Stavros Kourkoulis

Abstract: The response of either intact or fractured and restored marble architraves under bending is the object of the present paper. The study is motivated by the needs of the scientists, working for the extensive restoration program of the Parthenon Temple on the Acropolis of Athens, for an in-depth knowledge of the stress and strain fields developed in restored structural elements when they are placed back in their initial position. A recently introduced procedure is employed for the calculation of the reinforcement required for the restoration. A numerical model with contact elements is developed for the simulation of a prismatic architrave (epistyle) resting on marble supports (capitals, abacuses) and subjected to various types of bending. The points most prone to fail are located for both the intact and the restored architraves and it is concluded that the reproduction of actual bending conditions in the laboratory may lead to erroneous conclusions if the results are not interpreted carefully taking into account the exact way of applying the external loads. The most important findings of the numerical analysis are compared to those of previous experimental studies and are juxtaposed to the conclusions drawn from the study of the present state of the monument. © 2009 Elsevier B.V.

Abstract: The Brazilian disk test, namely the diametric compression of a circular disk by radial loads that are uniformly distributed along two symmetric arcs of its periphery, is studied using the method of complex potentials introduced by Kolosov and Muskhelishvili. The rock is assumed to be linear elastic. Closed form full-field solutions are obtained for both the stress and the displacement fields, assuming either plane-stress or plane-strain conditions. The theoretical analysis highlights some critical features of the stresses and the displacements immediately adjacent to the load contact areas, revealing the limitations of the linear elastic solutions. The problem is also studied experimentally by carrying out a series of Brazilian disk tests, according to the ISRM suggestions, with specimens mainly made from Dionysos marble. In addition, a limited number of tests are carried using specimens made from porous natural building stones or from PMMA. The results of the theoretical solution are compared with those of the experiments, and the agreement is satisfactory, at least in the regions of the disk where the stresses developed during loading remain below the linearity limit of the materials. © 2009 Elsevier Ltd. All rights reserved.

Abstract: The present study aims to the design of a finite-element model simulating accurately the pullout behaviour of cylindrical pedicle screws and predicting their pullout force. Three commercial pedicle screws, subjected to pure pullout from synthetic bone, were studied experimentally. The results were used for the design, calibration and validation of a finite-element model. Special attention was paid to the accurate simulation of the failure inside the host material under shear. For this purpose, a bilinear cohesive zone material model was adopted, controlling the mode-II debonding of neighbouring elements in the vicinity of the screw. Comparison between experimental and numerical results proved that the implementation of this approach can significantly enhance the accuracy of the numerical simulation of a screw's mechanical behaviour under pure pullout loads. The numerical model was used for the parametric study of various factors affecting the pullout performance of a cylindrical pedicle screw. It was concluded that the major parameter influencing the pullout force is the outer radius (increasing its value by 36% increases the pullout force by 34%). The influence of the purchase length of the screw is of similar quantitative nature. The respective dependence on the thread inclination, depth and pitch was significantly weaker. © 2009 IPEM.

Abstract: The dependence of the mechanical properties of natural building stones on the size and the shape of the specimens is studied experimentally. Attention is focused to the Kefalonia porous stone, a candidate substitute of the Kenchreae porous stone used by ancient Greeks for the erection of the Epidaurean Asklepieion. Series of uniaxial compression tests were carried out using both cubic and cylindrical specimens of various sizes. A number of mechanical properties were determined including the peak stress, the modulus of elasticity, the stress drop after the peak stress, the peak strain and the strain energy density up to the peak load. A strong dependence of the above properties on both the dimensions and the shape of the specimens was concluded. In addition, it was indicated that the dependence of some of the above properties on the size of the specimens is not monotonous. The conclusions drawn are in good agreement with similar ones obtained for Dionysos marble, the material used today for the restoration of the Parthenon temple of Athens as well as for the "Conchyliates" shell-stone the material that has been used for the construction of the Zeus Temple at Olympia. © 2009 Elsevier Ltd. All rights reserved.

