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The term “stable” in engineering first appears at the days of Archimedes and Aristotle, referring to the movement of a body with a focus on its implementation to the orbit of a planet around the sun. In modern times, a more rigorous definition was given with the use of mathematics without fully solving the relevant problems, such as the three-body problem. Thus, 'stable' is considered to be the movement of a body on a path, when after a small positive differential, it returns to its initially indented path.

Fracture mechanics, a science that has been recently developed, has focused on the extension of a crack inside a solid material. This extension is a phenomenon of instability since it is about the breaking of the bonds which maintain the continuity of the solid matter structure. For a fuller description of the fracture phenomenon of a solid material, new concepts and new measurable mechanical parameters have been introduced, such as the stable or unstable expansion of a pre-existing crack and the stable or unstable propagation orbit of the tip of the crack.

The distinguished research of Dr. Dimitrios Zaharopoulos, professor of Democritus University of Thrace, can predict the propagation orbit of a crack inside materials which behave in a fragile manner and can also answer to the question that has emerged in Fracture Mechanics in recent years as to when the orbit is stable and unstable.

Groundbreaking theory on the stability/instability of a crack path propagation


Until recently all the efforts to fully resolve the problem of determining the propagation path of the tip of the crack as well as of its kind have failed, except from a few test cases with favorable geometry.

The method proposed is based on the so-called case of the maximum slope of the density of deformation energy (HMG of SED) and reads as follows:

The path that follows the edge of the crack is the curve that results from the maximum slope of the density of deformation energy stored per unit volume of the solid body, in absolute value. In other words, it is the ravine in the contour map of the density of deformation energy.

The level of stability occurs from the acidity etching of the curve of the gorge on the map contour. The ambiguity of the etching leads to chaotic behavior of the apparent path of the edge of the crack.

The above mentioned universal assumption can offer results through map editing of density contour of deformation energy. In this map someone can carve for any test piece of two or three dimensions, by using high-performance computer programs, as long as it simulates the geometry and boundary conditions of the test piece by the finite elements method. By applying the above simple procedure results have shown for the first time the complexity of the behavior of many different samples. Test pieces made of fragile material which were proof stressed at the Laboratory of Mechanics of the Department of Civil Engineering of DUTY as well as findings from the international literature confirmed the foreseeable mechanical behavior with the proposed method.

International Recognition

The professor of the Democritus University of Thrace, Zaharopoulos Dimitrios, with his suggested method based on the assumption of maximum slope of the power distortion in volume unit of a material, which is successfully applied in many problems of Fracture Mechanics, has been recognized by the international research community in this specific filed of Fracture Mechanics.

He has been invited to a series of conferences with most important that of the Academy of Sciences and the Atomic Energy Commission of Hungary, which was held in Hungary in September 2012 as well as in Austria in October 2012, entitled: "The 14th International Congress on Mesomechanics".

Furthermore he holds the first places until today in the Google Search under the key phrase “Crack Path Stability” of ‘Google’ web browser.

He is a permanent reviewer of «Engineering Fracture Mechanics» journal of Elsevier while for two consecutive years he held the 12th place among the 25 most important publications of the «Theoretical and Applied Fracture Mechanics» journal.


Zaharopoulos Dimitrios, Professor, Department of Civil Engineering, School of Engineering, Democritus University of Thrace.