Concurrent Multiscale Modelling for Structural Integrity

One aims to address the problem of multiscale manifestations of phenomena surrounding deformation,
fracture and damage that dynamically change the multiplicity of contacts within the complex assemblies
comprised within an aerospace engine. Mathematically, the key challenge arises from the fact that highly
dynamic events are commonly simulated using Finite Elements (in space) and Finite Differences (in time)
discretisation, whereby refinement within the same model at the same length scale introduces numerical
errors that are known and quantifiable. Hence, an opportunity arises, with increasing computational power,
for the mass-conserving and energy dissipative problems in limited portions of the overall domain, to be
considered by the following:
* Exploration of novel algorithms that are compatible with finite element simulations to reduce
computational cost without sacrificing accuracy
* Assessing the accuracy of the computation via error estimators
* Determining the size of the sub-domain needed for further sub-discretisation, whilst considering the
need for material heterogeneities and structure
* Conducting the mapping of fields from higher to lower length scales concurrently
* Computing the response of materials at the lower length scales and returning them back to the
portions of the domain at the scales above
These mass-conserving energy dissipative problems, where roughly 5-10% of the domain will require
refinement are exemplified by the real-life scenario of "birdstrike". This very small area contains the high
frequency stress waves, whereas the rest of the domain acts in an elastic manner. Energy dissipative impact
events such as birdstrike are an example of these kinds of problems and are prominent issues for gas turbine
engines. It is well known that refinement methods at the same scale that lead to different sized finite
elements can produce spurious waves and the filtering of stress waves. Therefore, the very localised plastic
strain obtained in applications, like the above, provide strong motivation for the study of multiscale
simulations as one looks to better understand the behaviour in portion of the domain where elements do not
behave elastically.
This project falls within the EPSRC ASiMoV (Large scale computation of complex multi-body assemblies), of
which involves collaborators from the University of Cambridge, Bristol University, University of Warwick and
EPCC (Edinburgh). Industrially, the project is closely tied to Rolls Royce plc, where the consortium's key aim is
to run large scale thermo-mechanical-electromagnetic simulations of gas turbine engines on high
performance computers.