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Abstract: For the development of innovative connections for the restoration of the integrity of structural elements of ancient stone temples, it is imperative, among others, to understand the reasons of the 'pull-out' phenomenon. Pull-out can be defined as the gradual or abrupt removal of the reinforcing bars from the body of the structural member, without prior failure of neither the marble nor the bars. An analytic solution is not yet available and in this context, a combined experimental and numerical analysis was undertaken in an effort to enlighten the failure mechanisms activated during the phenomenon. The experimental part included a series of pull-out tests with prismatic specimens made from Dionysos marble in which threaded metallic bars were planted in drilled holes. The adhesion between the marble and the bar was achieved using a suitable cementitious material. The criterion adopted for the design of the connections is to avoid completely the failure of marble. The parameters studied included the depth and the pitch of the thread of the reinforcing bars. The experimental set-up comprising suitable supporting and measuring systems was improvised, given the absence of a standard, relevant to this particular problem. Based on the experimental results, a design criterion is introduced allowing for a predefined amount of slip between the reinforcing bar-cement interface and the marble body. In addition, a numerical model is developed, calibrated on the basis of the experimental results. It is concluded that the form of the thread influences considerably the carrying capacity: denser pitches lead to higher ultimate load and energy consumption while the coarser ones favour parasitic bending effects and a flexible behaviour. In addition, the medium depth for each pitch leads to a stiffer and stronger behaviour. © 2009 Blackwell Publishing Ltd.

Abstract: Flutes are longitudinal grooves sculptured on the perimeter of the columns of ancient Greek or Roman temples. It is widely accepted that flutes were sculptured mainly for aesthetic reasons. However, strong indications exist that the presence of flutes somehow changes the overall mechanical behaviour of the column. This could be expected due to the singularities introduced by the imposed abrupt change in the boundary conditions of the specimen, where the friction boundary of the base meets the free boundary of the lateral surface. Following the previous line of thought it was decided to check this hypothesis by studying the mechanical behaviour of a typical drum of a column of the Parthenon Temple of the Acropolis of Athens. These columns have 20 flutes and their shape is accurately described as an arc of an ellipse. The study was carried out both numerically and experimentally. The parameters studied included the number and the shape of the flutes as well as the type of loading. It was concluded that the presence of flutes significantly modifies the stress and strain fields developed especially under torsion. In addition, the fluted drum appeared to be stiffer in comparison with the non-fluted one. © 2009 Blackwell Publishing Ltd.

Abstract: The stress field developed in the human lumbar vertebral bone due to the presence of transpedicular fixation screws is studied in an attempt to quantify the force required to pull the screw out of the bone. The study is focused on the pure pull-out phenomenon, namely the case in which the external loads act parallel to the longitudinal axis of the screw. The parameters considered are the penetration ratio, i.e. the ratio of the screw length divided by the distance from the posterior pedicle entrance site to the anterior vertebral cortex, and the filling ratio, i.e. the ratio of the major diameter of the screw divided by the transverse diameter of the pedicle. The study is carried out numerically with the aid of the finite element method. The analysis takes into account both the variation of the mechanical properties of the bone in terms of the distance from its surface as well as the geometrical details of a typical transpedicular screw. The results of the analysis are compared with existing experimental data from the literature and the comparison is very satisfactory. © 2009 World Scientific Publishing Company.

Abstract: In restoration works of antique Greek temples individual marble blocks are connected together to form a single element, e. g. an architrave. Due to the demand of reversibility of the intervention, this is done in the Acropolis of Athens by means of titanium threaded bars that are inserted in the marble, in predrilled holes filled with cement mortar. This way of restoration corresponds to a partial rehabilitation of the architraves. This paper presents experimental investigations on the pull-out behaviour of such anchors. The tests are performed in specially designed equipment. Failure takes place for all tests in the interface between the mortar and the marble. It has been shown that the form of the thread influences considerably the carrying capacity. Possible limit states are introduced. © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG.

