Effect of sample pre-cracking method and notch geometry in plane strain fracture toughness tests as applied to a PMMA resin

The influence of test method factors (notch shape, square or angular, and pre-cracking method, by tapping onto or pressing a razor blade) on the results obtained in plane strain fracture toughness test according to standard ASTM D5045 using SENB specimens made of a commercial PMMA resin were investigated. Results were analyzed quantitatively by comparing the obtained K-IC values and qualitatively by observing their effect on the Moire fringes observed using photoelasticity, showing that, at 95% significance level, the K-IC values are affected by the pre-cracking method, with the most conservative value being obtained when natural pre-cracks were introduced by tapping onto a razor blade (K-IC = 1.15 +/- 0.11 MPa.m(0.5)). This correlates with a perturbation in the stress field close to the pre-crack tip observed in the photoelasticity test sample when it was introduced by pressing the razor blade. Surprisingly, notch geometry only slightly affects the results. (C) 2012 Elsevier Ltd. All rights reserved.

Diabetic patients with and without peripheral neuropathy reveal different hip and ankle biomechanical strategies during stair descent

Background: The progression of diabetes and the challenge of daily tasks may result in changes in biomechanical strategies. Descending stairs is a common task that patients have to deal with, however it still has not been properly studied in this population. Objectives: We describe and compare the net joint moments and kinematics of the lower limbs in diabetic individuals with and without peripheral neuropathy and healthy controls during stair descent. Method: Forty-two adults were assessed: control group (13), diabetic group (14), and neuropathic diabetic group (15). The flexor and extensor net moment peaks and joint angles of the hip, knee, and ankle were described and compared in terms of effect size and ANOVAs (p<0.05). Results: Both diabetic groups presented greater dorsiflexion [large effect size] and a smaller hip extensor moment [large effect size] in the weight acceptance phase. In the propulsion phase, diabetics with and without neuropathy showed a greater hip flexor moment [large effect size] and smaller ankle extension [large effect size]. Conclusion: Diabetic patients, even without neuropathy, revealed poor eccentric control in the weight acceptance phase, and in the propulsion phase, they showed a different hip strategy, where they chose to take the leg off the ground using more flexion torque at the hip instead of using a proper ankle extension function.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

The effect of hip abduction on the EMG activity of vastus medialis obliquus, vastus lateralis longus and vastus lateralis obliquus in healthy subjects

Abstract Study design Controlled laboratory study. Objectives The purposes of this paper were to investigate (d) whether vastus medialis obliquus (VMO), vastus lateralis longus (VLL) and vastus lateralis obliquus (VLO) EMG activity can be influenced by hip abduction performed by healthy subjects. Background Some clinicians contraindicate hip abduction for patellofemoral patients (with) based on the premise that hip abduction could facilitate the VLL muscle activation leading to a VLL and VMO imbalance Methods and measures Twenty-one clinically healthy subjects were involved in the study, 10 women and 11 men (aged X = 23.3 ± 2.9). The EMG signals were collected using a computerized EMG VIKING II, with 8 channels and three pairs of surface electrodes. EMG activity was obtained from MVIC knee extension at 90° of flexion in a seated position and MVIC hip abduction at 0° and 30° with patients in side-lying position with the knee in full extension. The data were normalized in the MVIC knee extension at 50° of flexion in a seated position, and were submitted to ANOVA test with subsequent application of the Bonferroni multiple comparisons analysis test. The level of significance was defined as p ≤ 0.05. Results The VLO muscle demonstrated a similar pattern to the VMO muscle showing higher EMG activity in MVIC knee extension at 90° of flexion compared with MVIC hip abduction at 0° and 30° of abduction for male (p < 0.0007) and MVIC hip abduction at 0° of abduction for female subjects (p < 0.02196). There were no statistically significant differences in the VLL EMG activity among the three sets of exercises tested. Conclusion The results showed that no selective EMG activation was observed when comparison was made between the VMO, VLL and VLO muscles while performing MVIC hip abduction at 0° and 30° of abduction and MVIC knee extension at 90° of flexion in both male and female subjects. Our findings demonstrate that hip abduction do not facilitated VLL and VLO activity in relation to the VMO, however, this study included only healthy subjects performing maximum voluntary isometric contraction contractions, therefore much remains to be discovered by future research

