Journal articles: 'Bulge Theory'

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Farley, F. J. M., R. C. T. Rainey, and J. R. Chaplin. "Rubber tubes in the sea." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1959 (January 28, 2012): 381–402. http://dx.doi.org/10.1098/rsta.2011.0193.

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A long tube with elastic walls containing water is immersed in the sea aligned in the direction of wave travel. The waves generate bulges that propagate at a speed determined by the distensibility of the tube. If the bulge speed is close to the phase velocity of the waves, there is a resonant transfer of energy from the sea wave to the bulge. At the end of the tube, useful energy can be extracted. This paper sets out the theory of bulge tubes in the sea, and describes some experiments on the model scale and practical problems. The potential of a full-scale device is assessed.

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Gent, A. N., and W. Kim. "Bulging of Rubber through Apertures." Rubber Chemistry and Technology 64, no. 5 (November 1, 1991): 813–21. http://dx.doi.org/10.5254/1.3538593.

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Abstract 1. When rubber bulges through an aperture, the bulge height varies linearly with applied pressure. It also varies linearly with radius or width of the aperture when the dimensions of the rubber block are much larger than the aperture, in good agreement with linear elasticity theory. When the block is not much larger than the radius or width of the aperture, a simple empirical factor provides a satisfactory correction. 2. FEM results were in good agreement with experiment in all cases and confirmed the empirical correction for relatively large apertures. 3. Bulge profiles were calculated to be elliptical in all cases. 4. Results for an elastic solid are wholly consistent with Roscoe's results for a viscous liquid. 5. Changing slip conditions at the interface had a surprisingly small effect. The exact theory, Equations (5) and (7), is based upon a nonslip condition. When a fully lubricated condition was employed instead, so that free sliding was allowed at the interface, the maximum bulge heights predicted by FEM were only about 5% higher than before for a circular aperture and about 12% higher for a slit. Experimental observations of bulge heights with dry and lubricated interfaces were in good agreement with these predictions. 6. Bulge heights through small apertures provide a simple means of measuring pressure at contact surfaces.

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Bambach, Markus. "Comparison of the Identifiability of Flow Curves from the Hydraulic Bulge Test by Membrane Theory and Inverse Analysis." Key Engineering Materials 473 (March 2011): 360–67. http://dx.doi.org/10.4028/www.scientific.net/kem.473.360.

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In the hydraulic bulge test, flow curves are determined by applying a hydrostatic pressure to one side of a clamped sheet metal specimen, which bulges freely into a circular cavity under the pressure. The pressure and various data such as bulge height, curvature and equivalent strain at the pole are recorded and used to calculate the flow curve of the specimen material using analytical equations based on membrane theory. In the determination of the flow curve, the elastic behavior of the specimen, the elastic-plastic transition and bending effects are neglected, and the flow curves calculated this way are affected by these simplifications. An alternative to this procedure is an inverse analysis, which proceeds by searching for a flow curve that minimizes the difference between computed and measured data, e.g. bulge height vs. pressure. An inverse analysis based on a finite element model takes into account elastic and bending effects but since it involves the solution of an optimization problem, it is not clear whether it yields more accurate results than membrane theory. The objective of this paper is to compare the ‘identifiability’ of a given flow curve from the bulge test by direct identification based on membrane theory and by inverse analysis with different objective functions to be minimized. Using a re-identification procedure, it is shown that an inverse analysis can improve the results of the direct identification if a suitable objective function is chosen.

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Pruitt, Lesley. "Rethinking youth bulge theory in policy and scholarship: incorporating critical gender analysis." International Affairs 96, no. 3 (May 1, 2020): 711–28. http://dx.doi.org/10.1093/ia/iiaa012.