Abstract: The damage of either intact or notched marble beams under bending is studied with both destructive and non-destructive techniques, in an effort to assess the reliability of the non-destructive methods in the case of rock-type materials. The specimens are made from Dionysos marble, the material used for the restoration of the Parthenon Temple of the Acropolis of Athens. The experimental results for the intact specimens are compared with the predictions of a damage model, while for the notched specimens the comparison is realised using the predictions of a numerical analysis employing the finite element method. The comparison is satisfactory indicating that the non-destructive technique of ultrasounds employed can be safely used for the description of the damage of rock-type materials. This conclusion is of vital importance since the non-destructive techniques constitute the only experimental method, the use of which is permitted in case of monuments possessing the characteristic of 'unique'. Copyright © 2006 Inderscience Enterprises Ltd.

Abstract: Some characteristics of the process zone developed around the tips of cracks as well as the fractography of the fracture surfaces constitute the subject of the present paper. The study was carried out using Scanning Electron Microscopy for the determination of the Crack Tip Opening Displacement, while numerical analysis and experimental results were combined for the determination of the.J-integral. A modern particulate Metal Matrix Composite and its matrix alloy were used for the fabrication of relatively thin tensile specimens of two different types, i.e. single- and double-edge-notched. Dependence of the above quantities on the thickness of the specimen is detected: both the critical Crack Tip Opening Displacement and the critical J-integral are found to increase in an almost linear manner with thickness. For comparison, intact prismatic specimens were considered, in 'order to study the dependence of ductility and fracture on the thickness of the specimen. It is observed that they depend also on the specimen thickness in a similar manner. Variation of these two properties with the direction of the specimen with respect to the rolling axis is also detected, indicating the importance of the plastically induced anisotropy due to the manufacturing process. Concerning the mechanisms leading to failure, it is concluded that void coalescence is active although void nucleation due to the presence of particles appears to be unavoidable.

Abstract: The failure of orthotropic materials, traditionally described by Hill's criterion, in terms of the anisotropy ratio r, i.e. the ratio of transverse to through thickness increments of logarithmic strain, is studied in the present work. In spite of the critical role of r for the description of the failure of such materials, its quantification is not yet standardized. Based on results obtained from long series of experiments r is here quantified, for the case of a modern particulate composite material, extensively used in aerospace applications. The variation of r versus the level of the plastic strain is determined and it is concluded that its values depend both on the orientation of the specimen and load with respect to the initial orthotropy axes as well as on the plastic strain induced in case the specimen and load are not oriented along one of the axes of orthotropy.

Abstract: A technical bending theory of beams accounting for nonlinearity due to damage and bimodularity of brittle rocks was proposed in Part I. In order to check the validity of the above theory, a series of three-point bending (3PB) tests has been carried out using Dionysos marble beams that have been sampled from the same extracted block. Although the modeling of the 3PB test is considerably more complicated than that of the four-point bending test, the experimental procedure in the former test is simpler than in the later test and most importantly, the location of the fracture is better controlled in the 3PB test. Herein, it is demonstrated that the test results have very good repeatability and they support the above technical theory. The bending tests also indicate that Dionysos marble is characterized by different elastic modulus in compression (E_c) and in tension (E_t) at small loads, such that the relation m = E_c/E_t ≅ 0.8 holds true. This relationship of elastic moduli for this type of marble is also supported independently by uniaxial compressions and direct tension tests on test specimens cored from the same marble block. A plausible physical explanation for this type of marble anisotropy has yet to be made. This observed difference cannot be explained by considering the rock simply as a material with cracks. It may be attributed to pure micromechanical reasons such as the complex microstructure of this type of rock, characterized by a complex previous loading history (metamorphism). Until such an explanation is available, the apparent behavior can be used in analyzing the stress-strain behavior of rocks. Further, the 3PB experiments indicate that fracture of marble starts always at the bottom fiber of the middle cross-section of the beam and the failure extension strain is the same with that occurring in the direct tension test. This last result is due to the fact that the central section of marble beam is almost under extensional strain, which in turn is caused by the combinations of the concentrated load and Poisson's effects. The damage parameter that enters the direct tension stress-strain law was obtained independently from longitudinal strain measurements at the outermost compression and extension fibers, as well as, from bending curvature and deflection measurements. This value of the damage factor is in accordance with the damage measured from the direct tension tests. It is also demonstrated that a linear Timoshenko-type theory containing an intrinsic length scale is able to approximate the nonlinear deflection behavior of Dionysos marble beams. Finally, based on a suggestion by Ludwig Prandtl, the stress-strain relationships in unconfined compression and direct tension, as well as Poisson's ratio, of Dionysos marble were derived from bending tests. © 2001 Elsevier Science Ltd. All rights reserved.

