Elastic-plastic homogenization of polymeric thin-walled lattice structures for prototypal structural applications

The demand for lightweight components, yet mechanically robust, has driven the exploration of lattice structures. These forms offer superior weight-to-strength ratios compared to traditional bulk materials making them suitable for structural applications and easily achievable with additive manufacturing. This study investigates the elastic-plastic behaviour of Polyamide 12 (PA12) lattice structures manufactured via multi jet fusion (MJF), and experimental, numerical, and theoretical approaches are combined to develop a robust framework for the mechanical homogenization of these structures. Tensile tests were performed on bulk samples to characterise the constitutive behaviour. The obtained elastic-plastic model was then employed in the homogenization process, which was performed through the application of periodic boundary conditions on a representative volume element (RVE) with finite element analysis. In particular, given that the hardening of RVE depends on load direction, a simplified approach is proposed to describe the anisotropic plastic behaviour. This combines Hill yielding criterion and Levy-Mises plastic flow rule, and it accounts for direction-dependent hardening, enabling efficient prediction of lattice behaviour under complex loading scenarios. In addition, the elastic-plastic homogenized properties were calculated by varying the aspect ratio (AR) of the unit cell, thus obtaining mathematical expressions to describe the dependence of homogenized mechanical properties on AR. The elastic-plastic homogenization process was validated both numerically and experimentally through two geometries of optimized graded strut-based lattice specimens. The outcomes of numerical and experimental tensile tests on the lattice specimens were compared with the corresponding numerical results obtained from tensile tests on homogenized specimens. The comparison demonstrated the ability of the homogenized model to describe numerical and experimental tensile tests with a good level of accuracy. Findings highlight the potential of the proposed methodology for structural optimization and mechanical performance prediction in applications which require lightweight and durable materials, such as automotive, aerospace, and biomedical devices.