Funded PhD position at the University of Southampton, UK

There is an opening for a funded PhD in mechanical engineering at the University of Southampton starting Fall 2023 or Spring 2024, under the supervision of Dr. Benjamin Cameron. This will involve the development of novel theoretical/computational methods to extract material properties from digital image correlation (or digital volume correlation) data in complex settings. See below for a more detailed description of the project. 

Students with an interest in numerical methods, partial differential equations, solid mechanics, mechanical engineering, and/or mathematics are encouraged to apply.

If you are interested, please contact Dr. Cameron directly at b.c.cameron@soton.ac.uk with your CV.

Project description:

This PhD is focussed on a new theoretical/computational method to measure material properties in places where they are really difficult to measure: e.g. in a shock wave, in a shear band, or at a crack tip. These are all of critical importance in many engineering problems such as car crashes, manufacturing processes, or geotechnical slope stability – but it remains an ongoing technical challenge. Once the material behaviour in these settings is understood, we can conduct far more accurate simulations, such as finite element simulations, enabling a new generation of engineering design and prototyping.

Cameras and 3D x-ray imaging have enabled huge amounts of data to be obtained even from simple experiments. We want to develop a new method to obtain the material stress-strain behaviour from the observed deformation field, essentially the reverse of the finite element method which obtains the deformation from the material behaviour.

Your PhD will be focussed on in depth theoretical/computational development of the method, however, there will also be some experimental design and implementation to obtain data. As the PhD is very interdisciplinary, you will learn different computational procedures, solid mechanics, partial differential equations, machine learning, and experimental design, and you will become familiar with a lot of different experimental equipment. Later on in your PhD, depending on your interest, you will have the opportunity to go deeper into something that you’re interested in, such as machine learning, high speed imaging, or one specific material/application. This is an ideal PhD project for someone who wants to become familiar with a range of things rather than being narrowly focussed on one specific area. Ideally, you would have a strong interest several of the following subjects: vector calculus, partial differential equations, linear algebra, and numerical methods, coding, and/or solid mechanics.

The basic idea of the method you will be working on is as follows. The deformation is recorded using a camera (dots are spray painted so the position and strain field can be determined using digital image correlation (DIC)). A system of partial differential equations are solved to obtain the stress using the finite volume method (similar to the finite element method). Then once we have the stress and strain, we can directly calculate material properties. For the example of a necking tensile specimen, one can determine the stress-strain behaviour right inside the neck at strains at 100%, compared to ~10% using conventional methods.