview

Lecture 32: Lec 31: Linearization of Internal Virtual Work and External Virtual Work

Lecture 33: Lec 32: Discretization of Kinematic Quantities, Equilibrium Equations

Lecture 34: Lec 33: Discretization of Linearized Equilibrium Equations

Lecture 35: Lec 34: Newton Raphson Method

Lecture 36: Lec 35: Line Search Method

Lecture 37: Lec 36: Arc Length Method, Solved Examples

Lecture 38: Lec 37: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Introduction

Lecture 39: Lec 38: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Formulation

Lecture 40: Lec 39: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - FEM

Lecture 41: Lec 40: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Results