# Meshfree Methods and Peridynamics for Fracture Mechanics

- Institution: IIT-ISM Dhanbad
- Department: Civil Engineering
- Teacher: Prof. Pranesh Roy
- Level: Graduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/105105002)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/105105002)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This is an advanced course which discusses the limitations of classical solid mechanics and associated finite element method for problems involving cracks or discontinuities and how to overcome these drawbacks by using meshfree methods, peridynamics, and phase field method. The primary focus of this course is to provide the students with state-of-the-art computational methods for modeling and simulation of problems involving large deformation, material nonlinearity, damage, and fracture. Upon successful completion of this course, the students should be able to derive numerical approximation to the equations of motion using various meshfree methods and solve problems involving large deformation and fracture, formulate governing equations in peridynamics framework to solve crack initiation and propagation problems, and develop phase field based models to solve crack propagation problems.

Intended audience: M.Tech. and Ph.D. students of Structural Engineering specialization of Civil Engineering

Prerequisites: B.Tech. level Mechanics of Solids or Strength of Materials, Numerical Methods, Basic Finite Element Method.

## Lectures

1. [Lecture 01: Calculus of variations](https://invisiblenetwork.ai/learn/nptel/105105002/9d1c8a4ad1eb) (YouTube)
2. [Lecture 02: Calculus of variations (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/71cd79b2a978) (YouTube)
3. [Lecture 03: Tensor Analysis](https://invisiblenetwork.ai/learn/nptel/105105002/5c249a788ca3) (YouTube)
4. [Lecture 04: Tensor Analysis (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/a3df68839e6b) (YouTube)
5. [Lecture 05: Tensor Analysis (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/9a793387f6e2) (YouTube)
6. [Lecture 06 : Stress tensor](https://invisiblenetwork.ai/learn/nptel/105105002/5de975c25fc0) (YouTube)
7. [Lecture 07 : Strain tensor](https://invisiblenetwork.ai/learn/nptel/105105002/137fc9c08172) (YouTube)
8. [Lecture 08 : Strain tensor and constitutive equation](https://invisiblenetwork.ai/learn/nptel/105105002/c63ac9d0a18b) (YouTube)
9. [Lecture 09 : Balance laws](https://invisiblenetwork.ai/learn/nptel/105105002/13d13ed14c26) (YouTube)
10. [Lecture 10 : Weak or variational formulation](https://invisiblenetwork.ai/learn/nptel/105105002/58c5b40e197b) (YouTube)
11. [Lecture 11 : Variational principles in elasticity](https://invisiblenetwork.ai/learn/nptel/105105002/862450aad16e) (YouTube)
12. [Lecture 12 : Direct stiffness method](https://invisiblenetwork.ai/learn/nptel/105105002/d73d29e216c0) (YouTube)
13. [Lecture 13 : Finite element method](https://invisiblenetwork.ai/learn/nptel/105105002/c26099588423) (YouTube)
14. [Lecture 14 : Finite element method(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/a17d3385aca1) (YouTube)
15. [Lecture 15 : Finite element method(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/8e640a2eaf63) (YouTube)
16. [Lecture 16 : Finite element method(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/f9e6babcfdad) (YouTube)
17. [Lecture 17 : Finite element method(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/88de05df4107) (YouTube)
18. [Lecture 18 : Linear elastic fracture mechanics](https://invisiblenetwork.ai/learn/nptel/105105002/429cffd5f4fc) (YouTube)
19. [Lecture 19 : Linear elastic fracture mechanics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/acc687cc98f5) (YouTube)
20. [Lecture 20 : Linear elastic fracture mechanics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/91faac788604) (YouTube)
21. [Lecture 21 : Meshfree particle methods: Smoothed particle hydrodynamics](https://invisiblenetwork.ai/learn/nptel/105105002/3fa4ed6c6a6a) (YouTube)
22. [Lecture 22 : Smoothed particle hydrodynamics](https://invisiblenetwork.ai/learn/nptel/105105002/c93c517ba10d) (YouTube)
23. [Lecture 23 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/1c079c33b6a8) (YouTube)
24. [Lecture 24 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/955a60bbde3a) (YouTube)
25. [Lecture 25 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/d5a8f1d3dce5) (YouTube)
26. [Lecture 26 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/6a47a1813c64) (YouTube)
27. [Lecture 27 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/e13c231bda89) (YouTube)
28. [Lecture 28 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/f2e654ad5a58) (YouTube)
29. [Lecture 29 : Smoothed particle hydrodynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/ebe2e327e497) (YouTube)
30. [Lecture 30 : SPH and Reproducing Kernel Particle Method](https://invisiblenetwork.ai/learn/nptel/105105002/3ec9d2da5fce) (YouTube)
31. [Lecture 31 : Reproducing Kernel Particle Method](https://invisiblenetwork.ai/learn/nptel/105105002/b8405191ffc9) (YouTube)
32. [Lecture 32 : Method of weighted residuals](https://invisiblenetwork.ai/learn/nptel/105105002/3dcc2c10461e) (YouTube)
33. [Lecture 33 : Galerkin methods and meshfree Galerkin methods](https://invisiblenetwork.ai/learn/nptel/105105002/9cd04f929886) (YouTube)
34. [Lecture 34 : Element-free Galerkin method](https://invisiblenetwork.ai/learn/nptel/105105002/090c17180053) (YouTube)
35. [Lecture 35 : Element-free Galerkin method(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/6b2e67cd2335) (YouTube)
36. [Lecture 36 : Peridynamics](https://invisiblenetwork.ai/learn/nptel/105105002/52e35c529eb2) (YouTube)
37. [Lecture 37 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/36a8e13b3162) (YouTube)
38. [Lecture 38 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/e9b88ab7a0e6) (YouTube)
39. [Lecture 39 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/9ca54ec0e4ab) (YouTube)
40. [Lecture 40 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/b8632dc80954) (YouTube)
41. [Lecture 41 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/7f294f6756df) (YouTube)
42. [Lecture 42 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/20b02ab6bf30) (YouTube)
43. [Lecture 43 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/16295996bd4a) (YouTube)
44. [Lecture 44 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/ab3b4bce67a5) (YouTube)
45. [Lecture 45 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/1db3d6752b9d) (YouTube)
46. [Lecture 46 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/479214019752) (YouTube)
47. [Lecture 47 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/aafad899c7bb) (YouTube)
48. [Lecture 48 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/2b72618f2abd) (YouTube)
49. [Lecture 49 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/ce54926e7298) (YouTube)
50. [Lecture 50 : Peridynamics(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/3a69d7d5da7f) (YouTube)
51. [Lecture 51 : Phase field theory](https://invisiblenetwork.ai/learn/nptel/105105002/4bc50a829674) (YouTube)
52. [Lecture 52 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/170452d86205) (YouTube)
53. [Lecture 53 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/1dccc254f103) (YouTube)
54. [Lecture 54 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/3357b0072f2b) (YouTube)
55. [Lecture 55 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/74dda7469235) (YouTube)
56. [Lecture 56 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/c5519143919f) (YouTube)
57. [Lecture 57 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/d06c943149d8) (YouTube)
58. [Lecture 58 : Phase field theory (Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/7bfca7aa242f) (YouTube)
59. [Lecture 59 : Coupling various numerical methods](https://invisiblenetwork.ai/learn/nptel/105105002/567f3bd2c544) (YouTube)
60. [Lecture 60 : Coupling various numerical methods(Continued)](https://invisiblenetwork.ai/learn/nptel/105105002/44853eb1e7c0) (YouTube)