Stavros K. Kourkoulis

The Stress Field in a Standardized Brazilian Disc: The Influence of the Loading Type Acting on the Actual Contact Length

The aim of the present study was to determine the stress field developed in a Brazilian disc under conditions closely approaching those of the actual test executed according to the standardized procedure suggested by the International Society for Rock Mechanics. Advantage is taken of a recently introduced analytic solution for a mixed fundamental contact problem where the disc and the jaw are considered as a system of two interacting elastic bodies. Using the outcomes of that study, the complex potentials method is employed here for the solution of a first fundamental problem for a Brazilian disc under a parabolic load distribution. Analytic full-field formulae for the components of the stress field developed in the disc are given. The solution is then applied for the case of a disc made from Dionysos marble. The results are compared to existing ones obtained from solutions adopting statically equivalent loads either in the form of distributed (uniform or sinusoidally) radial pressure acting along the actual contact rim or in the form of diametrically acting point (line) loads. While the stress field in the major part of the disc seems to be rather insensitive to the exact load application mode, critical differences are detected in the vicinity of the loaded arc of the disc. The solution is assessed according to the results of a short series of Brazilian disc tests with PMMA specimens. The agreement between theoretical predictions and experimental data is satisfactory. Finally, it is indicated that, as opposed to previous solutions, the stress field (even at the disc’s center) is a non-linear function of the externally applied load depending, among others, indirectly on the properties of the disc’s and jaw’s materials, the combination of which dictates the extent of the contact angle.

A parametric study of cylindrical pedicle screw design implications on the pullout performance using an experimentally validated finite element model

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 screws 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.

Influence of nonlinearity and double elasticity on flexure of rock beams — II. Characterization of Dionysos marble

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 compression 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 combination 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.

The influence of the insertion technique on the pullout force of pedicle screws: an experimental study.

Study Design. The pullout strength of a typical pedicle screw was evaluated experimentally for different screw insertion techniques. Objective. To conclude whether the self-tapping insertion technique is indeed the optimum one for self-tapping screws, with respect to the pullout strength. Summary of Background Data. It is reported in the literature that the size of the pilot-hole significantly influences the pullout strength of a self-tapping screw. In addition it is accepted that an optimum value of the diameter of the pilot-hole exists. For non self-tapping screw insertion it is reported that undertapping of the pilot-hole can increase its pullout strength. Finally it is known that in some cases orthopedic surgeons open the threaded holes, using another screw instead of a tap. Methods. A typical commercial self-tapping pedicle screw was inserted into blocks of Solid Rigid Polyurethane Foam (simulating osteoporotic cancellous bone), following different insertion techniques. The pullout force was measured according to the ASTM-F543–02 standard. The screw was inserted into previously prepared holes of different sizes, either threaded or cylindrical, to conclude whether an optimum size of the pilot-hole exists and whether tapping can increase the pullout strength. The case where the tapping is performed using another screw was also studied. Results. For screw insertion with tapping, decreasing the outer radius of the threaded hole from 1.00 to 0.87 of the screws outer radius increased the pullout force 9%. For insertion without tapping, decreasing the pilot-holes diameter from 0.87 to 0.47 of the screws outer diameter increased its pullout force 75%. Finally, tapping using another screw instead of a tap, gave results similar to those of conventional tapping. Conclusion. Undertapping of a pilot-hole either using a tap or another screw can increase the pullout strength of self-tapping pedicle screws.

A comparative biomechanical study for complex tibial plateau fractures: Nailing and compression bolts versus modern and traditional plating

AIM To compare the biomechanical properties of a newly proposed technique, utilizing intramedullary nailing and compression bolts, for the osteosynthesis of intra-articular proximal tibial fractures with meta-diaphyseal comminution, with modern and conventional plating techniques. METHODS Fifteen left tibia 4th generation composite Sawbones models (in 3 groups of 5 for each technique) with identically reproduced type VI Schatzker tibial plateau fractures, including meta-diaphyseal dissociation, were used. Three different techniques of osteosynthesis were tested: (a) a new technique that combines intramedullary nailing and compression bolts, (b) internal fixation with a single lateral locking plate and (c) internal fixation with dual buttress plating technique. The model-device constructs were successively subjected to 500N, 1000N and 1500N load levels with five cycles applied at each level on both articular compartments and a final load cycle to failure. Four parameters were recorded for each technique: the average reversible or irreversible displacement in vertical subsidence, the horizontal diastasis of the intra-articular fracture, the average passive construct stiffness and the load to failure. RESULTS The new intramedullary nailing technique provided rigid intra-articular osteosynthesis being statistically similar to dual buttress plating for subsidence at medium and higher load levels. At the same time the proposed technique provided statistically equivalent stiffness values to the single lateral locking plate incarnating the rational of biologic fixation. Average load to failure was 1611N for single lateral locking plates, 2197N for intramedullary nailing and 4579N for dual buttress plating. The single lateral locking plate technique had the worse results in interfragmentary displacement while dual buttress plating was superior in stiffness from the other 2 techniques. The mode of failure differed between techniques, with collapse of medial plateau occurring exclusively in the single lateral locking plates group. CONCLUSION The proposed new technique of intramedullary nailing and compression bolts demonstrates a flexural behaviour similar to single lateral locking plates, which complies with the terms and benefits of biological fixation, while at the same time maintains a rigid intra-articular stability similar to the stiff dual buttressing plating technique.

