SC11 Georges Cailletaud

Short Course

 ”Plasticity and creep: from basic concepts to finite element implementation”
by Georges Cailletaud (MINES ParisTech, Centre des Matériaux)

The main purpose of this course is to create a synergy between people interested in material modeling from a microstructural point of view and those who work on constitutive equations. The ultimate goal is to have in hand good – physically based – models available in the current commercial finite element codes and to use them for the computation of industrial components and structures.

10:00 – 10:30 Registration
10:30 – 11:30 Session 1. Rheology. This session reviews the different types of linear and nonlinear behavior of materials, time-independent plasticity, viscoplasticity, viscoelasticity. As an introduction to rheology, it is devoted to explain the various types of relations linking stress, strain, and their time derivatives. In order to reflect more accurately the nature of the equations, it is limited for now to a description under onedimensional loading. The different concepts are introduced based on various elements such as springs and shock absorbers, rheological models. The concept of internal variable is described and the way various effects (ratchetting, aging, strain memory…) can be modelled is presented.
11:30 – 11:45 Coffee break
11:45 – 12:45 Session 2. Criteria. Having characterized the flow under onedimensional loading, the construction of general constitutive equations requires the definition of a yield surface, which characterizes the place from where (visco-)plastic flow operates. This section covers both the case of materials that are only sensitive to the stress deviator, and the material sensitive to hydrostatic pressure. Just as there are a bunch of rheological models, there is a wide variety of criteria describing the yield surface. Multisurface models (for crystal plasticity) are also briefly presented.
12:45 – 14:00 Lunch break (lunch not included)
14:00 – 15:00 Session 3. 3D formulation. This session combines the achievements of the previous two hours to build a general framework for 3D models, ready to implement in a computation code. In a first approach, we consider only models without hardening, for which the yield strength (possibly reduced to the origin in the case of certain models of viscoplasticity) remains unchanged throughout the loading. The effect of strain hardening is then introduced following a modular approach in order to have in hand the best quality/price model for a given application.
15:00 – 15:15 Coffee break
15:15 – 16:15 Session 4. FE implementation.   This last session shows a general technique that allows to easily implement in a finite element code any type of model  based on the previous formalism (i.e., using building bricks such as potential, plastic flow, isotropic/kinematic hardening). Explicit and implicit formulations are compared. Typical examples taken from the ZéBuLoN software, developed at MINES ParisTech, ONERA and NWNumerics are offered to illustrate the methodology. At the end of the course, it is expected that the students are able to implement their own models in user material subroutines of the main commercial codes.


Handouts All slides in pdf format will be provided at the beginning of the SC. They will be available on the teaching site (http://mms2 NULL.ensmp under the form of a new module. The contents of this site is regulated by the Creative Commons contract ( (http://creativecommons, allowing the reader to share, remix and reuse the available documents.


Speaker Georges Cailletaud is Professor of mechanics of materials at MINES ParisTech (Paris, France). He is the head of the CNRS research unit “Centre des Matériaux” and Deputy Director of the Mechanics and Materials Department of MINES ParisTech. He got his engineering degree from Ecole Centrale Paris (1975), then a PhD (1979) and a Thèse d’état (1987) from Université Paris VI (France).  His research is first focused on model development: Plasticity and viscoplasticity theories, thermomechanical fatigue, crystal plasticity, brittle failure, creep-fatigue failure, multiaxial fatigue, cyclic tests. He works on new model classes, at the macroscale (multipotential models), and in the micro-macro framework (self-consistent approach for polycrystals). He is also interested in numerical studies: FE code, integration procedures for highly non linear models, development of FE code. He has been involved in the development of ZébuLoN project for more than 25 years. He is the co-author of more than 120 journal papers and of one book (“Non-Linear Mechanics of Materials”- Springer, 2010).