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ATHENS - MP06 - Nonlinear Computational Mechanics

Sigle: MP6924, ECTS: 2

Objectifs du cours

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 software 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...
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 users, 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).


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.


  • Basic material models :  material modeling, 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, foams and cellular systems, 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).

Modalités d'évaluation

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).

Modalités pédagogiques

Le programme journalier du cours sera consultable 10 jours environ avant le début de l'enseignement sur www.ensmp.fr (rubrique Ingénieurs civils).


The course will have a website, that will be updated one week before the course. This will be an evolution (in english) of the following old site: http://mms2.ensmp.fr/msi_paris/accueil_msi_paris.php
Students are also invited to navigate on: http://mms2.ensmp.fr/ef_paris/accueil_ef_paris.php

Equipe pédagogique


Chargé(s) d'enseignement

Michel BELLET ; Lionel FOURMENT ; Arjen ROOS
Sigle MP6924
Année 2ème & 3ème année
Niveau Graduate 1st year, Graduate 2nd year
Crédits ECTS 2
Coefficient 2
Nb. d'heures 37
Nb. de séances 30
Type de cours Descriptifs complémentaires
Semestre 4, 6
Période Printemps
  • Matériaux
Dernière mise à jour:
20 Jun 2017 11:17 par julien