# Fracture Mechanics *A joint Master course of Ecole Nationale des Ponts et Chaussées, Institut Polytechnique de Paris, Sorbonne Université* To confirm you enrollement in this class, please fill this form https://framaforms.org/fracture-mechanics-1727090311 We kindly ask you to create an account on [Github](https://www.github.com) to share materials with you, give assignements, and provide computational tools. ## General informations ### Teachers - Véronique Lazarus (veronique.lazarus@ensta-paris.fr), ENSTA/IPP - Corrado Maurini (corrado.maurini@sorbonne-universite.fr), Institut Jean Le Rond d'Alembert, Sorbonne Université ### Schedule and rooms **Important**: Starting from 1st oct: - French class 13.14.109 - English class 24.34.201 We ask that (this is important to garantee a balance in the number of students): - All the students having selected French as a preferred language to attend the French class - All the students having selected English or indifferent as a preferred language to attend the English class The room are posted on the following calendar. Please check before going each day. The room can have last-minute changes. - [html format](https://calendar.google.com/calendar/embed?src=uarpr9gmur6hj67ekrppomd2bg%40group.calendar.google.com&ctz=Europe%2FParis) - [ical format]( https://calendar.google.com/calendar/ical/uarpr9gmur6hj67ekrppomd2bg%40group.calendar.google.com/public/basic.ics) Except the first lecture, the class will be given in parallel in French and in English (same time, Tuesday 9h-12h, Jussieu Campus) by Veronique Lazarus (French) and Corrado Maurini (English). The program will be the same for the two versions. There will be a unique final exam. A plan of the Jussieu campus can be found [here]( https://sciences.sorbonne-universite.fr/vie-de-campus-sciences/accueil-vie-pratique/plan-du-campus) ### Slack channel We use [slack](https://slack.com) as a communication tool. Please join our workspace by subscribing at the following space: - https://join.slack.com/t/su-mastersolides/shared_invite/zt-2q2t1ut6d-nOzicdC1OkzgdBxDmdzkbA. *IMPORTANT:* Please, subscribe using your name and not fancy nicknames. We need to be able to identify you. Short version of the url: https://s.42l.fr/msolides - Join the channel `m2-2024-fracture` inside the slack workspace. We will post on the channel `m2-2024-fracture` all the comunications related to the course. You can post your questions related to the course. You can also send us private mesxx§xsages within the slack workspace. You may wish to join also the channel `m2-2024` to have general information and advertisements about the master in Sorbonne. ### Course Material Course material will be distributed in the following shared folder: - https://sdrive.cnrs.fr/s/z5oCtm54ERGokSi ## References We suggest two basic references, available in the shared folder : - J.J. Marigo, Plasticité et Rupture, cours de l'Ecole Polytechnique (in French), Edition 2016 - P.Suquet, Plasticité et Rupture, cours de l'Ecole Polytecnique (in French) A summary in English of the above references can be found in the course of Laura De Lorenzis at ETH (also available in the shared folder) Further suggested references are - J.B Leblond, Mécanique de la rupture fragile et ductile, Hermès - Lavoisier, 2003 (available in the university libraries) - T.L. Anderson, Fracture Mechanics. Fundamentals and applications, CRC Press, Taylor & Francis Group, 2005 - MEALORII Damage Mechanics and Local Approach to Fracture-Ch. 5 and Ch.12 - https://doi.org/10.5281/zenodo.10125170 The online course at http://www.ltas-cm3.ulg.ac.be/FractureMechanics/?p=welcome can be also an additional freely available reference. ## Syllabus Preliminary program: - Lecture 1, 24/09/2024 - Introduction to fracture - Short review of linear elasticity and its variational formulation - Stress criteria and defects in linear elasticity - Lecture 2, 01/10/2024 - Stress singularities (anti-plane case, analytical solutions) - Stress singularities in plane elasticity, fracture modes, fracture toughness, Irwin criterion - Lecture 3, 08/10/2024 - Energetic (variational) approach to fracture, Griffith’s theory - Lecture 4, 15/10/2024 - Energetic (variational) approach to fracture, Griffith’s theory - Lecture 5, 22/10/2024 - Crack propagation - Lecture 6, 05/11/2024 - Crack propagation/fatigue - Lecture 7, 12/11/2024 - Examples - Lecture 8, 19/11/2024 - Examples/Seminar Exam: 26/11/2024, Jussieu Final grade: max (final exam, 80% final exam + 20% homework) ## Computational notebooks Computational notobooks with applications to fracture mechanics are available at the link below: - https://newfrac.github.io/fenicsx-fracture/ in this class we will use in particular: - Meshing: https://newfrac.github.io/fenicsx-fracture/notebooks/linear-elasticity/00-Mesh.html - Linear elasticity: https://newfrac.github.io/fenicsx-fracture/notebooks/linear-elasticity/01-LinearElasticity.html - Linear elastic fracture mechanics : https://newfrac.github.io/fenicsx-fracture/notebooks/linear-elasticity/02-LEFM.html The notebooks are based on the finite element library FEniCSx (https://fenicsproject.org). A tutorial on FEniCSx is available: https://jsdokken.com/dolfinx-tutorial/ Completely the Howework requires to use the library on your laptop. We suggested the following method to install the library on your laptop: - If you are on **linux** or **macosx**, install `https://anaconda.org` and a terminal write - `git clone https://github.com/newfrac/fenicsx-fracture.git` (Dowload the codes) - `cd fenicsx-fracture` - `conda env create -f fenicsx-fracture.yml --yes`(Install the required packages on a python enviroment) - `conda activate fenicsx-fracture` (Activate the python enviroment) - `jupyter-lab` (Open a Jupyter notebook on your browser) - If you are on Widows, use *docker* following the instructions at https://newfrac.github.io/fenicsx-fracture/Index.html - If other methods fails, try the online services with everthing pre-installed: - https://mybinder.org/v2/gh/newfrac/fenicsx-fracture/HEAD - https://codespaces.new/msolides-2024/fenicsx-fracture?quickstart=1 ## Howework - You find the homework subject [here](https://sdrive.cnrs.fr/index.php/f/53555543) - You should submit the homework as a pdf of maximum 4 pages in the folder https://sdrive.cnrs.fr/s/nmZEtQSeHXTBRs9 - Dateline: November ~~15th~~ **18th 2024, 11:00 am**. - One pdf for each group of two students. Name of the file: name1name2.pdf