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Fractal Fract
Special Issues
Fracture Analysis of Materials Based on Fractal Nature
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Fracture Analysis of Materials Based on Fractal Nature

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (25 March 2025) | Viewed by 4889

Special Issue Editors

Dr. Luis Eduardo Kosteski

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Guest Editor
Engineering Post Graduation Program, Federal University of Pampa (UNIPAMPA), Alegrete 97546-550, Brazil
Interests: fracture mechanics; fractals; concrete; numerical simulations
Dr. Leandro Ferreira Friedrich

E-Mail Website
Guest Editor
Engineering Post Graduation Program, Federal University of Pampa (UNIPAMPA), Alegrete 97546-550, Brazil
Interests: fracture mechanics; fractal nature; numerical simulations; structural health monitoring
Prof. Dr. Jie Xu

E-Mail Website
Guest Editor
School of Civil Engineering, Research Center of Large-Span Spatial Structures, Tianjin University, Tianjin 300350, China
Interests: fracture behavior; structural health monitoring and resilience; high-performance materials
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It has been observed that the fracture surface of metals, rock, concrete, and many other disordered or heterogeneous materials can be described by fractals characterized by random self-similarity, i.e., they exhibit statistically similar morphologies at different scales of observation. This aspect cannot be ignored or even replaced by a mean field when the fracture analysis of such materials occurs since many length scales interact during the material failure process. In this case, the fundamental character of the phenomenon from a physical and topological point of view can be represented by the fractal description of the material.

Furthermore, it can be explained that the behavior of a material depends on its microstructural disorder and its relation to its size at the macro scale. The microstructural disorder is a scale-independent material property less important when increasing the structural size. From a fractal point of view, this represents the change from a non-integer dimension to an integer dimension, that is, Euclidean space. Various researchers have used this idea to investigate concepts directly or indirectly related to the scale effect, fracture, acoustic emission, and fractality.

This Special Issue focuses on further advancing research on topics related to the fractal approach to the fracture analysis of materials using experimental testing, numerical simulation, and structural health monitoring. Topics that are invited for submission include (but are not limited to) the following:

  • Size effect based on the fractal theory;
  • Fractal analysis and its applications in fracture mechanics;
  • Applications of fractal approaches to fracture failure and damage of materials under different loading conditions;
  • Fractal/multi-fractal analysis for structural health monitoring.

Dr. Luis Eduardo Kosteski
Dr. Leandro Ferreira Friedrich
Prof. Dr. Jie Xu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • size effect
  • fracture
  • damage
  • experimental analysis
  • acoustic emission
  • numerical simulations

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Published Papers (4 papers)

