A numerical study of lattice metamaterial in mixed finite element models

Additive technologies open new possibilities for creating personalized implants with inhomogeneous structures. Numerical analysis of such endoprostheses is accompanied by some difficulties associated with the geometric irregularity, local thickness differences, and complex spatial topology caused by microstructural features, which requires the development of specialised approaches to discretisation. This motivates the development of models combining different element types to achieve a balance between computational efficiency and accuracy. The work is devoted to numerical modeling of lattice metamaterials manufactured using additive technologies. The object of the study is a metamaterial with a lattice structure intended for use in intramedullary nails. Five finite element models including beam, shell and solid elements in different combinations and with different boundary conditions were developed to investigate the stress-strain state. The mesh convergence of von Mises stresses at three characteristic points of the structure and the resultant reaction force was evaluated for each model. The in-situ tests data of lattice and solid specimens were used to verify the numerical results. The magnitude of the resultant response in the numerical simulation was higher than the median in-situ test data, but was within the confidence interval. The solid-only model showed the largest magnitudes of the resultant response when the boundary conditions were varied. The mixed model including beam, shell and solid elements showed the most accurate match with the experimental data. At the same time, the balance between accuracy and computational time was provided by the model consisting solely of beam elements. The elastic modulus from in-situ experiments of solid specimens was used in the calculations. The obtained results emphasize the specifics of numerical modeling of irregular porous structures, including the presence of macro- and mesoporosity, residual stresses and geometric errors during manufacturing or operation, and the importance of verification of numerical models with in-situ test data to improve the reliability of predicting the behaviour of implants in clinical conditions.