Topology optimization of imperfect lattice materials built with process-induced defects via Powder Bed Fusion

•Manufacturing defects impart anisotropy to elastic moduli of lattice materials.•Topology optimization problem reformulated to account for geometric defects.•Optimized elasticity gradients depend on defects and building direction.•Manufacturing defects affect global compliance. Lattice materials built via additive manufacturing feature process-induced defects that impact their mechanical properties and optimum design. This work presents a methodology to integrate geometric defects in a density-based formulation for topology optimization of additively built lattice materials. The method combines imperfect unit cell models capturing their geometric defects with a homogenization scheme upscaling their effective properties, into a topology optimization formulation. The method is of general application, and it is here demonstrated through the application to two cell topologies, the Tetrahedron-based and the Octet-truss unit cells, called to satisfy specific geometric constraints. Verification is performed through the solution of two well-known benchmark problems in 3D: the fixed-beam and the L-shaped beam, assumed to consist of either defect-free or imperfect lattice materials. The impact of process-induced defects, and cell orientation is demonstrated on the elastic anisotropy of the unit cell, the optimized gradients of relative density and the global compliance of the beams. The results highlight the significance of accounting for geometric defects in topology optimization of additively built lattice materials.