Review on Fractal Analysis of Porous Metal Materials

Wang, J. Z.; Ma, Jingling; Ao, Qingbo; Zhi, Hu; Tang, Hongxiao

doi:10.1155/2015/427297

Cited by 9 publications

(4 citation statements)

References 20 publications

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“…Moreover, there are a large number of previous reports on the mechanical metamaterials using 3D printing technology, which has significant improve their potential and practical applications [28][29][30][31][32]. Wang et al [33] had employed the 3D printing technology to design a mechanical metamaterial with large stretchability, bionic stress-strain curve matching, and imperfection insensitivity by tuning the geometric parameters.…”

Section: Introductionmentioning

confidence: 99%

Fractal design of 3D-printing mechanical metamaterial undergoing tailorable zero Poisson’s ratio

Liu,

Lu,

Lau

2023

Smart Mater. Struct.

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With the development of mechanical metamaterials, structures with large and nonlinear deformations have attracted great research passions for their increasingly applications. Although it has been studied for decades, the mechanics of conflict between large deformation with non-buckling has not been well understood. In this study, a new type of mechanical metamaterial, of which the large deformation is achieved without buckling, has been proposed to achieve the zero Poisson’s ratio using fractal design. Effects of fractal iteration ( i ) and connection angle ( α ) on the Poisson’s ratio and mechanical stress-strain behaviors of 3D printing mechanical metamaterial were studied by finite element analysis and experimental tests. Finally, constitutive relationships among loading force, Poisson’s ratio, iteration time and connection angle have been explored and discussed to achieve a large and non-buckling deformation.

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Section: Introductionmentioning

confidence: 99%

Fractal design of 3D-printing mechanical metamaterial undergoing tailorable zero Poisson’s ratio

Liu,

Lu,

Lau

2023

Smart Mater. Struct.

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“…Fractal dimension has been successfully used in problems from the domain of computer vision, for example facial recognition [21] and many others [22]. Fractal analysis is already broadly used in material science and its main fields of application include geometrical characteristics of the surface, grain size and materials porosity [23][24][25]. Moreover, some attempts for implementation of fractal dimension in microstructure analysis were also made [26].…”

Section: Introductionmentioning

confidence: 99%

Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness

Zając¹,

Płatek²,

Wachel³

et al. 2022

Adv. Sci. Technol. Res. J.

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Application of computational methods in engineering and science constantly increases, which is also visible in sector of material science, often with promising results. In following paper, authors would like to propose fractal dimension, a mathematical method of quantifying self-similarity and complexity of spatial patterns, as robust method of hardness estimation of low carbon steels. A dataset of microstructure images and corresponding Vickers hardness measurements of S235JR steel under different delivery conditions was created. Then, three different computational methods for evaluation of materials hardness based on microstructure image were tested. In this paper those methods are called: (i) Otsu-based index, (ii) fractal dimension index and (iii) vision transformer index. The results were compared with method used in literature for similar problems. Comparison showed that fractal dimension performs better than other evaluated methods, in terms of median absolute error, which value was equal to 4.12 HV1, which is significantly lower than results achieved by Otsu-based index and vision transformer index, which were 4.49 HV1 and 5.07 HV1 respectively. Those results can be attributed to the relative robustness of fractal dimension index, when compared to other methods. Robust estimation is preferable, due to the high amount of noise in the dataset, which is a consequence of the nature of used material.

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“…As design science moves into the twenty-first century, a comprehensive understanding of friction has arisen, and friction is anticipated to be taken into account while improving and designing various machine units. Fractals can be found in a wide range of materials, including crystal development, fracture theory, thin coatings, and porous materials, to name a few (Mandelbrot, 1977;Bai-Lian, 2002;Park et al, 2010;Wang et al, 2015;Janahmadov et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

A Review on Treating Tribological Problems with Fractals

Lăpuşteanu

Paleu

2022

Bulletin of the Polytechnic Institute of Iași. Machine Constructions Section

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Fractals and chaos theory provide means of modeling dynamic changes in micro and nano topography on friction surfaces caused by various tribological mechanisms and processes. Friction and wear phenomena in tribological systems can be interpreted on a macroscopic scale. With the development of miniaturized scale and nanoscale systems, it has been launched the hypothesis that macro-level systems cannot reflect the microscale and nanoscale phenomena. A conclusive case is given by the calculation of frictional torque in microscale orientation, in this situation being found that models created by bearing producers cannot validate experimental results. By applying the “box-counting” method, it is possible to estimate the fractal dimension both directly and indirectly by comparing the area-perimeter-scale relations. Based on scaling equations, a system was created for this operation. The conclusion is that all existing theories in tribology should be adapted to take into account fractal size and fractal roughness.

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Review on Fractal Analysis of Porous Metal Materials

Cited by 9 publications

References 20 publications

Fractal design of 3D-printing mechanical metamaterial undergoing tailorable zero Poisson’s ratio

Fractal design of 3D-printing mechanical metamaterial undergoing tailorable zero Poisson’s ratio

Fractal Dimension as Robust Estimate of Low Carbon Steels Hardness

A Review on Treating Tribological Problems with Fractals

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