Adaptation and validation of FFT methods for homogenization of lattice based materials

An FFT framework which preserves a good numerical performance in the case of domains with large regions empty space is proposed and analyzed for its application to lattice based materials. Two spectral solvers specially suited resolve problems containing phases zero stiffness are considered (1) Galerkin approach combined MINRES linear solver discrete differentiation rule (2) modification displacement penalizes indetermination strains regions, leading fully determined equation. The several approaches smooth out surface, on modifying actual voxels not embedded or space. accuracy resulting assessed an octet-lattice by comparison FEM solutions different relative densities discretization levels. It shown that adapted Voigt surface smoothening was best considering accuracy, efficiency h-convergence. With respect it observed becomes competitive compared cells above ≈7%. Finally, show real potential presented, frameworks used simulate behavior printed using direct 3D tomographic data as input. include explicitly simulation roughness internal porosity from fabrication process. simulations allowed quantify reduction well stress localization ≈ 50% near pores.