Utilizing Fractals for Modeling and 3D Printing of Porous Structures

Abstract

Porous structures exhibiting randomly sized and distributed pores are required in biomedical applications (producing implants), materials science (developing cermet-based materials with desired properties), engineering applications (objects having controlled mass and energy transfer properties), and smart agriculture (devices for soilless cultivation). In most cases, a scaffold-based method is used to design porous structures. This approach fails to produce randomly sized and distributed pores, which is a pressing need as far as the aforementioned application areas are concerned. Thus, more effective porous structure design methods are required. This article presents how to utilize fractal geometry to model porous structures and then print them using 3D printing technology. A mathematical procedure was developed to create stochastic point clouds using the affine maps of a predefined Iterative Function Systems (IFS)-based fractal. In addition, a method is developed to modify a given IFS fractal-generated point cloud. The modification process controls the self-similarity levels of the fractal and ultimately results in a model of porous structure exhibiting randomly sized and distributed pores. The model can be transformed into a 3D Computer-Aided Design (CAD) model using voxel-based modeling or other means for digitization and 3D printing. The efficacy of the proposed method is demonstrated by transforming the Sierpinski Carpet (an IFS-based fractal) into 3D-printed porous structures with randomly sized and distributed pores. Other IFS-based fractals than the Sierpinski Carpet can be used to model and fabricate porous structures effectively. This issue remains open for further research.

Verifying the Accuracy of 3D-Printed Objects Using an Image Processing System

“…As mentioned before, 3D printing has revolutionized the process of fabricating complex objects such as topologically optimized structures and porous structures, paving the way for innovative solutions in various fields and industries [4][5][6][7]. Unlike simple objects, complex objects may consist of loose shells, thin walls, and other difficult-to-fabricate features, resulting in sustainable inaccuracy [31,32].…”

“…Its unique capabilities provide an array of opportunities to explore innovative design ideas [1][2][3]. It has particularly emerged as a highly dependable manufacturing process for fabricating complex objects, including topologically optimized parts and porous structures [4][5][6][7]. Furthermore, this process has developed a reputation for effectively managing the production of small-volume, high-variety products.…”

Verifying the Accuracy of 3D-Printed Objects Using an Image Processing System

“…3D printing fabricates objects by adding materials layer-by-layer [1][2][3]. This manufacturing process has particularly emerged as a highly dependable process for fabricating complex objects, including topologically optimized parts and porous structures [4][5][6][7]. Furthermore, this process has developed a reputation for effectively managing the production of small-volume, high-variety product.…”

Influence of size on the compressive properties of cellular structures manufactured by additive technologies

“…A large number of articles base their research on the generation of beams, which are then subjected to bending tests that make it possible to determine a wide range of coefficients and variables relevant to the selection of the appropriate material or infill pattern [16,17]. From a fractal point of view, however, the infinite possibility of generating cells should be constantly emphasized [18,19]. However, the only limitation to making a sufficient number of iterations is the type of 3D printer used to print each component.…”