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.
Highlights
Porous metals, called metallic foams, are increasingly used in many different applications, especially in the aerospace and medical fields [1, 2]
Simulations based on numerical techniques such as finite elements are generally used in the design process to determine the optimal porosity and morphology of the foam
Numerical simulations using the complete and detailed geometry of the entire porous structure become impracticable in terms of computational cost as soon as the studied geometry comprises a large number of pores
Summary
Called metallic foams, are increasingly used in many different applications, especially in the aerospace and medical fields [1, 2]. A multiscale modeling approach, otherwise known as a homogenization technique, must be used [3], and the behavior of a porous volume is assumed to be similar to that of a fully dense homogeneous volume having fictive properties (Young’s modulus, yield stress, thermal resistance, etc.). This strategy is frequently used for heterogeneous materials such as composites or foams. For a foam material having a given morphology, these fictive properties are related to the porosity level through the use of scaling relations [4], which are generally obtained by performing finite element simulations on a relatively small volume of porous material. The unit cell is the smallest geometry that is copied in several directions to obtain the ordered porous structure
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