scholarly journals Review about the Application of Fractal Theory in the Research of Packaging Materials

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 860
Author(s):  
Qingshan Duan ◽  
Jiejie An ◽  
Hanling Mao ◽  
Dongwu Liang ◽  
Hao Li ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Theory ◽  
Inorganic Materials ◽  
Packaging Materials ◽  
Analysis Method ◽  
Characteristic Parameters ◽  
Fractal Characteristic ◽  
Fractal Characteristics ◽  
The Relationship

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

scholarly journals A study on the effects of the fractal characteristics of aggregates on the mechanical behavior of cemented sand and gravel

2021 ◽  
Vol 71 (342) ◽  
pp. e250
Author(s):  
L. Guo ◽  
S. Li ◽  
L. Zhong ◽  
L. Guo ◽  
L. Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Elastic Modulus ◽  
Fractal Theory ◽  
Peak Stress ◽  
Aggregate Gradation ◽  
Cemented Sand ◽  
Ordinary Concrete ◽  
Fractal Characteristics ◽  
Sand And Gravel ◽  
The Relationship

Owing to complex aspects of cemented sand and gravel (CSG), such as included unscreened aggregates, CSG properties differ from those of ordinary concrete. Fractal theory is introduced to study the effects of aggregate characteristics on CSG properties, quantifying aggregate gradation and shape. Numerical simulation and analyses show that: (1) improved aggregate gradation decreases the gradation fractal dimension and increases the CSG peak stress and elastic modulus; (2) more irregularly shaped aggregates increase the shape fractal dimension and decrease the CSG peak stress and elastic modulus; (3) the relationship quantified between aggregate characteristics and CSG mechanical properties provides a theoretical basis for aggregate allocation in engineering design and construction. Mixing artificial aggregates can improve aggregate gradation but reduces CSG performance. Appropriately blending artificial and on-site aggregates achieves optimal CSG performance; in this study, this is attained using 20% artificial aggregates added under standard gradation.

Analysis of Collapsible Loess Microstructure at Fractal Theory Based

2012 ◽  
Vol 204-208 ◽  
pp. 614-617
Author(s):  
Ming Yuan Shi ◽  
Zong Fang Chen ◽  
Hong Yan Zhang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Linear Relationship ◽  
Pore Radius ◽  
Fractal Theory ◽  
Fractal Characteristic ◽  
Geological Age ◽  
Collapsible Loess ◽  
Fractal Character ◽  
The Relationship

On the basis of publicized data, the fractal character of pore structure in loess is studied. We have determined fractal characteristic pore radius and discussed the relationship between fractal character values and collapsibility. Results show that there is a good linear relationship between and collapsibility, and fractal dimension can reflect geological age of loess section.

scholarly journals Review on Fractal Analysis of Porous Metal Materials

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
J. Z. Wang ◽  
J. Ma ◽  
Q. B. Ao ◽  
H. Zhi ◽  
H. P. Tang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Analysis ◽  
Material Characterization ◽  
Fractal Theory ◽  
Porous Metal ◽  
Processing Method ◽  
The Past ◽  
Metal Materials ◽  
The Relationship

Porous metal materials are multifunctional lightweight materials and have been used widely in industry. The structural and functional characters of porous metal materials depend on the pore structure which can be described effectively by the fractal theory. This paper reviews the major achievements on fractal analysis of pore structure of porous metal materials made by State Key Laboratory of Porous Metal Materials, China, over the past few years. These include (i) designing and developing a set of novel fractal analytical software of porous metal materials, (ii) the influence of material characterization and image processing method on the fractal dimension, and (iii) the relationship between the material performance and the fractal dimension. Finally, the outlooks of fractal theory applied in porous metal materials are discussed.

scholarly journals Effect of Grain Size on Microscopic Pore Structure and Fractal Characteristics of Carbonate-Based Sand and Silicate-Based Sand

2021 ◽  
Vol 5 (4) ◽  
pp. 152
Author(s):  
Shao-Heng He ◽  
Zhi Ding ◽  
Hai-Bo Hu ◽  
Min Gao
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Quartz Sand ◽  
Glass Bead ◽  
Fractal Theory ◽  
Calcareous Sand ◽  
Wide Range ◽  
Fractal Characteristics

In this study, a series of nuclear magnetic resonance (NMR) tests was conducted on calcareous sand, quartz sand, and glass bead with a wide range of grain sizes, to understand the effect of grain size on the micro-pore structure and fractal characteristics of the carbonate-based sand and silicate-based sand. The pore size distribution (PSD) of the tested materials were obtained from the NMR T2 spectra, and fractal theory was introduced to describe the fractal properties of PSD. Results demonstrate that grain size has a significant effect on the PSD of carbonate-based sand and silicate-based sand. As grain size increases, the PSD of sands evolves from a binary structure with two peaks to a ternary structure with three peaks. The increase in the grain size can cause a remarkable increase in the maximum pore size. It is also found that the more irregular the particle shape, the better the continuity between the large and medium pores. In addition, grain size has a considerable effect on the fractal dimension of the micro-pore structure. The increase of grain size can lead to a significant increase in the heterogeneity and fractal dimension in PSD for calcareous sand, quartz sand and glass bead.