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Abstract For decades ‘youth bulge’ theory has dominated understandings of youth in mainstream International Relations. Youth bulge theory has also become part of some public media analyses, mainstream political rhetoric, and even officially enshrined in the foreign policy of some states. Through the ‘youth bulge’ lens, youth—especially males—have been presented as current or future perpetrators of violence. However, this article argues that the youth bulge thesis postulated in mainstream IR is based on flawed theoretical assumptions. In particular, supporters of youth bulge theory fail to engage with existing research by feminist IR scholars and thus take on a biological essentialist approach. This has led to theoretical and practical misunderstandings of the roles youth play in relation to conflict, peace and security. These partial and biased understandings have also resulted in less effective policy-making. In critically reflecting on the ‘youth bulge’ thesis, this article argues that applying gender analysis is crucial to understanding the involvement of young people in general—and young men in particular—in conflict. Doing so will contribute to advancing more accurate analysis in scholarship and policy-making.

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Braun, Alexander, Markus Bambach, and Gerhard Hirt. "Investigation of a Bulge Test at High Temperatures and High Strain Rates Using a Finite-Element Simulation Study." Key Engineering Materials 622-623 (September 2014): 300–307. http://dx.doi.org/10.4028/www.scientific.net/kem.622-623.300.

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In recent years, hot stamping of sheet metal parts has emerged to satisfy the contrary demands of the automotive industry for components with increased strength at reduced weight. To analyse the material behaviour during these processes, a hot gas bulge test at high temperatures and high strain rates is promising, since the bulge test at room temperature has already proven itself as a useful test for the material characterization of sheet metals up to high strains. Therefore, a hot gas bulge test at elevated temperatures and high strain rates is being developed at the Institute of Metal Forming (IBF) in cooperation with the Institute for Fluid Power Drives and Controls (IFAS) at the RWTH Aachen. To verify if the concepts of the membrane theory, which are used for the evaluation of bulge tests at room temperature, are adaptable to such a hot gas bulge test, a simulation study using finite element calculations was conducted. The purpose of this simulation study is is to estimate the errors which occur if the equivalent stress at the bulge pole is calculated by using the membrane theory. In addition to this study several approaches were examined to obtain the sheet thickness at the bulge pole by measuring the bulge height. The study showed that a hot gas bulge test can be described very well by the membrane theory if the sheet thickness, the curvature at the bulge pole and the pressure inside the bulge are exactly known. However, substantial errors can occur if the sheet thickness at the bulge pole is determined by measuring the height of the bulge pole.

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Hwang, Yeong-Maw, and Yi-Kai Lin. "Evaluation of Flow Stresses of Tubular Materials Considering Anisotropic Effects by Hydraulic Bulge Tests." Journal of Engineering Materials and Technology 129, no. 3 (December 26, 2006): 414–21. http://dx.doi.org/10.1115/1.2744406.

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This paper aims to evaluate the stress-strain characteristics of tubular materials considering their anisotropic effects by hydraulic bulge tests and a proposed analytical model. In this analytical model, Hill’s orthogonal anisotropic theory was adopted for deriving the effective stresses and effective strains under a biaxial stress state. Annealed AA6011 aluminum tubes and SUS409 stainless-steel tubes were used for the bulge test. The tube thickness at the pole, bulge height, and the internal forming pressure were measured simultaneously during the bulge test. The effective stress-effective strain relations could be determined by those measured values and this proposed analytical model. The flow stress curves of the tubular materials obtained by this approach were compared with those obtained by the tensile test with consideration of the anisotropic effect. The finite element method was also adopted to conduct the simulations of hydraulic bulge forming with the flow stress curves obtained by the bulge tests and tensile tests. The analytical forming pressures versus bulge heights were compared with the experimental results to validate the approach proposed in this paper.

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Norwood, O’Tar T. "The Bulge Theory vs. Inaba’s Hypothesis vs. Traditional Theory of Hair Regeneration." International Society of Hair Restoration Surgery 3, no. 3 (March 1993): 12.1–12. http://dx.doi.org/10.33589/3.3.0012.

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Wang, Ming Wei, and Li Wen Zhang. "FE Simulation of Vacuum Hot Bulge Forming Process of BT20 Ti-Alloy Cylindrical Workpiece." Key Engineering Materials 392-394 (October 2008): 366–69. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.366.