Fracture resistance of endodontically treated teeth restored with different intraradicular posts with different lengths

Aim: This study compared the resistance to fracture of endodontically treated teeth restored with different intraradicular posts with different lengths and full coverage metallic crowns. Methods: Sixty extracted human canine teeth were randomly divided into 6 groups. Groups CP5, CP75 and CP10 were restored using custom cast post and core (CP) and groups PF5, PF75 and PF10 were restored with provisional pre-fabricated tin post (PF) and composite resin core at 5 mm, 7.5 mm and 10 mm of intraradicular length, respectively. The specimens were submitted to dynamic cyclic loading and those that resisted to this load were submitted to load compression using a universal testing machine. Compressive load was applied at a 45-degree angle to the long axis of the tooth until failure. Results: Kruskal-Wallis one-way analysis of variance by ranks showed statistically significant differences among the groups (p<0.0001). However, when the means were compared using the Tukey’s test, significant differences were noted between groups CP5 and CP10 and between groups CP10 and PF5. All groups presented root fractures and post displacements during mechanical cycling. All teeth in groups CP5 and PF5 failed the dynamic cycling test. Conclusions: This study showed that increasing intraradicular post length also increases resistance to fracture of endodontically treated teeth. On the other hand, most endodontically treated teeth restored with pre-fabricated tin posts (provisional posts) failed in the dynamic cycling test

Increased vertebral morphometric fracture in patients with postsurgical hypoparathyroidism despite normal bone mineral density

Background In human malaria, the naturally-acquired immune response can result in either the elimination of the parasite or a persistent response mediated by cytokines that leads to immunopathology. The cytokines are responsible for all the symptoms, pathological alterations and the outcome of the infection depends on the reciprocal regulation of the pro and anti-inflammatory cytokines. IL-10 and IFN-gamma are able to mediate this process and their production can be affected by single nucleotide polymorphisms (SNPs) on gene of these cytokines. In this study, the relationship between cytokine IL-10/IFN-gamma levels, parasitaemia, and their gene polymorphisms was examined and the participation of pro-inflammatory and regulatory balance during a natural immune response in Plasmodium vivax-infected individuals was observed. Methods The serum levels of the cytokines IL-4, IL-12, IFN-gamma and IL-10 from 132 patients were evaluated by indirect enzyme-linked immunosorbent assays (ELISA). The polymorphism at position +874 of the IFN-gamma gene was identified by allele-specific polymerase chain reaction (ASO-PCR) method, and the polymorphism at position -1082 of the IL-10 gene was analysed by PCR-RFLP (PCR-Restriction Fragment Length Polymorphism). Results The levels of a pro- (IFN-gamma) and an anti-inflammatory cytokine (IL-10) were significantly higher in P. vivax-infected individuals as compared to healthy controls. The IFN-gamma levels in primoinfected patients were significantly higher than in patients who had suffered only one and more than one previous episode. The mutant alleles of both IFN-gamma and IL-10 genes were more frequent than the wild allele. In the case of the IFNG+874 polymorphism (IFN-gamma) the frequencies of the mutant (A) and wild (T) alleles were 70.13% and 29.87%, respectively. Similar frequencies were recorded in IL-10-1082, with the mutant (A) allele returning a frequency of 70.78%, and the wild (G) allele a frequency of 29.22%. The frequencies of the alleles associated with reduced production of both IFN-gamma and IL-10 were high, but this effect was only observed in the production of IFN-gamma. Conclusions This study has shown evidence of reciprocal regulation of the levels of IL-10 and IFN-gamma cytokines in P. vivax malaria, which is not altered by the presence of polymorphism in the IL-10 gene.

