Course11210329640 lectures
Computational Continuum Mechanics
Prof. Sachin Singh Gautam · IIT Guwahati
About
Continuum mechanics as a full-fledged course is a very interesting but a challenging subject. Usually,its application within the nonlinear finite element codes is not clear to the student. Computational continuum mechanics tries to bridge this gap. Hence, it can be treated as an applied version of continuum mechanics course. It assumes no prior exposure to continuum mechanics. The course starts with sufficient introduction to tensors, kinematics, and kinetics. Then, the course applies these concepts to set up the constitutive relations for nonlinear finite element analysis of a simple hyperelastic material. This is followed by the linearization of the weak form of the equilibrium equations followed by discretization to obtain the finite element equations, in particular, the tangent matrices and residual vectors is discussed. Finally, the Newton-Raphson solution procedure is discussed along with line search and arc length methods to enhance the solution procedure.
Intended audience: Masters student and research scholarsPREREQUISITES : Introduction to Solid Mechanics I and II, A undergraduate course in Engineering Mathematics. Exposure to undergraduate course on numerical methods will be an added advantage.
Lectures
Week 1: Introduction
Week 2: Mathematical Preliminaries -1
- Lec 3: Tensor and Tensor Algebra - 1
- Lec 4: Tensor and Tensor Algebra - 2
- Lec 5: Tensor and Tensor Algebra - 3
- Lec 6: Tensor and Tensor Algebra - 4
Week 3: Mathematical Preliminaries - 2
- Lec 7: Linearization and directional derivative, Tensor analysis - 1
- Lec 8: Linearization and directional derivative, Tensor analysis - 2
- Lec 9: Worked Examples - 1
- Lec 10: Worked Examples - 2
Week 4: Kinematics - 1
- Lec 11: Idea of Motion, Material and Spatial Descriptions, Deformation Gradient Tensor
- Lec 12: Strain, Polar Decomposition - 1
- Lec 13: Polar Decomposition - 2, Volume and Area Change
Week 5: Kinematics - 2
- Lec 14: Worked Examples, Linearized Kinematics
- Lec 15: Velocity, Acceleration, Material Time Derivative
- Lec 16: Velocity Gradient, Rate of Deformation tensor, Area & Volume Rate, Reynolds Transport Theorem
- Lec 17: Solved Examples
Week 6: Kinetics - 1
- Lec 18: Conservation of Mass, Balance of Linear Momentum, Cauchy's Stress Principle - 1
- Lec 19: Cauchy's Stress Principle - 2, Cauchy Stress Tensor
- Lec 20: Objectivity, Stress Objectivity, Equilibrium Equations - 1
- Lec 21: Equilibrium Equations - 2, Principle of Virtual Work
Week 7: Kinetics - 2
- Lec 22: Work Conjugacy, First Piola-Kirchhoff Stress Tensor
- Lec 23: Second Piola-Kirchhoff Stress Tensor, Decomposition of Stress - 1
- Lec 24: Decomposition of Stress - 2, Objective Stress Measures
- Lec 25: Solved Examples
Week 8: Hyperelasticity - 1
- Lec 26: Constitutive Relations and Constraints, Hyperelasticity, Material Elasticity Tensor
- Lec 27: Spatial Elasticity Tensor, Solved Example
Week 9: Hyperelasticity - 2
- Lec 28: Isotropic hyperelasticity - material and spatial description, Hyperelastic models
- Lec 29: Isotropic Hyperelasticity, Neo-Hookean Material Model, Solved Examples
Week 10: Linearization
- Lec 30: Introduction, Linearization Process Overview
- Lec 31: Linearization of Internal Virtual Work and External Virtual Work
Week 11: Discretization
- Lec 32: Discretization of Kinematic Quantities, Equilibrium Equations
- Lec 33: Discretization of Linearized Equilibrium Equations
Week 12: Solution Procedure
- Lec 34: Newton Raphson Method
- Lec 35: Line Search Method
- Lec 36: Arc Length Method, Solved Examples
- Lec 37: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Introduction
- Lec 38: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Formulation
- Lec 39: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - FEM
- Lec 40: FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem - Results
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Guwahati
- Department
- Mechanical Engineering
- Teacher
- Prof. Sachin Singh Gautam
- Level
- Graduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed