RUB Bauwesen CompEng


Block lecture: "Energy Methods in Material Modeling" - Dr. Fechte-Heinen 

The block lecture will take place on the following dates:

- Sa., 8.11.14, 10-18:00
- Mi., 12.11.14, 17-21:00
- Mi., 19.11.14, 17-21:00
- Mi., 26.11.14, 17-21:00
- Mi., 03.12.14, 17-21:00
- Mi., 10.12.14, 17-21:00
- Sa., 13.13.14, 10-18:00

the place will be announced soon.

The goals of the course are fundamental knowledge about energy methods in material modelling,
the underlying mathematical concepts and numerical estimates for simulating
microstructural aspects of
the material behavior of solids.

Overview of the content:
In a variety of modern engineering materials, such as shape memory alloys or multiphase steels,
the transformation between different crystallographic phases is technically used to obtain outstanding material properties.
This course first gives a short introduction to these phase transformation phenomena and the underlying mechanisms.
Then, the origin of multiphase microstructures is discussed against the background of energy minimization.
Suitable mathematical concepts are shown which in principle allow the prediction of the microstructural
and macroscopic material properties of such materials.

Different approaches to numerically estimate the material behavior are given.
Finally, the theoretical and numerical concepts are exemplified establishing micromechanical material models
for shape memory alloys.

The structure of the course is as follows:

1. Introduction
1. Energy methods and material models
2. Examples: - martensitic microstructures - shape memory alloys - multiphase steels
2. Energy minimization of phase transforming materials
1. Boundedness
2. Coercivity
3. Notions of convexity
3. Estimates of the energetically optimal microstructure
1. Quasiconvexification
2. Convexification
3. Polyconvexification
4. Rank-1-convexification
4. Example: Shape memory alloys
1. Introduction and material model
2. Convexification
3. Translation method
4. Lamination