Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Savani: A variable resolution whole-mantle model of anisotropic shear velocity variations based on multiple data sets

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Bonding agent underneath sealant: shear bond strength to oil-contaminated

This study evaluated in vitro the shear bond strength of a resin-based pit-and-fissure sealant (Fluroshield - F) associated with either an ethanol-based (Adper Single Bond 2 - SB) or an acetone-based (Prime & Bond - PB) adhesive system under conditions of oil contamination. Mesial and distal enamel surfaces from 30 sound third molars were randomly assigned to 2 groups (n=30): I - no oil contamination; II - oil contamination. Contamination (0.25 mL during 10 s) was performed after 37% phosphoric acid etching with an air/oil spray. The specimens were randomly assigned to subgroups, according to the bonding protocol adopted: subgroup A - F was applied to enamel without an intermediate bonding agent layer; In subgroups B and C, SB and PB, respectively, were applied, light-cured, and then F was applied and light-cured. Shear bond strength was tested at a crosshead speed of 0.5 mm/min in a universal testing machine. Means (± SD) in MPa were: IA-11.28 (±1.84); IIA-12.02 (±1.15); IB-9.73 (±2.38); IIB-9.62 (±2.29); IC-28.30 (±1.63); and IIC-25.50 (±1.91). It may be concluded that the oil contamination affected negatively the sealant bonding to enamel and the acetone-based adhesive system (PB) layer applied underneath the sealant was able to prevent its deleterious effects to adhesion.

Shear bond strength of self-etch and total-etch bonding systems at different dentin depths

The purpose of this study was to evaluate the dentin shear bond strength of four adhesive systems (Adper Single Bond 2, Adper Prompt L-Pop, Magic Bond DE and Self Etch Bond) in regards to buccal and lingual surfaces and dentin depth. Forty extracted third molars had roots removed and crowns bisected in the mesiodistal direction. The buccal and lingual surfaces were fixed in a PVC/acrylic resin ring and were divided into buccal and lingual groups assigned to each selected adhesive. The same specimens prepared for the evaluation of superficial dentin shear resistance were used to evaluate the different depths of dentin. The specimens were identified and abraded at depths of 0.5, 1.0, 1.5 and 2.0 mm. Each depth was evaluated by ISO TR 11405 using an EMIC-2000 machine regulated at 0.5 mm/min with a 200 Kgf load cell. We performed statistical analyses on the results (ANOVA, Tukey and Scheffé tests). Data revealed statistical differences (p < 0.01) in the adhesive and depth variation as well as adhesive/depth interactions. The Adper Single Bond 2 demonstrated the highest mean values of shear bond strength. The Prompt L-Pop product, a self-etching adhesive, revealed higher mean values compared with Magic Bond DE and Self Etch Bond adhesives, a total and self-etching adhesive respectively. It may be concluded that the shear bond strength of dentin is dependent on material (adhesive system), substrate depth and adhesive/depth interaction.

Effect of casting atmosphere on the shear bond strength of a ceramic to Ni-Cr and Ni-Cr-Be alloys

The success of metal-ceramic restorations depends on an optimal bond between metal and ceramic. This study evaluated the effect of 3 casting atmospheres on the metal-ceramic bond strength (MCBS) of 2 Ni-Cr alloys, with beryllium (Fit Cast V) and without beryllium (Fit Cast SB). Sixty acrylic resin patterns (8 mm long and 5 mm diameter) were obtained using a fluorocarbon resin matrix. Wax was used to refine the surface of acrylic resin patterns that were invested and cast in an induction casting machine under normal, vacuum, and argon atmospheres at a temperature of 1340ºC. The castings were divested manually and airborne-particle abraded with 100-µm aluminum-oxide. Ten castings were obtained for each group. The IPS Classic V ceramic was applied (2 mm high and 5 mm diameter). The shear bond strength was tested in a mechanical testing machine with a crosshead speed of 2.0 mm/min. The MCBS data (MPa) were subjected to 2-way analysis of variance (α=0.05). There was no statistically significant difference (p>0.05) between the alloys or among the casting atmospheres. Within the limitations of this study, it may be concluded that the presence of beryllium and the casting atmosphere did not interfere in the MCBS of the evaluated metal-ceramic combinations

