Course code MP06
Course title Nonlinear Computational Mechanics
Institution Mines ParisTech
Course address Mines ParisTech, 60 boulevard Saint Michel
City Paris
Minimum year of study 4th year
Minimum level of English Good
Minimum level of French None
Key words Plasticity, material models, large deformation, finite element, computational mechanics
Language English
Professor responsible Matthieu MAZIERE (MINES ParisTech)
Participating professors Samuel FOREST, Matthieu MAZIERE, Vladislav YASTREBOV  (CDM, Mines ParisTech) Michel BELLET, Youssef MESRI (CEMEF, Mines ParisTech), Vincent CHIARUTTINI (ONERA)
Number of places Minimum: 6, Maximum: 20, Reserved for local students:

The field of Nonlinear Computational Mechanics has grown very rapidly during the last decade. Due to the dramatic power increase of computers and workstations, research  is very active. On the other hand, the development of robust and user friendly engineering softwares allows a wide range of applications in industry. The course presents an overview of the classical models and of the numerical methods used in the area, and shows how they can be applied in practical cases. Theory includes material and geometrical nonlinearities, and the numerical implementation in computer codes. Applications are taken from classical domains like aeronautical, spatial or car industry, but also from microelectronics, the field of energy for sustainable development, biomaterials, etc...

 More detailed objectives

Computer labs are planned in the cursus. Students will be invited to choose their style: as developers, they will have the opportunity to introduce new features in a selected finite element code; as user, they will have to perform finite element analyses on simple case studies involving material and/or geometrical nonlinearities. 


After the course, attendants should have a good knowledge of some basic aspects in mechanics of material, including the material constitutive equations, the numerical algorithms and the finite element procedures. They will have the ability :

- to choose a material model and the proper procedure to identify the material parameters from experiment;

- to perform calculations of the stress or temperature fields in nonlinear cases, and to successfully manage the iterative processes associated to nonlinearities;

- to deal with contact problems;

- to evaluate the quality of a FE result obtained with a nonlinear computation (mesh sensitivity, numerical integration).
Programme to be followed

Basic material models :  material modelling, including rheology, plasticity criterion, incremental theory of plasticity, 3D plastic flow, basic hardening rules. Identification procedures, inverse problems.

Advanced constitutive equations : cyclic and complex loadings, damage models, models for thermomechanical loadings, hyperelasticity, polymeric materials

Finite element formulation : elementary introduction of the method for thermal and mechanical applications. Newton technique, element assembly, tangent matrix. Integration of the constitutive equations, implicit algorithms.

Geometrical nonlinear and contact analysis, stabilization methods. Stability problems. Localization process. Mesh adaptation.

Coupled problems (thermal-metallurgical-mechanical interactions).

It is mandatory to have a basic knowledge of linear algebra and calculus, and a basic knowledge in continuum mechanics (stress, strain, linear elasticity)

Course is easier for students who have already attended a basic Finite Element course, and who have already manipulated a FE code (not required).

Being curious about mechanical problems, having a good knowledge of plasticity theory would be a must, but is not really needed.

A good practice of English speaking and reading is mandatory.

The course will have a website, that will be updated one week before the course:

Students are also invited to navigate on:

This last link is a linear FE course (mostly in french). The part of the theory will be smaller in « nonlinear computational mechanics » than for this one.
Course exam During the last afternoon devoted to computer labs, students are requested to show their numerical results in a 20-30 minute oral presentation (prepared by group of 2).