RICAM Colloquium - Gregoire Allaire
April 17, 2025, 13:00, SP2 416-2
This work is concerned with the so-called de-homogenization method for the topology optimization of lattice materials, i.e., porous structures made of periodically perforated material, where the microscopic periodic cell can be macroscopically modulated and oriented. Lattice materials are becoming increasingly popular since they can be built by additive manufacturing techniques. The de-homogenization method works in three steps. In a first (off-line) step the homogenized properties of the chosen parametrized periodicity cell are computed for a large range of parameter values. In a second (classical) step one optimizes a lattice structure for the homogenized formulation of the problem. Finally, the third (and most delicate) step is to project the optimal underlying microstructure, corresponding to the optimal homogenized properties, at a desired length-scale. The main difficulty in this de-homogenization approach is the reconstruction of a global orientation of the lattice.
The main novelty of our work is, in a plane setting, the conformal treatment of the optimal orientation of the microstructure. In other words, although the periodicity cell has varying parameters and orientation throughout the computational domain, the angles between its members or bars are conserved. One advantage of the de-homogenization method is its low computational cost. Several numerical examples are presented for compliance minimization in 2-d and 3-d case.
This is a joint work with Perle Geoffroy-Donders and Olivier Pantz.