An Average Strain Energy Density-based optimization procedure for design standardized tensile lattice specimens

Lattice structures are widely used in lightweight, high-performance applications, with additive manufacturing enabling the design of components with tailored mechanical properties. However, tensile testing of these structures remains challenging due to their complex geometry and gripping issues. This work proposes a two-steps optimization procedure able to design standard tensile lattice geometry. To efficiently simulate the mechanical behavior of complex lattice topologies, a reduced-order finite element model based on compensated beam theory is developed. To enhance the robustness of the simulations, a novel merit index based on average strain energy density is introduced, reducing mesh dependency. The methodology focuses on the optimization of two geometrical features of the tensile specimen, namely the gripping system and the transition region. These are mechanical components central for the definition of the force flow in the specimen and their characteristics are tuned to obtain an iso-stress condition in the specimen gauge length. To validate the optimization approach, a case study is developed for the BCC cell topology where different cell dimensions and lattice porosities are analyzed. Among the selected configurations, one having a cell side of 4 mm and a porosity of 70% underwent manufacturing and testing process. The material selected is PA12 and the manufacturing technique is MJF. Experimental tensile tests are performed taking advantage of a Digital Image Correlation (DIC) technique to retrieve in large detail the component deformation. A satisfactory agreement is found between finite element simulations and experimental data, validating the proposed optimization framework, paving the way for a standardization of the tensile specimen geometries for lattice structures.