Tension/compression anisotropy enhanced topology design

A strategy for tension/compression anisotropy enhancement of topology optimization approaches is presented. To this end, a spectral decomposition of stresses and strains into tension and compression contributions allows for a multi-material optimization that favors tension or compression affine materials, dependent on the predominant local state. Numerical computations hence yield the topology of a construction part with maximum stiffness at constraint design volume. Additionally, the spatial distribution of a tension affine and a compression affine material is optimized, which is motivated by concrete engineering: financially cheap material, for example concrete, is applied in compression dominant regions in favor of stiffer but more expensive material, which is applied only in tension dominant regions, for example steel. The enhancement is applied both to a classical (mathematical) optimization method and the thermodynamic topology optimization. Several numerical examples are investigated and yield design suggestions for tension/compression sensitive construction parts, e.g., for future lightweight structures made of reinforced concrete.