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# Inverse simulation: going from camera observations of a deformation to material properties using a new theoretical approach

Funding
Competition funded View fees and funding
Type of degree
Doctor of Philosophy
Entry requirements
2:1 honours degree View full entry requirements
Faculty graduate school
Faculty of Engineering and Physical Sciences
Closing date

## About the project

In this PhD project, you’ll develop a new theoretical and computational method for measuring difficult material properties, such as a shock wave, a shear band, or a crack tip. These properties are critical in engineering problems such as car crashes, manufacturing processes, or geotechnical slope stability. Once the material behaviour is understood, we can conduct accurate simulations, such as finite element simulations, to develop a new generation of engineering design and prototyping.

We can already gain a large amount of data from simple experiments by using cameras and 3D x-ray imaging. We want to develop a new method for obtaining the material stress-strain behaviour from the observed deformation field. This is essentially the reverse of the finite element method, which obtains the deformation from the material behaviour.

You'll be working on the theoretical and computational development of the new method, as well as experimental design and implementation to gather data. You’ll work across disciplines to learn different computational procedures, solid mechanics, partial differential equations, machine learning, and experimental design, and will become familiar with different experimental equipment. You will also have the opportunity to explore an area of interest such as machine learning, high speed imaging, or one specific material/application.

This project has a broad focus which will allow you to explore a range of different areas. Ideally, you would have an interest in several of these subjects:

• vector calculus
• partial differential equations
• linear algebra and numerical methods
• coding
• solid mechanics

### Basic method proposal

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 100%, compared to ~10% using conventional methods.