Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

• An approximate constitutive model is built for local material microstructure using a database model.
• The database is further reduced into a separated representation by means of tensor decomposition.
• The approximate constitutive law can well serve structural design with a reduced computational cost.

This paper builds on our recent work (Xia and Breitkopf, 2014) on multiscale structural topology optimization where at the microscopic scale, local materials are optimized concurrently according to current loading status. The former design framework requires intensive computational cost due to large number of repetitive local material optimizations. To circumvent this limitation, in the present work, we construct a reduced database model viewing the local material optimization process as a generalized constitutive behavior using separated representations. In this model, the database is built from a set of numerical experiments of local material optimizations in the macroscopic strain tensor space. Each value in the database corresponds to the strain energy density evaluated on a material microstructure, optimized according to the imposed macroscopic strain. By tensor decomposition, a continuous representation of the strain energy density is built as a sum of products of one dimensional interpolation functions. As a result of this a priori off-line step, the effective strain–energy and stress–strain relations required for macroscopic structural evaluation and optimization are provided in a numerically explicit manner. The results given by the reduced database model are compared with full-scale results. It is also shown that this explicit constitutive behavior representation can well serve multiscale structural design at a significantly reduced computational cost.