Influence of nonlinearity and double elasticity on flexure of rock beams — I. Technical theory

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.

Naturally Accepted Boundary Conditions for the Brazilian Disc Test and the Corresponding Stress Field

The stress field developed in the Brazilian disc is determined assuming that the disc is under the influence of a combination of two load distributions, namely normal (radial)- and shear (frictional)-stresses, both of them acting along two finite symmetric arcs of the disc periphery. The nature of the two distributions as well as the extent of the loaded arcs are obtained from the solution of the respective contact problem according to which the disc and the jaw are considered as a system of two elastic plane bodies in contact pressed against each other. Emphasis is given to the stresses due to friction since the stress field due to the specific distribution of radial pressure is already known. It is concluded that the role of friction cannot be ignored, especially in the immediate vicinity of the contact rim. Moreover, for high surface roughness the overall transverse normal stress component in this region becomes of tensile nature indicating increased possibility of premature local cracking (taking into account the low tensile strength of the materials tested using the Brazilian disc test). On the other hand, the stress field at the disc’s center is totally insensitive to both the exact distribution of radial pressure and also to the presence or absence of friction. It is thus indicated that in case fracture in the immediate vicinity of the contact rim is by some means suppressed (reducing for example drastically the coefficient of friction) the results of the Brazilian disc test correspond, in a satisfactory manner, to those predicted by Hondros’ classic approach.

Age- and region-related changes in the biomechanical properties and composition of the human ureter

The ureter has been largely overlooked heretofore in the study of the biomechanics of soft biological tissues, although there has been significant motivation to use its biomechanical properties as inputs to mathematical models of ureteral function. Herein, we used histological analysis for quantification of collagen contents and thickness/area of ureteral layers, with concomitant geometrical analysis of zero-stress and no-load states, and inflation/extension testing to biomechanically characterize with the Fung-type model the ureters from cadavers. The effects of age and gender on the regional distribution of those properties were examined. Tissue properties did not differ (p>0.05) between the left and right ureter. Regional heterogeneity was established that was profoundly age-related but seldom gender-related, based on the following evidence: 1) In younger subjects, the axial stress-circumferential strain curves of upper ureter were shifted to smaller stresses and model parameter a2 representing axial stiffness was smallest (p<0.05), i.e. upper ureter was the least stiff region axially; 2) upper ureter underwent axial stiffening with advanced age, evidenced by the increasing (p<0.05) parameter a2, and the stress-strain curves were uniformly exhibited along the ureter, evidenced by the non-varying (p>0.05) parameters C,a1,a2,anda4; 3) aging raised (p<0.05) the collagen content of upper ureter to favor a near-uniform regional distribution; 4) wall thickness increased with age, unlike the opening angle and residual strains, reflecting the thickening of outer (muscular) vs. inner (mucosal) layers in aged subjects, with significant differences (p<0.05) in some regions; and 5) gender affected little (p>0.05) the opening angle and morphometry of no-load and zero-stress states.

Regional distribution of circumferential residual strains in the human aorta according to age and gender.

The biomechanical response of the human aorta varies with axial location, but little is known about the respective variation of residual strains. Such data are available for common lab animals, but in the traditional opening angle measurement the aorta is considered as an ideal cylinder and average residual strains are measured, so that the spatial variations of local residual strains are not determined. The present study provides opening angle and residual strain data throughout the course and around the circumference of the aorta harvested during autopsy. Opening angle showed notable topographical variation; the highest value was at the top of aortic arch, declining abruptly toward the ascending aorta and to a near-constant value in the descending aorta, and rising in the abdominal aorta. The variation of curvature and of external but not internal residual stretch resembled that of opening angle. Extensive residual stress and wall thickness differences were evidenced among quadrants, with the more pre-stressed being also the thicker quadrants. Gender had overall minor effects, but aging led to increased parameters, occurring earlier in the distal aorta but at later stages becoming predominant proximally. Differences in caliber were pronounced in older subjects, unlike those in opening angle, residual stretches, and thickness that were striking in middle-aged subjects. By contrast, curvature decreased with aging in relation to the smaller percentwise opening angle differences. Detailed knowledge of the zero-stress/no-load geometry of the human aortic wall is critical for an in-depth understanding of aortic physiology, while providing the basis for comparison with disease.

Interconnected Epistyles of Marble Monuments Under Axial Loads

The restoration of destroyed connections of epistyles joined together by means of metallic connectors is among the most difficult problems encountered by scientists working for the conservation/restoration of monuments made of marble. The complexity of the geometry and the interaction of three completely different materials (metal-filling material-marble) constituting the connection render the study (either experimental or analytic) extremely complicated. In this direction a numerical analysis is presented here in order to deeply understand the response of a typical ancient connection subjected to axial loads as well as to quantify the influence of some geometric parameters on its response. The parameters studied include the length of the connector, the width of its flanges, the depth of the groove (mortise), the existence or not of relieving space and the filling material’s volume. The numerical model was calibrated and validated according to the results of an earlier experimental study realized on the worksite of the Parthenon Temple. It was concluded that the interventions required to relieve the stress field by changing the size of the connector are disproportional to the respective positive effect on the response of the connection. Moreover it was proved that the most beneficial parameter is the relieving space.