**1. Introduction**

Generally, solid is composed of stereoscopic structure. The stereoscopic structure is a model based on two-dimension, three-dimension, and four-dimension in a space. The two-dimension is two axis like horizontal direction and vertical direction in a plane. The three-dimensional structure has three axes such as x, y, and z coordination, for instance, a vector. The four-dimensional structure has four axes such as optical illusion, for example, a cubic box. If the box is torn at every corner, then it can make a two-dimensional plane. If it is folded up, it can make a cubic box. This is called as tesseract, hypercube, or 8-cell regular octachoron. These are based on a geometrical concept in mathematics. It is the four-dimensional object called as hypercube or tesseract shown in **Figure 1**.

Applications of the hypercube were shape or size optimization for non-probabilistic description of uncertainty as computer aided optimum design of structure [1], optimal communication algorithms for hypercubes [2], parallel computing on a hypercube [3], structure connectivity [4], and so on.

It is interested in to create a unit cell model like honeycomb or open-cell in a sandwich core structure.

**Figure 1.** *Schematic of a hypercube.*

Hypercube originates from a point, which is a hypercube of dimension zero [5, 6]. If the point moves to another point, it makes a line, which is a unit hypercube of dimension one. If the line moves out in a perpendicular direction, it makes a square, which is a unit hypercube of dimension two. If the square moves to a perpendicular direction, it makes a cube, which is a unit hypercube of dimension three. And if the cube moves to the fourth dimension, it is called a four-dimensional hypercube as a unit tesseract.

In the engineering material field, one of the simplest lightweight truss model is truss cubic, which is defined by Gibson and Ashby [7]; it is a model of hexagonal truss to define an ideal solution for honeycomb, open cell, or closed cell model. This is based on the three-dimensional stereoscopic structure. It can create a model which is hypercube truss model composed of a hexagonal truss inside and a hexagonal truss inside. Thus, this paper is focused on studying the hypercube concept to make a unit model to apply for a sandwich core structure.

If tesseract is composed of two regular hexahedrons, i.e., one is for outer structure and the other is for inner structure, with or without diagonal truss, then two types of model can be defined such as the core-filled or the core-spaced shape. That is, it depends with or without a truss in a diagonal direction. Therefore, this paper is focused on studying two models defined as Type 1 and Type 2.

According to the reported papers on the mechanical properties of structures that are 3D printed with powders recently, there are advantages and disadvantages.

The merits are to make a shape easily, to save time, to create a complex shape without any limited shape, and to make a high-quality part for the application in the aerospace or biomedical industry. Demerits are a high cost to create a product, a limited space to make a product, a limited materials such as metal powders, a required high quality equipment to produce high quality product, a need to hire a professional engineers to take control the equipment, etc.

Three-dimensional printing skill is not a magic to create anything; it requires techniques to be used with materials. The most important is what the application is. Thus, depending on the skills of the materials, the quality of a product is decided. Recently, 3D printing skill is announced as a revolution in manufacturing technique and it has been developed more and more. From the beginning of the skill, it is defined various techniques like fused deposition modeling (FDM) [8, 10], selective laser sintering (SLS) [9], direct light processing (DLP) [7, 8, 12], stereolithography (SLA) [11, 13], laminated object manufacturing (LOM) [11, 14], stereolithography (SL) [14], mask projection stereolithography (MPSL) [14], three-dimensional printing (3DP) [14], droplet

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**Figure 2.**

**3. 3D printing equipment (DMLS)**

*Samples made by the 3D printing DMLS skill: (1) is Type 1 and (2) is Type 2.*

*Research of Lightweight Structures for Sandwich Core Model*

deposition manufacturing (DDM) [14], and fused filament fabrication (FFF) [15, 16]. Based on these techniques, new skills are currently being developed and announced.

To validate mechanical properties, tension and compression with a specimen made by ASTM standard are required. Many researchers found a specimen made by 3D printing have anisotropy and they shows mechanical properties are not shown in constant. They carried out experiments with different materials and with 3D printing. However, they show different properties depending on the 3D skill, equipment, applying material, additive manufacturing speeding, and so on. There are many

This chapter concentrated on the investigation of stiffness or strength for unit cell models made by DMLS 3D printing. And it is hope to find mechanical proper-

For designed models, it is defined as an ideal mathematical solution. Based on the previous researchers, lattice or truss model defined as open cell model may have a correlation between relative elastic modulus as a function of relative density or between relative compressive yield strength as a function of relative density. Thus, **Figure 2** shows Type 1 and Type 2 shape. The next section shows details on stiffness or strength for both the models. Type 1 is core-filled model and Type 2 is a core-spaced model. Each model is created by the DMLS technique. And then both models are tested by compression. Before experimental testing for Type 1 and Type 2, they are checked for material properties of a specimen based on ASTM E8/E8M [25]. The specimen is made by DMLS and then tested by tension and compression to check the material properties.

It used 3D printing machine which is defined as EOS M290. This is the DMLS (Direct Metal Laser Sintering) skill to make a specimen. It has a property summarized in **Table 1**. It shows more detailed information for the equipment. Among

droplet as liquid status. The drip metal is added layer by layer to make a shape.

ties of various unit models to make a sandwich core structure.

Nowadays, a common skill of the 3D printing is direct metal laser sintering (DMLS) [17, 18]. It uses laser with metal powders, which is Laser beam melt metal powders to be

*DOI: http://dx.doi.org/10.5772/intechopen.86852*

kinds of effective variables [19–24].

**2. Hypercube models**

*Research of Lightweight Structures for Sandwich Core Model DOI: http://dx.doi.org/10.5772/intechopen.86852*

deposition manufacturing (DDM) [14], and fused filament fabrication (FFF) [15, 16]. Based on these techniques, new skills are currently being developed and announced.

Nowadays, a common skill of the 3D printing is direct metal laser sintering (DMLS) [17, 18]. It uses laser with metal powders, which is Laser beam melt metal powders to be droplet as liquid status. The drip metal is added layer by layer to make a shape.

To validate mechanical properties, tension and compression with a specimen made by ASTM standard are required. Many researchers found a specimen made by 3D printing have anisotropy and they shows mechanical properties are not shown in constant. They carried out experiments with different materials and with 3D printing. However, they show different properties depending on the 3D skill, equipment, applying material, additive manufacturing speeding, and so on. There are many kinds of effective variables [19–24].

This chapter concentrated on the investigation of stiffness or strength for unit cell models made by DMLS 3D printing. And it is hope to find mechanical properties of various unit models to make a sandwich core structure.
