PhD Studentship: Numerical Modelling of Impact and Friction

University of Bristol - Engineering Mathematics

The project:

This project is part of a research theme investigating dynamic behaviour of frictional contact. The project will focus on numerical simulation of frictional contact. Simulation of frictional contact is problematic, because most methods predict non-unique solutions. These numerical methods are also badly conditioned due to the multiple time and length-scales present in the problem. In contrast, theory tells us that the continuum contact problem has unique solutions. This means that there is room for improvement. A recent result [1] addresses this issue in an analytical setting and for point contact only. There is now a rigorous model reduction technique that retains uniqueness and other essential qualitative features of continuum contact problems. The task is therefore to extend this new method so that it can be implemented in numerical schemes.

The main task is to adapt a finite element, boundary element or collocation method using the rigorous model reduction technique [1]. The project does not aim to implement the method in a full-featured finite element software, instead we will take a semi-analytical approach and focus on simple examples, initially. We will start with a classical problem, when an elastic rod hits a rigid surface so that impact and friction need to be considered simultaneously. (This is one representation of Painleve's paradox.) Further tasks involve extending the method to surface-surface contact to study how frictional contact ruptures [2].

[1] R. Szalai, Model reduction of infinite dimensional piecewise-smooth systems,

[2] O. Ben-David, G. Cohen, J. Fineberg The Dynamics of the Onset of Frictional Slip, Science, 330(6001), pp. 211-214, (2010)

If you are interested in this potential PhD project, please visit for more details on funding and eligibility criteria.

How to apply:

Candidates should get in touch prior to applying, as a letter of support from the intended supervisor is required (Dr Robert Szalai,

Please make an online application for this project at Please select > on the Programme Choice page. You will be prompted to enter details of the studentship in the Funding and Research Details sections of the form.

Candidate requirements: 

A minimum of 2.1 honours degree in Applied Mathematics, Physics, Mechanical, and Aerospace Engineering or similar is required.

Basic skills and knowledge required

Experience with programming in MATLAB or other similar scientific programming language (Julia, SciPy) is essential.


If awarded, the successful candidate will be offered one or both of the following: 
• full UK/EU/Overseas PhD tuition fees 
• a tax-free bursary at the current RCUK rate (£14,553 p.a. in 2017/18)


Please contact Dr Robert Szalai,

For general enquiries, please email

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South West England