Influence of Boundary Conditions on the Simulation of a Diamond-Type Lattice Structure: A Preliminary Study

Abstract

Emergent additive manufacturing processes allow the use of metallic porous structures in various industrial applications. Because these structures comprise a large number of ordered unit cells, their design using conventional modeling approaches, such as finite elements, becomes a real challenge. A homogenization technique, in which the lattice structure is simulated as a fully dense volume having equivalent material properties, can then be employed. To determine these equivalent material properties, numerical simulations can be performed on a single unit cell of the lattice structure. However, a critical aspect to consider is the boundary conditions applied to the external faces of the unit cell. In the literature, different types of boundary conditions are used, but a comparative study is definitely lacking. In this publication, a diamond-type unit cell is studied in compression by applying different boundary conditions. If the porous structure’s boundaries are free to deform, then the periodic boundary condition is found to be the most representative, but constraint equations must be introduced in the model. If, instead, the porous structure is inserted in a rigid enclosure, it is then better to use frictionless boundary conditions. These preliminary results remain to be validated for other types of unit cells loaded beyond the yield limit of the material.

Mechanical performance of additively manufactured uniform and graded porous structures based on topology-optimized unit cells

“…It’s for sure true that performing any simulation on an assembly different from the real macrostructure, results in deviation of the results. In a study by Terriault and Brailovski, 51 this deviation is discussed for different boundary conditions applied on a unit cell of a lattice structure. Based on this study, FE simulations were conducted on a columnar model under a periodic boundary condition.…”

“…It should be noted that applying this type of boundary condition in symmetric lattice structures leads to the most reliable results close to the entire structure analysis if the boundaries of the macrostructure can move freely. 51…”

“…It should be noted that applying this type of boundary condition in symmetric lattice structures leads to the most reliable results close to the entire structure analysis if the boundaries of the macrostructure can move freely. 51 As topology optimized results of TOSCA consist of tetrahedral pieces, 3 D solid linear elements of 4-node tetrahedral elements (C3D4) were employed to mesh the solid lattice models with six degrees of freedom per node. Also, 3-node triangular shell elements (S3R) were assigned to the thin-walled lattice structures.…”

Thermoauxetic Behavior of Composite Structures

“…However, the results were also validated for samples built of greater number of unit cells as well as with periodic structure. It has been shown [ 49 ] that results obtained for increasing number of repeating unit cell should converge to the results obtained for unit cell with periodic boundary conditions applied. Such convergence was also noticeable in our studies and exemplary results for selected numbers of unit cells Nc and repeating unit cell (RUC) are presented in Figure 7 a.…”