Fraunhofer Institute for Industrial Mathematics ITWMDescription
In aircraft construction, paints that actively counteract corrosion have been used for a long time. The toxic chromates currently used as corrosion inhibitors must be replaced by environmentally friendly alternatives. Structural optimisation by numerical simulation of diffusion processes can help to select particularly promising candidates from the multitude of possible formulations. Stochastic structural models are needed for this. Stochastic germ-grain models are basically suitable for this. The challenge lies in modelling the high variability with regard to the size and shape distribution of the typical grain and the interaction of different structural components with sufficient accuracy. Structural information is obtained from nano-computed tomography.
In this PhD project
1. a stochastic model for compact grains is developed, which allows the simulation of complex grain shapes on the basis of a few parameters
2. germ-grain models whose typical grain follows a mixture distribution are simulated
3. the covariances of the grain fractions are analysed on the basis of 3D image data and adapted to these observations
4. realisations of the geometry models for the simulation of the diffusion processes are generated and adapted to measurements.
For the typical grain, deterministic basic bodies and their random scaling and deformation by compression or stretching of axes are initially considered. More complex grain models are cells of stochastic mosaics. Laguerre mosaics [L] or hyperplane mosaics [H] are suitable here.
[L] K. Losch, S. Schuff, F. Balle, T. Beck, C. Redenbach (2019) A Stochastic Microstructure Model for Particle Reinforced Aluminium Matrix Composites. Journal of Microscopy. 273 (2), 115-126
[H] Ballani, F., van den Boogaart, K.G. (2014) Weighted Poisson Cells as Models for Random Convex Polytopes. Methodol Comput Appl Probab 16, 369–384