Effect of temporary cements on the shear bond strength of luting cements

OBJECTIVE: The purpose of this study was to evaluate, by shear bond strength (SBS) testing, the influence of different types of temporary cements on the final cementation using conventional and self-etching resin-based luting cements. Material and Methods: Forty human teeth divided in two halves were assigned to 8 groups (n=10): I and V (no temporary cementation); II and VI: Ca(OH)2-based cement; III and VII: zinc oxide (ZO)-based cement; IV and VIII: ZO-eugenol (ZOE)-based cement. Final cementation was done with RelyX ARC cement (groups I to IV) and RelyX Unicem cement (groups V to VIII). Data were analyzed statistically by ANOVA and Tukey's test at 5% significance level. RESULTS: Means were (MPa): I - 3.80 (±1.481); II - 5.24 (±2.297); III - 6.98 (±1.885); IV - 6.54 (±1.459); V - 5.22 (±2.465); VI - 4.48 (±1.705); VII - 6.29 (±2.280); VIII - 2.47 (±2.076). Comparison of the groups that had the same temporary cementation (Groups II and VI; III and VII; IV and VIII) showed statistically significant difference (p<0.001) only between Groups IV and VIII, in which ZOE-based cements were used. The use of either Ca(OH)2-based (Groups II and VI) or ZO-based (Groups III and VII) cements showed no statistically significant difference (p>0.05) for the different luting cements (RelyX TM ARC and RelyX TM Unicem). The groups that had no temporary cementation (Groups I and V) did not differ significantly from each other either (p>0.05). CONCLUSION: When temporary cementation was done with ZO- or ZOE-based cements and final cementation was done with RelyX ARC, there was an increase in the SBS compared to the control. In the groups cemented with RelyX Unicem, however, the use of a ZOE-based temporary cement affected negatively the SBS of the luting agent used for final cementation.

Influence of light-curing unit systems on shear bond strength and marginal microleakage of composite resin restorations

The aim of the present study was to evaluate the influence of different photopolymerization (halogen, halogen soft-start and LED) systems on shear bond strength (SBS) and marginal microleakage of composite resin restorations. Forty Class V cavities (enamel and dentin margins) were prepared for microleakage assessment, and 160 enamel and dentin fragments were prepared for the SBS test, and divided into 4 groups. Kruskal-Wallis and Wilcoxon tests showed statistically significant difference in microleakage between the margins (p < 0.01) with incisal margins presenting the lowest values. Among the groups, it was observed that, only at the cervical margin, halogen soft-start photo polymerization presented statistically significant higher microleakage values. For SBS test, ANOVA showed no statistical difference (p > 0.05) neither between substrates nor among groups. It was concluded that Soft-Start technique with high intensity end-light influenced negatively the cervical marginal sealing, but the light-curing systems did not influence adhesion.

Adhesion of an endodontic sealer to dentin and gutta-percha: shear and push-out bond strength measurements and SEM analysis

The use of an adequate method for evaluation of the adhesion of root canal filling materials provides more reliable results to allow comparison of the materials and substantiate their clinical choice. The aims of this study were to compare the shear bond strength (SBS) test and push-out test for evaluation of the adhesion of an epoxy-based endodontic sealer (AH Plus) to dentin and gutta-percha, and to assess the failure modes on the debonded surfaces by means of scanning electron microscopy (SEM). Three groups were established (n=7): in group 1, root cylinders obtained from human canines were embedded in acrylic resin and had their canals prepared and filled with sealer; in group 2, longitudinal sections of dentin cylinders were embedded in resin with the canal surface smoothed and turned upwards; in group 3, gutta-percha cylinders were embedded in resin. Polyethylene tubes filled with sealer were positioned on the polished surface of the specimens (groups 2 and 3). The push-out test (group 1) and the SBS test (groups 2 and 3) were performed in an Instron universal testing machine running at crosshead speed of 1 mm/min. Means (±SD) in MPa were: G1 (8.8±1.13), G2 (5.9±1.05) and G3 (3.8±0.55). Statistical analysis by ANOVA and Student's t-test (a=0.05) revealed statistically significant differences (p<0.01) among the groups. SEM analysis showed a predominance of adhesive and mixed failures of AH Plus sealer. The tested surface affected significantly the results with the sealer reaching higher bond strength to dentin than to gutta-percha with the SBS test. The comparison of the employed methodologies showed that the SBS test produced significantly lower bond strength values than the push-out test, was skilful in determining the adhesion of AH Plus sealer to dentin and gutta-percha, and required specimens that could be easily prepared for SEM, presenting as a viable alternative for further experiments.

