Fractal Mechanics of Engineering Materials, 2nd Edition

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Guest Editor
Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia
Interests: fractal mechanics; constitutive modelling; fatigue and fracture mechanics; damage mechanics; experimental methods (DIC, fractal, hybrid expt-FEA)
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Guest Editor
Faculty of Mechanical Engineering, Universität der Bundeswehr München, Munich, Germany
Interests: fractal mechanics; fracture mechanics; experimental mechanics; computational mechanics; advanced materials and structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerous engineering materials are inhomogeneous and inherit complex structures that exhibit statistical scale invariance over several length scales. These materials and structures include metals and alloys, geomaterials (rocks and aggregates), nanocomposites, engineered coatings and interfaces. The straining of these materials is quantified with appropriate theories within the domains of continuum, fracture, and damage mechanics. The fractality of geometrical features such as microstructures, granular aggregates, surface morphological irregularities and fatigue cracks can be quantified in terms of their fractal dimensions. The fractal analysis of these self-similar and multi-scale features aims to correlate the fractal geometry with meaningful mechanical quantities at micro-to-macro scale. These include mechanical properties, fracture toughness, crack-tip driving force and fracture potentials. Several methods including digital image correlation (DIC) as well as optical and scanning electron microscopy (SEM) have been employed in acquiring microscopic images of the material regions representing the phenomenon of interest. These images are then analyzed to establish relevant fractal parameters including fractal dimension and fractional fractal dimension. Several algorithms for greyscale thresholding, image partitioning and pixel counting are available and continuously being improved. The resulting fractal parameters could serve as material variables in the classical and new/unconventional approaches to continuum mechanics, LEFM, fatigue crack growth analysis, and damage mechanics.

This Special Issue on "Fractal Mechanics of Engineering Materials" aims to present the state-of-the-art research methodologies and outcomes in fractal approaches for engineering materials. Therefore, we invite authors to submit quality review papers, research articles, and technical notes addressing the fractal aspects of engineering materials and related issues. Research topics are described by, but not limited to, the following keywords:

  • Materials: metals and alloys, geomaterials (rocks, aggregates), polymers, composites, nanomaterials, ceramics, functionally graded materials (FGMs), interfaces, modified surfaces, etc
  • Continuum mechanics
  • Fracture mechanics: LEFM, EPFM
  • Fatigue and fatigue crack growth
  • Damage mechanics
  • Experimental mechanics: DIC, SEM, optical microscopy
  • Fractal analysis: theoretical development, image analysis, algorithms
  • Fractal dimension
  • Fractional fractal dimension
  • Computational method: FEA, BEM, numerical prediction

Prof. Dr. Mohd Nasir Tamin
Dr. Seyed R. Koloor
Guest Editors

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Keywords

  • fractal analysis
  • fractal dimension
  • fractal mechanics
  • continuum mechanics
  • fracture mechanics
  • fatigue and fatigue crack growth
  • damage mechanics
  • experimental mechanics

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Published Papers (1 paper)

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Research

19 pages, 5543 KiB  
Article
Shear Mechanism and Optimal Estimation of the Fractal Dimension of Glass Bead-Simulated Sand
by Xuefeng Li and Rui Wang
Fractal Fract. 2024, 8(10), 578; https://doi.org/10.3390/fractalfract8100578 - 30 Sep 2024
Viewed by 705
Abstract
Spherical glass beads weaken the influences of particle morphology, surface properties, and microscopic fabric on shear strength, which is significant for revealing the relationship between macroscopic particle friction mechanisms and the particle size distribution of sand. This paper explores the shear mechanical properties [...] Read more.
Spherical glass beads weaken the influences of particle morphology, surface properties, and microscopic fabric on shear strength, which is significant for revealing the relationship between macroscopic particle friction mechanisms and the particle size distribution of sand. This paper explores the shear mechanical properties of glass beads with different particle size ratios under different confining pressures. It obtains the particle size ratio and fractal dimension D through an optimal mechanical response. Simultaneously, we explore the range of the fractal dimension D under well-graded conditions. The test results show that the strain-softening degree of Rs is more obvious under a highly effective confining pressure, and the strain-softening degree of Rs can reach 0.669 when the average particle size d¯ is 0.5 mm. The changes in the normalized modulus ratio Eu/Eu50 indicate that the particle ratio and arrangement are the fundamental reasons for the different macroscopic shear behaviors of particles. The range of the peak effective internal friction angle φ is 23 °~35 °, and it first increases and then decreases with the increase in the effective confining pressure. As the average particle size increases, the peak stress ratio MFL and the peak effective internal friction angle φ first increase and then decrease, and both can be expressed using the Gaussian function. The range of the fractal dimension D for well-graded particles is 1.873 to 2.612, and the corresponding average particle size d¯ ranges from 0.433 to 0.598. Under the optimal mechanical properties of glass beads, the particle size ratio of 0.25 mm to 0.75 mm is 23:27, and the fractal dimension D is 2.368. The study results provide a reference for exploring friction mechanics mechanisms and the optimal particle size distributions of isotropic sand. Full article
(This article belongs to the Special Issue Fractal Mechanics of Engineering Materials, 2nd Edition)
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