Combining neural networks with multiscale techniques for lattice unit cell design

Resumo

Complex non-linear mapping between the input and output data is one of the advantages of neural net-
works. The aim of this work is to train a neural network to generate the optimum unit cell topology for a given

constitutive elastic matrix. In order to reverse homogenization, the neural network maps the correlation between

the shape of the unit cell and the constitutive elastic characteristics. With data produced from a collection of var-
ious geometries, a dataset of elastic properties and respective geometries was developed. All of these geometries

underwent homogenization using periodic boundary conditions. To lessen their impact on the homogenized consti-
tutive matrix, the lattice was modeled as a biphasic material, with the solid phase having the material’s properties

and the remaining area of the representative volume element (RVE) being treated as the void phase. To make it
possible to directly impose the periodic boundary conditions, a uniform mesh of square 2D elements was used.

The dataset includes truss-like unit cells based on the FCC and BCC systems, as well as gyroid-like unit-cells, sim-
plified to a 2D representation. In order to increase the dataset, operations between basic unit cell geometries were

applied as well as rotations of the unit cell. The neural network is capable of suggesting unit cells. The non-linear
mapping between the unit cell elastic properties and geometry reduces the computational cost of running structural
optimization to create a unit cell which presents the required properties, for example.