Evaluation of movements of lower limbs in non-professional ballet dancers: hip abduction and flexion

Background The literature indicated that the majority of professional ballet dancers present static and active dynamic range of motion difference between left and right lower limbs, however, no previous study focused this difference in non-professional ballet dancers. In this study we aimed to evaluate active movements of the hip in non-professional classical dancers. Methods We evaluated 10 non professional ballet dancers (16-23 years old). We measured the active range of motion and flexibility through Well Banks. We compared active range of motion between left and right sides (hip flexion and abduction) and performed correlation between active movements and flexibility. Results There was a small difference between the right and left sides of the hip in relation to the movements of flexion and abduction, which suggest the dominant side of the subjects, however, there was no statistical significance. Bank of Wells test revealed statistical difference only between the 1st and the 3rd measurement. There was no correlation between the movements of the hip (abduction and flexion, right and left sides) with the three test measurements of the bank of Wells. Conclusion There is no imbalance between the sides of the hip with respect to active abduction and flexion movements in non-professional ballet dancers.

A comparative radiographic investigation of femoroacetabular impingement in young patients with and without hip pain

OBJECTIVE: To compare the existence of radiographic abnormalities in two groups of patients, those with and without hip pain. METHODS: A total 222 patients were evaluated between March 2007 and April 2009; 122 complained of groin pain, and 100 had no symptoms. The individuals in both groups underwent radiographic examinations of the hip using the following views: anteroposterior, Lequesne false profile, Dunn, Dunn 45º, and Ducroquet. RESULTS: A total of 1110 radiographs were evaluated. Female patients were prevalent in both groups (52% symptomatic, 58% asymptomatic). There were statistically significant differences between the groups in age (p<0.0001), weight (p = 0.002) and BMI (p = 0.006). The positive findings in the group with groin pain consisted of the presence of a bump on the femoral head in the anteroposterior view (p<0.0001) or in the Dunn 45º view (p = 0.008). The difference in the a angle in the anteroposterior, Dunn, Dunn 45º, and Ducroquet views for all of the cases studied was p,0.0001. The joint space measurement differed significantly between groups in the Lequesne view (p = 0.007). The Lequesne anteversion angle (ρ) and the femoral offset measurement also differed significantly (p = 0.005 and p = 0.0001, respectively). CONCLUSIONS: We conclude that the best views for diagnosing a femoroacetabular impingement are the anteroposterior pelvic orthostatic, the Dunn 45º, and the Ducroquet views. The following findings correlated with hip pain: a decrease in the femoral offset, an increase in the α angle, an increase in the Lequesne ρ angle, a decrease in the CE angle of Wiberg, a thinner articular space and the presence of a bump on the femoral head-neck transition.

In vitro fracture resistance of glass-fiber and cast metal posts with different designs

PURPOSE: To evaluate the in vitro fracture resistance of roots with glass-fiber and metal dowels with different designs. METHODS: Fifty-endodontically treated maxillary central incisors were embedded in acrylic resin. Ten of them received only the coronary preparation, and the remaining forty were embedded (except for 4mm of the cervical area) after removing the clinical crowns. Specimens were divided into five groups (n=10): control (teeth with only coronary preparation), cylindrical cast dowel, conical cast dowel, cylindrical glass-fiber dowel and conical glass-fiber dowel. Specimens were subjected to an increasing compressive load (N) until fracture. RESULTS: ANOVA indicated significant difference (P<.05) among the groups, and the Tukey-Kramer´s test identified these differences. The control group (867±243 N) presented the highest values and was statistically similar to cylindrical glass-fiber dowel group (711±180 N). There is no significant difference among the metal dowel cylindrical (435±245 N) or conical (585±164 N) group and conical glass-fiber dowel (453±112 N). Cylindrical glass-fiber dowel (711±180 N) and conical cast dowel and core (585±164 N) groups had intermediate values and did not differ from each other. CONCLUSIONS: Cylindrical glass fiber dowels represent a viable alternative to the cast-metal dowel cylindrical or conical. Cylindrical glass fiber dowels also increase endodontically treated incisors' resistance to fracture.