Abstract: As a rule, solids display nonlinearity during loading in the relation between strains and stresses. Deviations from Hooke's linear constitutive law were also registered in the range of initial, small loads both in uniaxial compression and tension of crystalline rocks. Nonlinearity of strain in rocks is manifested primarily in the stress dependency of tangent or secant elasticity modulus and Poisson's ratio and is caused by closure, initiation, propagation and linkup of pre-existing and new microcracks, frictional sliding along cracks, growth of dislocations, etc. Many experimenters and standardization procedures assume that the dependence of the strain on the applied stress is linear and for practical calculations only two elasticity constants are used: The tangent or secant elasticity modulus at 50% of the failure load in compression and Poisson's ratio at the same stress level. Apart from nonlinearity many rock types and concretes have quite different stress-strain relations in tension and compression. Yet direct tensile testing is seldom performed because of its many inherent difficulties. Such unrecognized double elasticity and nonlinearity of rocks can invalidate a stress analysis, and in addition, produce a meaningless overestimate (or underestimate) of tensile strength based upon the modulus of rupture derived from a bending test. In Part I of the present study, it is shown that both double elasticity and nonlinearity have a profound effect on flexural strength of rocks as predicted by application of fundamental continuum damage mechanics relations and an appropriate technical theory. The proposed theory is validated in Part II of this work, in which an appropriate back-analysis procedure is suggested for the characterization of the mechanical properties of Dionysos marble in the uniaxial tension and compression regime from properly designed three-point bending tests. © 2001 Elsevier Science Ltd. All rights reserved.

Abstract: The influence of the plastically induced anisotropy on the formability of particulate metal matrix composites (MMCs) is studied with the aid of the strain ratio, R, and the concept of the forming limit diagram (FLD). Series of simple tension experiments were carried out for the determination of R both for the matrix material and the respective composite one. For the theoretical construction of the FLDs a modified version of the T-criterion of failure is employed, according to which materials fail by either yielding or fracture when their volume or shape change capacity is exhausted. The results are compared both with the theoretical predictions obtained by the same criterion, but ignoring the plastic anisotropy, and also with the experimental results obtained from a series of in-plane and out-of-plane sheet forming experiments. It is concluded that neglecting the plastic anisotropy may lead to fallacious conclusions.

Abstract: The propagation of a crack into a material whose mechanical and thermal properties depend on the temperature field developed around the running crack tip is studied in the present work. This is achieved by employing the Non Steady Heat Source model, for the calculation of the temperature field surrounding the crack tip region, the dynamic version of the T-criterion of failure and the experimental data concerning the variation of thermal and mechanical properties of the material with temperature. It is proved that in the immediate vicinity of the crack tip the material properties show steep gradient. Thus, if a failure criterion is to be applied for the prediction of the path of an already traveling crack, then the current values of the mechanical properties should be taken into account. Otherwise, fallacious conclusions may be drawn. The results obtained are in satisfactory agreement with the limited experimental evidence available from literature concerning both the intensity of the temperature field developed and, also, the direction of the crack propagation.

