Computational Continuum Mechanics
About Course
Computational Continuum Mechanics
Computational Continuum Mechanics as a fullfledged course is a very interesting but 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 the continuum mechanics course. It assumes no prior exposure to continuum mechanics. The course starts with a 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 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 are discussed. Finally, the NewtonRaphson solution procedure is discussed along with line search and arc length methods to enhance the solution procedure.
INTENDED AUDIENCE: Masters student and research scholars
Course Content
Computational Continuum Mechanics

Computational Continuum Mechanics [Intro Video]
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Lec 1: Origin of nonlinearities – 1
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Lec 2: Origin of nonlinearities – 2
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Lec 3: Tensor and Tensor Algebra – 1
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Lec 4: Tensor and Tensor Algebra – 2
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Lec 5: Tensor and Tensor Algebra – 3
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Lec 6: Tensor and Tensor Algebra – 4
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Lec 7: Linearization and directional derivative, Tensor analysis – 1
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Lec 8: Linearization and directional derivative, Tensor analysis – 2
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Lec 9: Worked Examples – 1
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Lec 10: Worked Examples – 2
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Lec 11: Idea of Motion, Material and Spatial Descriptions, Deformation Gradient Tensor
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Lec 12: Strain, Polar Decomposition – 1
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Lec 13: Polar Decomposition – 2, Volume and Area Change
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Lec 14: Worked Examples, Linearized Kinematics
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Lec 15: Velocity, Acceleration, Material Time Derivative
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Lec 16:Velocity Gradient, Rate of Deformation tensor, Area & Volume Rate, Reynolds Transport Theorem
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Lec 17: Solved Examples
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Lec 18: Conservation of Mass, Balance of Linear Momentum, Cauchy’s Stress Lec 18: Principle – 1
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Lec 19: Cauchy’s Stress Principle – 2, Cauchy Stress Tensor
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Lec 20: Objectivity, Stress Objectivity, Equilibrium Equations – 1
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Lec 21: Equilibrium Equations – 2, Principle of Virtual Work
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Lec 22: Work Conjugacy, First PiolaKirchhoff Stress Tensor
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Lec 23: Second PiolaKirchhoff Stress Tensor, Decomposition of Stress – 1
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Lec 24: Decomposition of Stress – 2, Objective Stress Measures
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Lec 25: Solved Examples
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Lec 26: Constitutive relations and constraints, Hyperelasticity, Material elasticity tensor
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Lec 27: Spatial Elasticity Tensor, Solved Example
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Lec 28: Isotropic hyperelasticity – material and spatial description, Hyperelastic models
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Lec 29: Isotropic Hyperelasticity, NeoHookean Material Model, Solved Examples
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Lec 30: Introduction, Linearization Process Overview
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Lec 31: Linearization of Internal Virtual Work and External Virtual Work
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Lec 32: Discretization of Kinematic Quantities, Equilibrium Equations
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Lec 33: Discretization of Linearized Equilibrium Equations
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Lec 34: Newton Raphson Method
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Lec 35: Line Search Method
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Lec 36: Arc Length Method, Solved Examples
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Lec 37: FE Formulation of Ductile Fracture in Dynamic ElastoPlastic Contact Problem – Introduction
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Lec 38: FE Formulation of Ductile Fracture in Dynamic ElastoPlastic Contact Problem – Formulation
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Lec 39: FE Formulation of Ductile Fracture in Dynamic ElastoPlastic Contact Problem – FEM
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Lec 40: FE Formulation of Ductile Fracture in Dynamic ElastoPlastic Contact Problem – Results
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