Incidence of lower limb bone fractures in female individuals of Aracaju (Sergipe), Brazil

Studies indicate that the number of hip bone fractures caused by osteoporosis may rise from 1.66 to 6.26 million until 2050, worldwide. For this reason, implementation of preventive measures becomes a necessity. Female individuals are usually more affected due to a variety of factors including old age, early menopause, chronicle disease in the family history, calcium deficit, as well as the lack of physical exercise (sedentary individual). The aim of this study was to estimate the incidence of hip and lower limb fracture in female individuals’ resident in Aracaju city. From the period of January 2008-2009, around of 300 fracture cases were of lower limb analyzed from females. The incidence of femur fractures in women increased according to age group, 66.17 individuals per 10,000 inhabitants (over 60 years-old). These findings allow us to conclude that the incidence of hip and lower limb bone fractures among women over 60 years were more significant in the femur.

Hip-hop and Construction of Group Identity in a Stigmatized Area. : A Field Study regarding Cultural Capital among Roma Youths in Konik, Montenegro.

This research aimed for an extended knowledge and understanding of young people in stigmatized areas and their construction of group identity. With a focus on Roma youths in Konik, Montenegro, and their involvement in hip-hop we wanted to explore what this culture meant to them in relation to their context. An ethnographic approach was used in collecting the empirical data through observations, interpreting music lyrics and conducting qualitative semi-structured interviews. Five young Roma boys from Konik, all involved in hip-hop, were interviewed. Theoretical perspectives on identity, youth culture and stigmatization were central. In addition, Bourdieu’s theory regarding cultural capital was emphasized and connected to youths and hip-hop. The empirical material showed that involvement in hip-hop provided the Roma youths with a group identity that they referred to in positive terms. Contextual factors of stigmatization excluded the Roma group from the majority population and the engagement in hip-hop created a possibility for the youths to be someone. The cultural capital gained through hip-hop was not used to verify and legitimate an authentic Roma identity. It was rather a way for them to create boundaries towards the negative elements in their community.

Primary stability in cementless total hip replacement: measurement techniques and aided-surgery

