Fractal Mechanics of Engineering Materials, 2nd Edition

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

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.

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

• Fractal Mechanics of Engineering Materials in Fractal and Fractional (8 articles)