# Contact Mechanics

Options for contact analysis are available in many commercial finite element programs. The goal of this class is a deep understanding of the mathematical and computational “secrets” behind robust algorithms and to enable students to think critically and to arrive at sound judgements of the results.

Tyre deformed by the contact with the soil

You are interested in sophisticated mechanical problems, you want to investigate further numerical methods, join our contact mechanics module!

You will learn the general principles on the mathematical description and computational treatment of contact problems by Finite Element Approximation.

You will also be able to review sophisticated modeling approaches and solution techniques and to judge the computed results under consideration of the model assumptions.

## Contents: computational aspects for contact mechanics

• In detail, the following issues will be tackled:
• Introduction and needs for computational techniques for the analysis of contact problems; historical review and motivation based  on simple problems from basic engineering mechanics
• Analytical solutions based on elastic half-space assumptions, engineering modeling approaches
• Treatment of unilateral constraints, mathematical aspects and computational issues
• Brief repetition on non-linear continuums mechanics and related Finite Element techniques
• Kinematics of contact of deformable bodies, differential geometry approach
• Computational treatment of unilateral (frictionless) contact within a Finite Element framework
• Computational treatment of frictional tangential contact within a Finite Element framework
• Outlook for sophisticated engineering applications, e.g.:
• rolling contact,
• contact at microscopic length scales,
• thermo-mechanical contact, heat transfer and frictional heating,
• homogenization,

## Material & Methods

Algorithms are developed and experienced based on an existing open finite element system written in Matlab language.

Example of previous student project: rough surface contact

Schematic representation of the contact between two rough surfaces at lower scale

## Evaluation

Evaluation is based on final project which consists of:

• a final report in an article template,
• an oral presentation as a seminar for all other participants.

The project topic is established in accordance with own student interests.

## References

P. Wriggers, Computational Contact Mechanics, Springer, 2006.
T.A. Laursen, Computational Contact and Impact Mechanics,  Springer, 2003.