Multiscale modelling and optimization of complex unit cell based materials for large deformations
We consider heterogeneous porous materials made of metals or polymers, where the microstructure consists of unit cells that are arranged periodically on a Cartesian grid and may show e.g. bistable or auxetic properties. Such materials can be produced by additive manufacturing methods, such as 3D printing. The focus of this talk is on the optimization of the material's interior structure with the aim to obtain the desired macroscopic material behavior under mechanical loading.
Since the macroscopic material behavior depends mainly on the unit cell design, the microstructure has to be taken into account in the simulation and optimization of such metamaterials. Therefore, a multiscale approach has to be introduced, where the effective behavior of the unit cells is used. The description of the unit cells is challenging and cannot be tackled by standard homogenization techniques. Especially the high diversity of possible microstructure designs motivates the introduction of a multiscale model, which uses a database of precomputed microstructures.
For the modeling of the unit cell's mechanical behavior, a database is constructed, where the averaged stress are stored as functions of the strain state, internal variables and geometric parameters of the microstructure. For the fast generation of the database parallel computing is used.
Finally, numerical examples are presented for the solution of the multiscale optimal design problem.