Abstract: The failure of notched beams made from Dionysos-Pentelicon marble is studied in the present work, both experimentally and numerically. A series of properly designed three point bending tests were carried out using specimens with notches of various depths. The strain variation at strategic points of the specimens, as well as the deflection of the lower fibers and the notch mouth opening displacement were recorded during the tests as functions of the applied load. The experimental results were compared with the respective ones obtained from a linear elastic and isotropic numerical solution based on the Indirect Boundary Element Method. The agreement between them was found to be satisfactory for most quantities compared. Some discrepancies observed are critically discussed. It is indicated that ignoring the nonlinearity of the stress-strain relation as well as the anisotropy and microstructure of this type of marble may lead to fallacious conclusions.

Abstract: A gradient bending theory is developed based on a strain energy fonction that includes the classical Bernoulli-Euler term, the shape correction term (microstructural length scale) introduced by Timoshenko, and a term associated with surface energy (micromaterial length scale) accounting for the bending moment gradient effect. It is shown that the last term is capable to interpret the size effect in three-point bending (3PB), namely the decrease of the failure load with decreasing beam length for the same aspect ratio. This theory is used to describe the mechanical behaviour of Dionysos-Pentelikon marble in 3PB. Series of tests with prismatic marble beams of the same aperture but with different lengths were conducted and it was concluded that the present theory predicts well the size effect.

Abstract: The mechanical behaviour of a soft-shellstone, the so called conchyliates, is studied here. Series of experiments were conducted with specimens obtained both from recent excavations and ancient blocks from the Olympia site. The mechanical properties were found to depend on the age of the material as well as on the point of the excavation. This observation and the failure mode indicated that to model the behaviour of conchyliates a Continuum Fracture Mechanics theory should be adopted, according to which the axial displacement rather than the strain is the parameter better describing the post failure behaviour under the formation of a perplex set of fractures. The agreement between theoretical predictions and experimental evidence was satisfactory for the case of newly excavated material. A recently developed honeycomb crushing model is shown to describe better the behaviour of ancient material, for which the failure mode was combination of cracking and localization of deformation.

Abstract: The mechanical behaviour of Metal Matrix Composites and their respective matrix alloys, that find extensive use in aerospace applications, is studied in the present work, from the Fracture Mechanics point of view. Experiments were executed in Single Edge Notched specimens with various initial crack inclinations and the Crack Opening Displacement was recorded versus externally applied load. An empirical criterion was established permitting easy, in situ inspection of the safety and further loading capacity of cracked structural members, already in function. A preliminary relationship between critical Crack Opening Displacement and failure criteria is indicated. The influence of the anisotropy induced by the rolling direction is also studied. © 1997 Elsevier Science Ltd.

Abstract: The problem of the abrupt change of the direction of a crack, propagating with high velocity, is studied in the present work. The study is based on a unified approach of the directional instability phenomena, which accompany running cracks. According to this approach, the running tip is simulated by a prebranched configuration, consisted of two microcracks of arbitrary lengths and orientations. The final macroscopically observed result depends both on these, a priori unknown, relative lengths and orientations of the two microcracks, and also on the stress level and crack velocity.

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Abstract: The variation of the dynamic elastic modulus in the immediate vicinity of the tip of the running crack was studied through an iterative procedure, based on the theoretical expressions for the stress-field components and the experimental relation between strain rate and elastic modulus. It was found that the elastic modulus varied strongly around the tip of the crack, both in radial and polar sense. Also it was observed that the polar distribution of the elastic modulus presented clear off-axis extrema in directions that were in good agreement with experimentally measured branching angles, thus indicating a possible relation between these two phenomena. © 1993 Chapman & Hall.