Dynamic and steady: shear rheological properties of xanthan and guar gums dispersed in yellow passion fruit pulp (Passiflora edulis f. flavicarpa)

Yellow passion fruit pulp is unstable, presenting phase separation that can be avoided by the addition of hydrocolloids. For this purpose, xanthan and guar gum [0.3, 0.7 and 1.0% (w/w)] were added to yellow passion fruit pulp and the changes in the dynamic and steady - shear rheological behavior evaluated. Xanthan dispersions showed a more pronounced pseudoplasticity and the presence of yield stress, which was not observed in the guar gum dispersions. Cross model fitting to flow curves showed that the xanthan suspensions also had higher zero shear viscosity than the guar suspensions, and, for both gums, an increase in temperature led to lower values for this parameter. The gums showed different behavior as a function of temperature in the range of 5 - 35ºC. The activation energy of the apparent viscosity was dependent on the shear rate and gum concentration for guar, whereas for xanthan these values only varied with the concentration. The mechanical spectra were well described by the generalized Maxwell model and the xanthan dispersions showed a more elastic character than the guar dispersions, with higher values for the relaxation time. Xanthan was characterized as a weak gel, while guar presented a concentrated solution behavior. The simultaneous evaluation of temperature and concentration showed a stronger influence of the polysaccharide concentration on the apparent viscosity and the G' and G" moduli than the variation in temperature.

Transpressive dextral shear in the Italva-Itaperuna section, Northern State of Rio de Janeiro, Brazil

Structural analysis carried out on a segment of the Neoproterozoic Ribeira Belt, southeastern Brazil, show that it represents part of the transpressive dextral orogen related to the Central Mantiqueira Province. NNE-trending and steeply dipping regional mylonitic belts form anastomosed geometry, and describe a map-scale, S-C-like structure that is characterized by their deflection towards NE near the Além Paraíba Lineament. Lithological and structural control related to deformation partition were responsible for the formation of felsic mylonitic granulites with S-type granites lenses developed in ductile shear zones, alternated with less deformed intermediate to basic granulites associated with charnockites. The dextral shear sense indicators are consistent with transpressive deformation in the region and are common especially at the border of the main shear zones. The presence of S-type leucogranite may lead to variations of linear and planar relationships, which result in local extension zones. These elements are consistent with oblique continental collision considering the São Francisco Craton as a stable block.

ACE as a Mechanosensor to Shear Stress Influences the Control of Its Own Regulation via Phosphorylation of Cytoplasmic Ser(1270)

Objectives: We tested whether angiotensin converting enzyme (ACE) and phosphorylation of Ser(1270) are involved in shear-stress (SS)-induced downregulation of the enzyme. Methods and Results: Western blotting analysis showed that SS (18 h, 15 dyn/cm(2)) decreases ACE expression and phosphorylation as well as p-JNK inhibition in human primary endothelial cells (EC). CHO cells expressing wild-type ACE (wt-ACE) also displayed SS-induced decrease in ACE and p-JNK. Moreover, SS decreased ACE promoter activity in wt-ACE, but had no effect in wild type CHO or CHO expressing ACE without either the extra-or the intracellular domains, and decreased less in CHO expressing a mutated ACE at Ser(1270) compared to wt-ACE (13 vs. 40%, respectively). The JNK inhibitor (SP600125, 18 h), in absence of SS, also decreased ACE promoter activity in wt-ACE. Finally, SS-induced inhibition of ACE expression and phosphorylation in EC was counteracted by simultaneous exposure to an ACE inhibitor. Conclusions: ACE displays a key role on its own downregulation in response to SS. This response requires both the extra- and the intracellular domains and ACE Ser(1270), consistent with the idea that the extracellular domain behaves as a mechanosensor while the cytoplasmic domain elicits the downstream intracellular signaling by phosphorylation on Ser(1270).

Shear Stress Induces Nitric Oxide-Mediated Vascular Endothelial Growth Factor Production in Human Adipose Tissue Mesenchymal Stem Cells

