Multi-Scale Simulation of Stress Wave Propagation for Accurate Geometric Representation of Materials

This research will involve the further development of a novel code for multi-scale simulations (using different meshes in the same simulation, fine and coarse) that model the behaviour of materials, with particular attention to wave phenomena (stress waves) that occur during the rapid mechanical excitations (i.e. vibration) of materials systems and structures.

The project will focus on the coupling mechanics (i.e. how a fine and coarse mesh interact with each other) during simulations, where fine meshing will be used on areas of a material where damage phenomena is expected, and therefore a coarse mesh will not accurately model the structure. However, a coarse mesh will be utilised in most places along the material during the same simulation, where the material is expected to have little deformity, whereby a coarse mesh is more than sufficient and this would significantly improve the computational time. The research will also focus on applications of NURBS (a well-known technique in the realm of research in numerical modelling, for ensuring that a simulation models a shape accurately) for modelling of complex geometries in particular, as the current finite element based simulations pose difficulties with accurate representation of a structures geometry.
The impact of the research will be the development of new computational mathematical techniques for tackling many of the typical problems that are associated with multi-scale modelling, as mentioned, these problems stem from issues in the coupling mechanics and the accurate representation of a materials geometry.

All engineering companies that apply finite element simulations to their work (nearly every large engineering company) wish for ways to reduce the computational time of their simulations as long as it does not sacrifice accuracy, therefore, the development of an accurate simulation technique where fine meshing (that takes a large amount of time) coupled accurately to a coarse mesh (that takes far less time) that can be applied to areas of less interest along a structure, would certainly have an impact on the industry, as long as the geometry of the actual structure can be modelled sufficiently well. Some companies will already be developing multi-scale code in-house, but the implementation of the new techniques that will be developed during this research will still have a large impact on the success of these solvers.

Aims and objectives;

1. Derive a novel mathematical technique for a more accurate modelling of coupling mechanics at the boundary between a fine and coarse mesh then the current industry techniques. A stress wave will then be simulated along a material and the accuracy of the computer simulation will be compared to experimental data.
2. Apply the use of NURBS to more accurately model the geometry of a structure. Due to the novelty of the multi-scale framework, a novel technique for applying NURBS will need to formulated both mathematically and computationally.

A stress wave will again be modelled and compared to experimental data.

This project falls within the EPSRC Materials Engineering - metals and alloys research area.
This project is part-funded by Rolls-Royce and so there will be some collaboration with them and their materials department. At this stage it is not decided how involved Rolls-Royce wish to be in the research, I am hoping they can experimentally model some aerospace grade metal and I can compare my results against this.