Primary stability of stems in cementless total hip replacements is recognized to play a critical role for long-term survival and thus for the success of the overall surgical procedure. In Literature, several studies addressed this important issue. Different approaches have been explored aiming to evaluate the extent of stability achieved during surgery. Some of these are in-vitro protocols while other tools are coinceived for the post-operative assessment of prosthesis migration relative to the host bone. In vitro protocols reported in the literature are not exportable to the operating room. Anyway most of them show a good overall accuracy. The RSA, EBRA and the radiographic analysis are currently used to check the healing process of the implanted femur at different follow-ups, evaluating implant migration, occurance of bone resorption or osteolysis at the interface. These methods are important for follow up and clinical study but do not assist the surgeon during implantation. At the time I started my Ph.D Study in Bioengineering, only one study had been undertaken to measure stability intra-operatively. No follow-up was presented to describe further results obtained with that device. In this scenario, it was believed that an instrument that could measure intra-operatively the stability achieved by an implanted stem would consistently improve the rate of success. This instrument should be accurate and should give to the surgeon during implantation a quick answer concerning the stability of the implanted stem. With this aim, an intra-operative device was designed, developed and validated. The device is meant to help the surgeon to decide how much to press-fit the implant. It is essentially made of a torsional load cell, able to measure the extent of torque applied by the surgeon to test primary stability, an angular sensor that measure the relative angular displacement between stem and femur, a rigid connector that enable connecting the device to the stem, and all the electronics for signals conditioning. The device was successfully validated in-vitro, showing a good overall accuracy in discriminating stable from unstable implants. Repeatability tests showed that the device was reliable. A calibration procedure was then performed in order to convert the angular readout into a linear displacement measurement, which is an information clinically relevant and simple to read in real-time by the surgeon. The second study reported in my thesis, concerns the evaluation of the possibility to have predictive information regarding the primary stability of a cementless stem, by measuring the micromotion of the last rasp used by the surgeon to prepare the femoral canal. This information would be really useful to the surgeon, who could check prior to the implantation process if the planned stem size can achieve a sufficient degree of primary stability, under optimal press fitting conditions. An intra-operative tool was developed to this aim. It was derived from a previously validated device, which was adapted for the specific purpose. The device is able to measure the relative micromotion between the femur and the rasp, when a torsional load is applied. An in-vitro protocol was developed and validated on both composite and cadaveric specimens. High correlation was observed between one of the parameters extracted form the acquisitions made on the rasp and the stability of the corresponding stem, when optimally press-fitted by the surgeon. After tuning in-vitro the protocol as in a closed loop, verification was made on two hip patients, confirming the results obtained in-vitro and highlighting the independence of the rasp indicator from the bone quality, anatomy and preserving conditions of the tested specimens, and from the sharpening of the rasp blades. The third study is related to an approach that have been recently explored in the orthopaedic community, but that was already in use in other scientific fields. It is based on the vibration analysis technique. This method has been successfully used to investigate the mechanical properties of the bone and its application to evaluate the extent of fixation of dental implants has been explored, even if its validity in this field is still under discussion. Several studies have been published recently on the stability assessment of hip implants by vibration analysis. The aim of the reported study was to develop and validate a prototype device based on the vibration analysis technique to measure intra-operatively the extent of implant stability. The expected advantages of a vibration-based device are easier clinical use, smaller dimensions and minor overall cost with respect to other devices based on direct micromotion measurement. The prototype developed consists of a piezoelectric exciter connected to the stem and an accelerometer attached to the femur. Preliminary tests were performed on four composite femurs implanted with a conventional stem. The results showed that the input signal was repeatable and the output could be recorded accurately. The fourth study concerns the application of the device based on the vibration analysis technique to several cases, considering both composite and cadaveric specimens. Different degrees of bone quality were tested, as well as different femur anatomies and several levels of press-fitting were considered. The aim of the study was to verify if it is possible to discriminate between stable and quasi-stable implants, because this is the most challenging detection for the surgeon in the operation room. Moreover, it was possible to validate the measurement protocol by comparing the results of the acquisitions made with the vibration-based tool to two reference measurements made by means of a validated technique, and a validated device. The results highlighted that the most sensitive parameter to stability is the shift in resonance frequency of the stem-bone system, showing high correlation with residual micromotion on all the tested specimens. Thus, it seems possible to discriminate between many levels of stability, from the grossly loosened implant, through the quasi-stable implants, to the definitely stable one. Finally, an additional study was performed on a different type of hip prosthesis, which has recently gained great interest thus becoming fairly popular in some countries in the last few years: the hip resurfacing prosthesis. The study was motivated by the following rationale: although bone-prosthesis micromotion is known to influence the stability of total hip replacement, its effect on the outcome of resurfacing implants has not been investigated in-vitro yet, but only clinically. Thus the work was aimed at verifying if it was possible to apply to the resurfacing prosthesis one of the intraoperative devices just validated for the measurement of the micromotion in the resurfacing implants. To do that, a preliminary study was performed in order to evaluate the extent of migration and the typical elastic movement for an epiphyseal prosthesis. An in-vitro procedure was developed to measure micromotions of resurfacing implants. This included a set of in-vitro loading scenarios that covers the range of directions covered by hip resultant forces in the most typical motor-tasks. The applicability of the protocol was assessed on two different commercial designs and on different head sizes. The repeatability and reproducibility were excellent (comparable to the best previously published protocols for standard cemented hip stems). Results showed that the procedure is accurate enough to detect micromotions of the order of few microns. The protocol proposed was thus completely validated. The results of the study demonstrated that the application of an intra-operative device to the resurfacing implants is not necessary, as the typical micromovement associated to this type of prosthesis could be considered negligible and thus not critical for the stabilization process. Concluding, four intra-operative tools have been developed and fully validated during these three years of research activity. The use in the clinical setting was tested for one of the devices, which could be used right now by the surgeon to evaluate the degree of stability achieved through the press-fitting procedure. The tool adapted to be used on the rasp was a good predictor of the stability of the stem. Thus it could be useful for the surgeon while checking if the pre-operative planning was correct. The device based on the vibration technique showed great accuracy, small dimensions, and thus has a great potential to become an instrument appreciated by the surgeon. It still need a clinical evaluation, and must be industrialized as well. The in-vitro tool worked very well, and can be applied for assessing resurfacing implants pre-clinically.

