Learn · Computational Continuum Mechanics
Lecture 27 of 40Week 8: Hyperelasticity - 1
Lec 27: Spatial Elasticity Tensor, Solved Example
Prof. Sachin Singh Gautam · IIT Guwahati
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- Computational Continuum Mechanics, IIT Guwahati (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Lec 1: Origin of nonlinearities - 1
- Lec 2: Origin of nonlinearities - 2
- 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
- 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
- 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
- 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
- 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
- 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
- Lec 26: Constitutive Relations and Constraints, Hyperelasticity, Material Elasticity Tensor
- Lec 27: Spatial Elasticity Tensor, Solved Example
- Lec 28: Isotropic hyperelasticity - material and spatial description, Hyperelastic models
- Lec 29: Isotropic Hyperelasticity, Neo-Hookean Material Model, Solved Examples
- Lec 30: Introduction, Linearization Process Overview
- Lec 31: Linearization of Internal Virtual Work and External Virtual Work
- Lec 32: Discretization of Kinematic Quantities, Equilibrium Equations
- Lec 33: Discretization of Linearized Equilibrium Equations
- 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