Reduced-order topology optimisation of high-resolution microstructures with internal contact

Exploiting the full potential of additive manufacturing methods requires a leap forward in advanced modelling and computing techniques.

While additive manufacturing enables the high-precision fabrication of architectured mechanical (meta)materials, its design is currently driven by human experience. As such, it could greatly benefit from numerical Topology Optimisation (TO) techniques. The µFFTTO project addresses two challenges of in-silico design of high-resolution architectured microstructures.

First, state-of-the-art finite element computational homogenisation approaches, even when accelerated with highly efficient Fast Fourier Transform (FFT) techniques, are too costly for microstructures discretised into billions of voxels.

I will significantly reduce their cost by developing a novel mesh coarsening technique based on low-rank tensor approximations.

Second, as the manufacturing resolutions reach micrometre accuracy and the surface-to-volume ratio increases, surface effects, including adhesive contact, need to be accounted for in the TO formulations. This project will incorporate adhesive interaction into the low-rank FFT-based computational homogenisation scheme.

As a result, the µFFTTO project will deliver computationally and memory affordable algorithms for microstructure TO on regular grids, which account for internal contacts with adhesion and are directly transferable to contemporary fabrication techniques.

The project will be conducted in cooperation with leading experts on multiscale modelling and additive manufacturing from the livMatS Cluster of Excellence, University of Freiburg, Germany, with an emphasis on future collaboration with and knowledge transfer to the Czech Republic and Slovakia.