Development of musculoskeletal models for the design and the pre-clinical validation of hip resurfacing prosthesis

Background. The surgical treatment of dysfunctional hips is a severe condition for the patient and a costly therapy for the public health. Hip resurfacing techniques seem to hold the promise of various advantages over traditional THR, with particular attention to young and active patients. Although the lesson provided in the past by many branches of engineering is that success in designing competitive products can be achieved only by predicting the possible scenario of failure, to date the understanding of the implant quality is poorly pre-clinically addressed. Thus revision is the only delayed and reliable end point for assessment. The aim of the present work was to model the musculoskeletal system so as to develop a protocol for predicting failure of hip resurfacing prosthesis. Methods. Preliminary studies validated the technique for the generation of subject specific finite element (FE) models of long bones from Computed Thomography data. The proposed protocol consisted in the numerical analysis of the prosthesis biomechanics by deterministic and statistic studies so as to assess the risk of biomechanical failure on the different operative conditions the implant might face in a population of interest during various activities of daily living. Physiological conditions were defined including the variability of the anatomy, bone densitometry, surgery uncertainties and published boundary conditions at the hip. The protocol was tested by analysing a successful design on the market and a new prototype of a resurfacing prosthesis. Results. The intrinsic accuracy of models on bone stress predictions (RMSE < 10%) was aligned to the current state of the art in this field. The accuracy of prediction on the bone-prosthesis contact mechanics was also excellent (< 0.001 mm). The sensitivity of models prediction to uncertainties on modelling parameter was found below 8.4%. The analysis of the successful design resulted in a very good agreement with published retrospective studies. The geometry optimisation of the new prototype lead to a final design with a low risk of failure. The statistical analysis confirmed the minimal risk of the optimised design over the entire population of interest. The performances of the optimised design showed a significant improvement with respect to the first prototype (+35%). Limitations. On the authors opinion the major limitation of this study is on boundary conditions. The muscular forces and the hip joint reaction were derived from the few data available in the literature, which can be considered significant but hardly representative of the entire variability of boundary conditions the implant might face over the patients population. This moved the focus of the research on modelling the musculoskeletal system; the ongoing activity is to develop subject-specific musculoskeletal models of the lower limb from medical images. Conclusions. The developed protocol was able to accurately predict known clinical outcomes when applied to a well-established device and, to support the design optimisation phase providing important information on critical characteristics of the patients when applied to a new prosthesis. The presented approach does have a relevant generality that would allow the extension of the protocol to a large set of orthopaedic scenarios with minor changes. Hence, a failure mode analysis criterion can be considered a suitable tool in developing new orthopaedic devices.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Fracture Mechanics Investigation of Structures with Defects

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities. This dissertation, concentrates on some of the fractural aspects of shaft and composite which have being increasingly used in modern structures, consists four chapters within two parts. Chapters 1 to 4 are included in part 1. In the first chapter, the basic knowledge about the stress and displacement fields in the vicinity of a crack tip is introduced. A review involves the general methods of calculating stress intensity factors are presented. In Chapter 2, two simple engineering methods for a fast and close approximation of stress intensity factors of cracked or notched beams under tension, bending moment, shear force, as well as torque are presented. New formulae for calculating the stress intensity factors are proposed. One of the methods named Section Method is improved and applied to the three dimensional analysis of cracked circular section for calculating stress intensity factors. The comparisons between the present results and the solutions calculated by ABAQUS for single mode and mixed mode are studied. In chapter 3, fracture criteria for a crack subjected to mixed mode loading of two-dimension and three-dimension are reviewed. The crack extension angle for single mode and mixed mode, and the critical loading domain obtained by SEDF and MTS are compared. The effects of the crack depth and the applied force ratio on the crack propagation angle and the critical loading are investigated. Three different methods calculating the crack initiation angle for three-dimension analysis of various crack depth and crack position are compared. It should be noted that the stress intensity factors used in the criteria are calculated in section 2.1.