Application of Fractal Theory in Aggregate Gradation Research

2012 ◽  
Vol 204-208 ◽  
pp. 1923-1928
Author(s):  
Bo Tan ◽  
Rui Hua Yang ◽  
Yan Ting Lai
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Aggregate Gradation ◽  
Structure Characteristics ◽  
Aggregate Distribution ◽  
Dimension Formula ◽  
Mass Fractal ◽  
Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

scholarly journals A Study of the Spatial Form of Maling Village, Henan, China

2020 ◽  
Vol 12 (18) ◽  
pp. 7350
Author(s):  
Qindong Fan ◽  
Fengtian Du ◽  
Hu Li
Keyword(s):  
Land Use ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stability Index ◽  
Spatial Form ◽  
Land Use Types ◽  
Fractal Characteristics ◽  
Spatial Shape ◽  
The Stability ◽  
The Village

In order to improve the study of the spatial form of villages, fractal theory is used to analyze the plane and facade of Maling Village, Changdai Town, Mengjin County, Luoyang City, Henan Province, China. The results show that the village facade and plane spatial shape of Maling Village have obvious fractal characteristics and the fractal dimension can be used as an important index to evaluate the plane and facade shape of the village. The fractal dimension of each land use type is between 1.2415 and 1.7443. The stability index of land use types in the village follows the order of village construction land > cultivated land > road > garden land > woodland > grassland. The research results can provide decision-making information for the rational use and planning of village land.

scholarly journals Evolution Rules of Fractures for Mudstone under Compression Shear Load and the Fractal Characteristics of Broken Blocks

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Zhaoyun Chai ◽  
Jinbo Bai ◽  
Haiyang Zhang ◽  
Pan Yang
Keyword(s):  
Fractal Dimension ◽  
Compression Test ◽  
Shear Fracture ◽  
Fractal Theory ◽  
Friction Angle ◽  
Shear Loading ◽  
Shear Load ◽  
Deformation And Failure ◽  
Fractal Characteristics ◽  
Logarithmic Relationship

Failure of rocks is commonly induced by compressive and shear coupling loading. Knowledge of the mechanism and process of deformation and failure of rocks under compressive shear loading condition is an important basis for the study of stability in rock engineering. Based on the nonlinear fractal theory, it is possible to examine the evolution rules of fractures in mudstone under compression shear load and the fractal characteristics of broken blocks using the shear compression test with variable angles of mudstone specimens in natural conditions. This research shows that the cohesion and friction angle parameters of rock samples are achieved by draw Mohr’s strength envelope according to the test date of variable-angle shear compression test. It also shows that the shape of load-displacement curves of rocks can be divided into four stages: compaction, elastic, plastic, and fracture, and the curve can accurately represent the transformation and breakage characteristics of rock during shear fracture. And the distribution of broken blocks shows a strong statistical resemblance to the fractal distribution, and the fractal dimension is able to reflect the distribution characteristics of broken blocks. With increasing the shear angle, the fractal dimension of broken blocks decreases in a logarithmic relationship.

EFFECT OF FRACTAL FRACTURES ON PERMEABILITY IN THREE-DIMENSIONAL DIGITAL ROCKS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940015 ◽  
Author(s):  
WEIFENG LV ◽  
GUOLIANG YAN ◽  
YONGDONG LIU ◽  
XUEFENG LIU ◽  
DONGXING DU ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Fractured Reservoirs ◽  
Three Dimensional ◽  
Absolute Permeability ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
The Relationship

The fracture has great impact on the flow behavior in fractured reservoirs. Fracture traces are usually self-similar and scale-independent, which makes the fractal theory become a powerful tool to characterize fracture. To obtain three-dimensional (3D) digital rocks reflecting the properties of fractured reservoirs, we first generate discrete fracture networks by stochastic modeling based on the fractal theory. These fracture networks are then added to the existing digital rocks of rock matrixes. We combine two low-permeable cores as rock matrixes with a group of discrete fracture networks with fractal characteristics. Various types of fractured digital rocks are obtained by adjusting different fracture parameters. Pore network models are extracted from the 3D fractured digital rock. Then the permeability is predicted by Darcy law to investigate the impacts of fracture properties to the absolute permeability. The permeability of fractured rock is subject to exponential increases with fracture aperture. The relationship between the permeability and the fractal dimension of fracture centers is exponential, as well as the relationship between permeability and the fractal dimension of fracture lengths.

INVESTIGATION OF DYNAMIC TEXTURE AND FLOW CHARACTERISTICS OF FOAM TRANSPORT IN POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940013 ◽  
Author(s):  
FEI WANG ◽  
HAIFENG LI ◽  
DONGXING DU ◽  
XU DONG
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Quantitative Description ◽  
Flow Characteristics ◽  
Transport In Porous Media ◽  
Steady Stage ◽  
Profile Control ◽  
Fractal Characteristics

Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

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