Inverse design of multiscale structures and meta-materials by topology optimization and dehomogenization

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• Prof. Ole Sigmund, Technical University of Denmark
• Friday 14 June 2024, 14:00-15:00
• Department of Engineering - tbc.

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The large geometrical freedom allowed by developments in additive manufacturing (AM) allows for realization of extreme, complex structures and has spurred a surge in the use and manufacturing of architected lattice structures and meta materials. Apart from purely structural applications, inverse design and multiscale optimization has applications in thermal, optical, hydraulic and many others.

Topology optimization (TO) is a highly efficient inverse design tool for optimizing complex problems modelled by partial differential equations and builds on voxel-based design parameterizations, deterministic optimization approaches based on adjoint methods for computing gradients. TO has been implemented as interactive apps (see TopOpt and TopOpt3D apps on AppStore) and has been applied to full-scale airplane wing design with discretizations by billions of finite elements on super computers.

Different paths may be considered for saving CPU costs. Although popular, and showing promise in many areas, AI or CNN -based approaches have so far not been proven efficient in solving TO problems directly. Main issues are high cost of training and data generation (high break-even costs) and low generality (change of boundary conditions requires retraining).

A promising path is multiscale optimization that makes use of the knowledge of the homogenized properties of extreme microstructures to perform the optimization on coarse meshes and sub-sequently realizing the multiscale structure by so-called dehomogenization. Dehomogenization is based on computer graphics techniques and the combined procedure thus has potential to be solved interactively on apps, as for the single scale apps mentioned above, albeit with much higher resolutions.

The talk will give a brief introduction to TO and a discussion of the relevance of various optimization techniques, followed by a deeper dive into multiscale and dehomogenization techniques that take stiffness, strength as well as local and global buckling stability of multiscale lattice structures into account. Time permitting, recent results on design of meta materials with extreme non-linear responses as well as non-perfect realizations will also be included.

This talk is part of the Engineering - Mechanics Colloquia Research Seminars series.

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