CONSTITUTIVE MODELLING OF MATERIALS, ADVANCED COURSE | FHL072 |

**Aim**

The course provides an understanding of the mathematical description of non-linear material behavior. The student will be provided with the mathematical tools necessary for establishing material models as well as and 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 viscoplaticity
- 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.

**Literature**

Ottosen, N. S. & Ristinmaa, M: The Mechanics of Constitutive Modelling. Elsevier, 2005.

CALFEM - A finite element toolbox to MATLAB. KFS.