(Created 2009-08-11.)
 COMPUTATIONAL INELASTICITY FHLN05

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. Optional for: F4, F4tvb, I4, M4, M4mo, Pi4, V4sa. Course coordinator: Professor Matti Ristinmaa, Matti.Ristinmaa@solid.lth.se, Hållfasthetslära. Prerequisites: FHL064 Finite Element Method or ETE110 Modelling and Simulation in Field Theory, or similar course. Assessment: The course is given in seminar form and treats modern aspects of constitutive modelling. Two project assignments should be solved in the course. Examination is based on the two project assignments. The projects consider materially non-linear problems, containing both a theoretical and a numerical part, which are used to solve a practical problem. The three parts will then provide a final grade. Home page: http://www.solid.lth.se.

Aim
The course provides an understanding of the mathematical description of non-linear material behaviour. The student will be provided with the mathematical tools necessary for establishing material models as well as the numerical background necessary for the numerical implementation.

Knowledge and understanding
For a passing grade the student must

• understand the assumptions and simplifications used in the mathematical description of a material model

• explain and use different non-linear elastic models

• understand the framework defining the theories of plasticity and viscoplasticity

• understand the assumptions done in a numerical implementation of a material model

Skills and abilities
For a passing grade the student must

• be able to establish the non-linear finite element formulation as well as the corresponding solution strategies

• write a materially non-linear finite element program

• implement a plasticity/viscoplasticity model

Judgement and approach
For a passing grade the student must

• have the capacity to follow the development taking place regarding material modelling, both with respect to theoretical and numerical issues.

Contents
In the course, non-linear material models are considered, as well as the numerical issues when the models are implemented into a non-linear finite element program.

In the course the following subjects are considered:

• Theory for non-linear elasticity, plasticity theory and different types of fracture criteria

• Finite element formulation of non-linear problems

• Implementation of non-linear material models into a finite element code.

The projects, in which non linear material problems are considered, consist of an analytical part and a numerical part. In the numerical part the material model is implemented. The program is then used for describing the response of a structure.

Literature
Ottosen, N. S. & Ristinmaa, M: The Mechanics of Constitutive Modelling. Elsevier, 2005.
CALFEM - A finite element toolbox to MATLAB. Studentlitteratur.