Multiscale isogeometric topology optimization for fatigue-resistant lattice materials with additive manufacturing-induced geometric defects

Lattice materials are being widely adopted for cyclic load-bearing applications, such as lattice hip implants. However, metal additive manufacturing-induced geometric defects and material imperfections act as stress raisers, strongly affecting their fatigue resistance. This study optimizes the fatigue resistance of structures made of defective lattice materials by introducing a multiscale isogeometric topology optimization (MITO) framework, which incorporates microscale fatigue damage constraints into the optimization process. The optimization objective is to minimize the structural compliance, subject to a global volume constraint and a worst-case microscale fatigue damage constraint aggregated via a modified p-norm function. The high-cycle fatigue damage of defective lattice materials is evaluated via the modified Soderberg criterion. To achieve clear and well-defined topology boundaries, a Heaviside projection scheme is embedded into the material interpolation model based on the solid isotropic material with penalization (SIMP) method. The sensitivities of the fatigue damage constraint with respect to the design variables are derived using the adjoint method, and the optimization is solved via the Method of Moving Asymptotes (MMA). Numerical examples of 2D and 3D benchmark structures with various defective lattice materials under different loading amplitudes demonstrate the robustness and effectiveness of the proposed method. The framework is further extended to incorporate the modified Goodman criterion, verifying its applicability under different fatigue evaluation models. The presented method offers an efficient design route for fatigue-resistant optimization of defective lattices.