Abstract: The phenomenon of directional instability of running cracks is studied by means of a "twin-crack" model. The running single crack tip is simulated by a cloud of microcracks under the form of hackles with random lengths and orientations, which, finally, are reduced into a flat front with two dominant microbranches at their corners. A suitable fracture criterion is applied in its double geometry in order to predict the future behaviour of this pattern. The predictions obtained agree well with existing experimental evidence concerning branching angles and give strong indications that other instability phenomena (such as curving, kinking and arrest) could be approached through the same model. It is finally concluded that directional instability is governed by two groups of factors, deterministic (macroscopic) and stochastic (microscopic), and, thus, the existence of sharp critical instability conditions seems not to be natural. © 1992.

Abstract: Crack curving, combined eventually with crack branching, phenomena in thin centrally-cracked plexiglas plates under tensile, high dynamic loadings were described. Affinities between crack curving and crack branching were studied at high-loading speeds, where crack curving is intimately related with crack branching. The large scattering and deviations between the values of the branching angles derived from the tests and those obtained by applying the classical macroscopic fracture criteria suggest a modification of these criteria to appropriately describe crack curving and branching phenomena. Such a modification of the fracture creteria should give better results especially when they could be applied to small-angle star-shaped geometries of two cracks emerging from the main crack. In such geometries the two cracks are either repelling each other, when their tips are closely spaced, or they are mutually attracted, when their tips are at larger distances. Hence, the branching angle must be at the equilibrium point between repelling and attracting forces of the two neighbouring crack tips. This model yields a value of the branching angle which is equal to the half value predicted by current fracture criteria applied in their initial form. Extensive experimental evidence agrees in general with these results. © 1991.

Abstract: An improved approach for the prediction of the branching angle of running cracks is presented. It is based on the assumption that from the early steps of propagation, ahead of the running main crack-tip a tuft of microcracks is formed, from which two symmetric microcracks prevail over the others at the final steps before macroscopic branching. Further expansion of these two microcracks, which can be predicted by existing macroscopic fracture criteria, results in macroscopic branching. The unknown initial orientation of the two dominant microcracks represents the stochastic part of the whole branching phenomenon, while the main crack geometry, velocity and external load refer to the deterministic part. The results obtained by applying the T-criterion for the expected branching angle show a satisfactory agreement with existing experimental data. © 1989.

Abstract: A systematic study of the angle of crack initiation in cracked plates of ductile materials is presented. A method of measurement is proposed concerning the gathering of the experimental data and their statistical treatment. It is shown that the slope of either the bisector, or the middle line of the extending crack branches can equally well represent this angle. It is also shown that post-mortem measurements always result in absolutely lower values of this quantity, as they are compared to in-vivo measurements. Post-mortem measurements constitute a significant source of errors. A second considerable source of errors is ignorance of the rigid-body rotation of the initial crack. An evaluation of the magnitude of this rotation can be obtained experimentally by the moiré method. The corrected results are in good agreement with the theoretical predictions of the T criterion. © 1987 Society for Experimental Mechanics, Inc.

Abstract: A recently introduced method for the calculation of the reinforcement required for joining together fractured structural elements of ancient monuments is evaluated in the present study both numerically and experimentally. The method is nowadays applied in the case of the architraves of the Parthenon Temple of the Acropolis of Athens. The numerical analysis is used for the study of the influence of the exact type of loading conditions on the stress field developed, as well as for the evaluation of the stresses developed at the contact area between the architrave and the supporting capitals. The experimental assessment includes the construction of an accurate model of one of the worst damaged architraves of the north colonnade of the Temple and its loading under multi-point bending. During the loading procedure the strains, the deflections and the opening of the cracks were recorded with the aid of a system of strain gauges, dial gauges and COD-clips, respectively. The analysis of the experimental data proved that the initially multi-fractured architrave behaved as an intact structural member for loading levels exceeding the maximum expected load about 100%. © 2006 Taylor & Francis Group.

Abstract: The punch-effect that perturbates the stress and strain fields in case of marble specimens subjected to three point bending is studied in the present work. The study is carried out both experimentally and numerically. It is indicated that ignoring the punch-effect leads to fallacious conclusions concerning the load carrying capacity of such materials.

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