It has been demonstrated that human adipose tissue-derived mesenchymal stem cells (hASCs) enhance vascular density in ischemic tissues, suggesting that they can differentiate into vascular cells or release angiogenic factors that may stimulate neoangiogenesis. Moreover, there is evidence that shear stress (SS) may activate proliferation and differentiation of embryonic and endothelial precursor stem cells into endothelial cells (ECs). In this work, we investigated the effect of laminar SS in promoting differentiation of hASCs into ECs. SS (10 dyn/cm(2) up to 96 h), produced by a cone plate system, failed to induce EC markers (CD31, vWF, Flk-1) on hASC assayed by RT-PCR and flow cytometry. In contrast, there was a cumulative production of nitric oxide (determined by Griess Reaction) and vascular endothelial growth factor (VEGF; by ELISA) up to 96 h of SS stimulation ( NO(2)(-) in nmol/10(4) cells: static: 0.20 +/- 0.03; SS: 1.78 +/- 0.38, n = 6; VEGF in pg/10(4) cells: static: 191.31 +/- v35.29; SS: 372.80 +/- 46.74, n = 6, P < 0.05). Interestingly, the VEGF production was abrogated by 5 mM N(G)-L-nitro-arginine methyl ester (L-NAME) treatment (VEGF in pg/10(4) cells: SS: 378.80 +/- 46.74, n = 6; SS + L-NAME: 205.84 +/- 91.66, n = 4, P < 0.05). The results indicate that even though SS failed to induce EC surface markers in hASC under the tested conditions, it stimulated NO-dependent VEGF production.

Influence of Aluminum Oxide Sandblasting Associated with Nd:YAG or Er:YAG Lasers on Shear Bond Strength of a Feldspathic Ceramic to Resin Cements

Objective: This in vitro study evaluated the influence of the surface pretreatment of a feldspathic ceramic on the shear bond strength of two different resin cements. Background Data: Although several conventional surface treatments have been used on feldspathic ceramic, few studies have investigated the effects of an alternative surface treatment, the association of aluminum oxide sandblasting with Nd:YAG and Er:YAG lasers. Methods: Sixty samples made of a feldspathic ceramic were divided into three groups (n = 20) and treated with (1) controlled-air abrasion with Al(2)O(3) + 10% hydrofluoric acid (HF), (2) Al(2)O(3) + Er:YAG laser, and (3) Al(2)O(3) + Nd:YAG laser. Afterward, silane (Dentsply) was applied on each treated surface. Each of the three main groups was divided into two subgroups (n = 10), where a different resin cement was employed for each subgroup. It was built a cylinder with resin cement (RelyX Arc) in subgroup (A) and with self-adhesive cement (RelyX U100) in subgroup (B). After 24 h at 37 degrees C, the prepared specimens were submitted to shear bond strength test and stereoscopic evaluation to determine the type of failure. Results: Bond strength mean values were not statistically significant for the surface treatment methods or resin cements. Conclusion: The null surface treatment proposed with aluminum oxide sandblasting associated with the Er:YAG or Nd:YAG laser and using cementation with self-adhesive cement can be an alternative bonding technique for feldspathic ceramic, since it was as effective as the conventional treatment with aluminum oxide sandblasting and hydrofluoric acid using the conventional resin cement.

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters. (c) 2008 American Institute of Physics.

Nonaxisymmetric magnetorotational instability in ideal and viscous plasmas

The excitation of magnetorotational instability (MRI) in rotating laboratory plasmas is investigated. In contrast to astrophysical plasmas, in which gravitation plays an important role, in laboratory plasmas it can be neglected and the plasma rotation is equilibrated by the pressure gradient. The analysis is restricted to the simple model of a magnetic confinement configuration with cylindrical symmetry, in which nonaxisymmetric perturbations are investigated using the local approximation. Starting from the simplest case of an ideal plasma, the corresponding dispersion relations are derived for more complicated models including the physical effects of parallel and perpendicular viscosities. The Friemann-Rotenberg approach used for ideal plasmas is generalized for the viscous model and an analytical expression for the instability boundary is obtained. It is shown that, in addition to the standard effect of radial derivative of the rotation frequency (the Velikhov effect), which can be destabilizing or stabilizing depending on the sign of this derivative in the ideal plasma, there is a destabilizing effect proportional to the fourth power of the rotation frequency, or, what is the same, to the square of the plasma pressure gradient, and to the square of the azimuthal mode number of the perturbations. It is shown that the instability boundary also depends on the product of the plasma pressure and density gradients, which has a destabilizing effect when it is negative. In the case of parallel viscosity, the MRI looks like an ideal instability independent of viscosity, while, in the case of strong perpendicular viscosity, it is a dissipative instability with the growth rate inversely proportional to the characteristic viscous decay rate. We point out, however, that the modes of the continuous range of the magnetohydrodynamics spectrum are not taken into account in this paper, and they can be more dangerous than those that are considered. (c) 2008 American Institute of Physics.