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Research

26 pages, 11141 KiB  
Article
Study on Surface Roughness and True Fracture Energy of Recycled Aggregate Concrete Using Fringe Projection Technology
by Meiling Dai, Weiyi Hu, Chengge Hu, Xirui Wang, Jiyu Deng and Jincai Chen
Fractal Fract. 2025, 9(3), 159; https://doi.org/10.3390/fractalfract9030159 - 4 Mar 2025
Viewed by 541
Abstract
This paper investigates the fracture surfaces and fracture performance of recycled aggregate concrete (RAC) using fringe projection technology. This non-contact, point-by-point, and full-field scanning technique allows precise measurement of RAC’s fracture surface characteristics. This research focuses on the effects of recycled aggregate replacement [...] Read more.
This paper investigates the fracture surfaces and fracture performance of recycled aggregate concrete (RAC) using fringe projection technology. This non-contact, point-by-point, and full-field scanning technique allows precise measurement of RAC’s fracture surface characteristics. This research focuses on the effects of recycled aggregate replacement rate, water-to-binder (w/b) ratio, and maximum aggregate size on RAC’s fracture properties. A decrease in the w/b ratio significantly reduces surface roughness (Rs) and fractal dimension (D), due to increased cement mortar bond strength at lower w/b ratios, causing cracks to propagate through aggregates and resulting in smoother fracture surfaces. At higher w/b ratios (0.8 and 0.6), both surface roughness and fractal dimension decrease as the recycled aggregate replacement rate increases. At a w/b ratio of 0.4, these parameters are not significantly affected by the replacement rate, indicating stronger cement mortar. Larger aggregates result in slightly higher surface roughness compared to smaller aggregates, due to more pronounced interface changes. True fracture energy is consistently lower than nominal fracture energy, with the difference increasing with higher recycled aggregate replacement rates and larger aggregate sizes. It increases as the w/b ratio decreases. These findings provide a scientific basis for optimizing RAC mix design, enhancing its fracture performance and supporting its practical engineering applications. Full article
(This article belongs to the Special Issue Fracture Analysis of Materials Based on Fractal Nature)
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21 pages, 8541 KiB  
Article
Fractal Scale Effect in Quasi-Brittle Materials Using a Version of the Discrete Element Method
by Luis Eduardo Kosteski, Leandro Ferreira Friedrich, Matheus Machado Costa, Caroline Bremm, Ignacio Iturrioz, Jie Xu and Giuseppe Lacidogna
Fractal Fract. 2024, 8(12), 678; https://doi.org/10.3390/fractalfract8120678 - 21 Nov 2024
Cited by 1 | Viewed by 922
Abstract
In engineering applications, it is crucial to consider the size dependence of a material’s mechanical properties and its overall behavior. One of the theories that quantifies this phenomenon in quasi-brittle materials is the cohesive fractal theory (CFT) introduced by Carpinteri and his collaborators. [...] Read more.
In engineering applications, it is crucial to consider the size dependence of a material’s mechanical properties and its overall behavior. One of the theories that quantifies this phenomenon in quasi-brittle materials is the cohesive fractal theory (CFT) introduced by Carpinteri and his collaborators. This theory describes the behavior of materials using fractal dimensions. To investigate whether the scale effect can be analyzed using the CFT, a version of the Lattice Discrete Element Method (LDEM) is employed. The accuracy of the LDEM in capturing the scale effect is evaluated through simulations of three primary tests. Specifically, rock specimens are subjected to tensile, compressive, and bending loads to determine their mechanical properties. The influence of material heterogeneity and boundary conditions is also examined. In scenarios involving tensile and bending loads, the localization of a significant crack leads to failure. According to the CFT, the sum of the fractal exponents is close to unity, with values of 1.0 (mean value) for tensile loading and 0.97 for bending loading. However, the compressive loading results do not exhibit this characteristic, as no single prominent crack leads to failure. Overall, the LDEM results are consistent with the CFT, effectively quantifying the scale effect without modifying the elementary constitutive law. Full article
(This article belongs to the Special Issue Fracture Analysis of Materials Based on Fractal Nature)
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18 pages, 7458 KiB  
Article
Detection of Short-Section Ballast Breakdown in Track: A Fractal Analysis Approach with Reduced Window Size
by Andrea Katharina Korenjak, Stefan Offenbacher and Stefan Marschnig
Fractal Fract. 2024, 8(11), 664; https://doi.org/10.3390/fractalfract8110664 - 15 Nov 2024
Viewed by 831
Abstract
Due to increasing demands on the available railway infrastructure, accurate estimates of safety-critical track condition as well as breakdowns of individual track components are crucial. This task can be supported by analyzing track measurement data. Ballast breakdown can be determined by analyzing the [...] Read more.
Due to increasing demands on the available railway infrastructure, accurate estimates of safety-critical track condition as well as breakdowns of individual track components are crucial. This task can be supported by analyzing track measurement data. Ballast breakdown can be determined by analyzing the longitudinal level using fractal analysis: Commonly, a window with a width of 150 m is dragged over the signal computing an approximation of a fractal dimension of the signal for each position of the window. However, while a large window size can be used to describe the condition of ballast and substructure simultaneously, it fails to precisely localize short-section ballast breakdowns in the track. With the objective of describing and detecting these local effects in the ballast bed, this work analyzes a set of 114 known weak ballast spots. By reducing the width of the sliding window, the position of short-section ballast breakdowns can be reliably depicted. The application of a modified version of fractal analysis allows for a more accurate targeted maintenance on a component-specific basis. Full article
(This article belongs to the Special Issue Fracture Analysis of Materials Based on Fractal Nature)
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16 pages, 3461 KiB  
Article
Pavement Crack Detection Using Fractal Dimension and Semi-Supervised Learning
by Wenhao Guo, Leiyang Zhong, Dejin Zhang and Qingquan Li
Fractal Fract. 2024, 8(8), 468; https://doi.org/10.3390/fractalfract8080468 - 12 Aug 2024
Cited by 2 | Viewed by 1709
Abstract
Pavement cracks are crucial indicators for assessing the structural health of asphalt roads. Existing automated crack detection models depend on large quantities of precisely annotated crack sample data. The irregular morphology of cracks makes manual annotation time-consuming and costly, thereby posing challenges to [...] Read more.
Pavement cracks are crucial indicators for assessing the structural health of asphalt roads. Existing automated crack detection models depend on large quantities of precisely annotated crack sample data. The irregular morphology of cracks makes manual annotation time-consuming and costly, thereby posing challenges to the practical application of these models. This study proposes a pavement crack image detection method integrating fractal dimension analysis and semi-supervised learning. It identifies the self-similarity characteristics within the crack regions by analyzing pavement crack images and using fractal dimensions to preliminarily determine the candidate crack regions. The Crack Similarity Learning Network (CrackSL-Net) is then employed to learn the semantic similarity of crack image regions. Semi-supervised learning facilitates automatic crack detection by combining a small amount of labeled data with a large volume of unlabeled image data. Comparative experiments are conducted on two public pavement crack datasets against the HED, U-Net, and RCF models to comprehensively evaluate the performance of the proposed method. The results indicate that, with a 50% annotation ratio, the proposed method achieves high-precision crack detection, with an intersection over union (IoU) exceeding 0.84, which is close to that of U-Net. Visual analysis of the detection results confirms the method’s effectiveness in identifying cracks in complex environments. Full article
(This article belongs to the Special Issue Fracture Analysis of Materials Based on Fractal Nature)
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