Section: New Results

Topology Optimization of Parametrized Stochastic Microstructures

Participants : Jonàs Martínez Bayona, Sylvain Lefebvre.

Different works have explored the topology optimization of parametrized periodic microstructures by the homogenization method. A promising venue of work lies in Additive Manufacturing technologies, that allow us to physically realize the intricate designs obtained with topology optimization. In order to fabricate the results, the parametrized microstructures must be projected at some finite scale taking into account the minimum printable size. However, for periodic microstructures it remains difficult to project and continuously grade the material properties since the boundary and transition between tiles has to be carefully handled.

We have an ongoing project in collaboration with Perle Geoffroy-Donders and Grégoire Allaire at École Polytechnique, to investigate the applicability of stochastic microstructures for topology optimization. This year we studied two different stochastic microstructures (isotropic and orthotropic) solely parametrized by an anisotropic metric and a Poisson point process. Both stochastic microstructures are amenable to efficient and scalable computation of their geometry. Unlike previous methods dealing with the projection of orthotropic microstructures the presented microstructures are able to easily follow a field of orthotropy orientation (see Figure 4).

Figure 4. Optimization of a bridge problem with an orthotropic material, and our parametric stochastic microstructure. Left: Optimized parameters of the microstructure (density, angle of orthotropy, and degree of orthotropy). Right: Projection of the stochastic microstructure at a finite scale.