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COMPUTATIONAL CONTINUUM MECHANICS

Duration: 33:56:00
Lectures: 39
Level: Beginner

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                       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 continue 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 hyper elastic 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.

1
COMPUTATIONAL CONTINUUM MECHANICS-Intro video
5:48
2
COMPUTATIONAL CONTINUUM MECHANICS-Lec 1 : Origin of nonlinearities – 1
1:02:14
3
COMPUTATIONAL CONTINUUM MECHANICS-Lec 2 : Origin of nonlinearities – 2
50:58
4
COMPUTATIONAL CONTINUUM MECHANICS-Lec 3 : Tensor and Tensor Algebra – 1
56:12
5
COMPUTATIONAL CONTINUUM MECHANICS-Lec 4 : Tensor and Tensor Algebra – 2
34:01
6
COMPUTATIONAL CONTINUUM MECHANICS-Lec 5 : Tensor and Tensor Algebra – 3
38:52
7
COMPUTATIONAL CONTINUUM MECHANICS-Lec 6 : Tensor and Tensor Algebra – 4
35:09
8
COMPUTATIONAL CONTINUUM MECHANICS-Lec 7 : Linearization and directional derivative, Tensor analysis – 1
38:26
9
COMPUTATIONAL CONTINUUM MECHANICS-Lec 8 : Linearization and directional derivative, Tensor analysis – 2
49:55
10
COMPUTATIONAL CONTINUUM MECHANICS-Lec 9 : Worked Examples – 1
36:00
11
COMPUTATIONAL CONTINUUM MECHANICS-Lec 10 : Worked Examples – 2
51:52
12
COMPUTATIONAL CONTINUUM MECHANICS-Lec 11 : Idea of Motion, Material and Spatial Descriptions, Deformation Gradient Tensor
57:55
13
COMPUTATIONAL CONTINUUM MECHANICS-Lec 12 : Strain, Polar Decomposition – 1
44:49
14
COMPUTATIONAL CONTINUUM MECHANICS-Lec 13 : Polar Decomposition – 2, Volume and Area Change
53:04
15
COMPUTATIONAL CONTINUUM MECHANICS-Lec 14 : Worked Examples, Linearized Kinematics
1:01:20
16
COMPUTATIONAL CONTINUUM MECHANICS-Lec 15 : Velocity, Acceleration, Material Time Derivative
33:42
17
COMPUTATIONAL CONTINUUM MECHANICS-Lec 16 : Velocity Gradient, Rate of Deformation tensor, Area & Volume Rate, Reynolds Transport Theorem
58:05
18
COMPUTATIONAL CONTINUUM MECHANICS-Lec 17 : Conservation of Mass, Balance of Linear Momentum, Cauchy’s Stress Principle – 1
49:07
19
COMPUTATIONAL CONTINUUM MECHANICS-Lec 18 : Cauchy’s Stress Principle – 2, Cauchy Stress Tensor
37:25
20
COMPUTATIONAL CONTINUUM MECHANICS-Lec 19 : Objectivity, Stress Objectivity, Equilibrium Equations – 1
49:51
21
COMPUTATIONAL CONTINUUM MECHANICS-Lec 20 : Equilibrium Equations – 2, Principle of Virtual Work
41:18
22
COMPUTATIONAL CONTINUUM MECHANICS-Lec 21 : Work Conjugacy, First Piola-Kirchhoff Stress Tensor
41:20
23
COMPUTATIONAL CONTINUUM MECHANICS-Lec 22 : Second Piola-Kirchhoff Stress Tensor, Decomposition of Stress – 1
36:45
24
COMPUTATIONAL CONTINUUM MECHANICS-Lec23-Decomposition of Stress – 2, Objective Stress Measures
57:54
25
COMPUTATIONAL CONTINUUM MECHANICS-Lec24-Constitutive relations and constraints, Hyperelasticity, Material elasticity tensor
50:48
26
COMPUTATIONAL CONTINUUM MECHANICS-Lec25-Spatial Elasticity Tensor, Solved Example
37:24
27
COMPUTATIONAL CONTINUUM MECHANICS-Lec26-Isotropic hyperelasticity – material and spatial description, Hyperelastic models
37:58
28
COMPUTATIONAL CONTINUUM MECHANICS-Lec27-Isotropic Hyperelasticity, Neo-Hookean Material Model, Solved Examples
58:48
29
COMPUTATIONAL CONTINUUM MECHANICS-Lec28-Introduction, Linearization Process Overview
30:32
30
COMPUTATIONAL CONTINUUM MECHANICS-Lec29- Linearization of Internal Virtual Work and External Virtual Work
1:00:01
31
COMPUTATIONAL CONTINUUM MECHANICS-Lec30- Discretization of Kinematic Quantities, Equilibrium Equations
1:00:09
32
COMPUTATIONAL CONTINUUM MECHANICS-Lec31- Discretization of Linearized Equilibrium Equations
50:04
33
COMPUTATIONAL CONTINUUM MECHANICS-Lec32- Newton Raphson Method
39:43
34
COMPUTATIONAL CONTINUUM MECHANICS-Lec33- Line Search Method
21:25
35
COMPUTATIONAL CONTINUUM MECHANICS-Lec34- Arc Length Method, Solved Examples
40:20
36
COMPUTATIONAL CONTINUUM MECHANICS-Lec35- FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem – Introduction
1:05:15
37
COMPUTATIONAL CONTINUUM MECHANICS-Lec36-FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem – Formulation
42:00
38
COMPUTATIONAL CONTINUUM MECHANICS-Lec37- FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem – FEM
45:40
39
COMPUTATIONAL CONTINUUM MECHANICS-Lec38-FE Formulation of Ductile Fracture in Dynamic Elasto-Plastic Contact Problem – Results
1:00:53

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COMPUTATIONAL CONTINUUM MECHANICS
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