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The vacuum hot bulge forming has been used in aerospace industry to manufacture cylindrical workpiece with improved mechanical properties and reduced fabrication cost. Vacuum hot bulge forming is based on the material soften and the stress relaxation theory. Different from other metal forming techniques, deformation of the workpiece takes place well below yield point and the amount of plastic deformation is directly relaxed to heating temperature and holding time. In this paper, a two-dimension thermo-mechanical coupled finite element model was developed. In this model, nonlinear radiation heat transfer and thermal physical properties of material depending on temperature were considered. This paper carried out numerical simulation of vacuum hot bulge forming of BT20 Ti-alloy cylindrical workpiece by using finite element software MSC.Marc. The temperature field, deformation field and stress field of hot bulge forming of BT20 Ti-alloy cylindrical workpiece were calculated. Numerical simulation results were accorded with experimental ones, which provided for the practice production as theory bases.

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Walton, N. A., M. J. Barlow, and R. E. S. Clegg. "Chemical Abundances in Galactic Bulge Pn." Symposium - International Astronomical Union 155 (1993): 581. http://dx.doi.org/10.1017/s0074180900172559.

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We present abundance determinations, in particular of carbon, and C/O ratios, for 11 Galactic bulge planetary nebulae (PN) based on our low resolution UV data from IUE observations and optical spectrophotometry from the Anglo-Australian Telescope. We compare the observed abundances with those predicted by dredge-up theory for the high metallicity Galactic bulge. The sample abundances are also contrasted with the abundances found for PN in the Galactic disk. The mean C/O ratio for the bulge PN is significantly lower than that found for Galactic disk PN. Further, we present an abundance analysis of the very metal-poor bulge PN M2-29. From an analysis of the differential extinction found from the observed ratios of the He ii 1640,4686Å lines, we find that the ultraviolet reddening law towards the bulge is steeper than in the solar neighbourhood.

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10

Ifedi, O., Q. M. Li, and Y. B. Lu. "Further Investigation of the Hydrostatic Bulge Test in a Plasticity Laboratory." International Journal of Mechanical Engineering Education 37, no. 2 (April 2009): 159–74. http://dx.doi.org/10.7227/ijmee.37.2.7.

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In plasticity theory, the effective stress–strain curve of a metal is independent of the loading path. The simplest loading path to obtain the effective stress–strain curve is a uniaxial tensile test. In order to demonstrate in a plasticity laboratory that the stress–strain curve is independent of the loading path, the hydrostatic bulge test has been used to provide a balanced biaxial tensile stress state. In our plasticity laboratory we compared several different theories for the hydrostatic bulge test for the determination of the effective stress–strain curve for two representative metals, brass and aluminium alloy. Finite element analysis (FEA) was performed based on the uniaxial tension test data. It was shown that the effective stress–strain curve obtained from the biaxial tensile test (hydrostatic bulge test) had a good correlation with that obtained in the uniaxial tensile test and agreed well with the analytical and FEA results. This paper may be used to support an experimental and numerical laboratory in teaching the concepts of effective stress and strain in plasticity theory.

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11

Martínez Palmeth, Luis Humberto, María Angelica Gonzalez Carmona, and José Miranda Castro. "Design and Analysis of a Bulge Test Device." Ingeniería e Investigación 41, no. 3 (June 2, 2021): e85756. http://dx.doi.org/10.15446/ing.investig.v41n3.85756.

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The aim of this work is to present the methodological process to design a device capable of performing Bulge tests. This kind of device allows obtaining more information about the plastic behavior of a material than the one provided by a traditional tensile test. The engineering specifications of the device were evaluated through the QFD methodology. Then, a basic design of the device was performed based on available analytical models such as thick-walled pressure vessel theory, annular plate theory, and a basic plasticity model for the biaxial stress state. Later, a detailed design of the device was proposed, which was evaluated by means of a 3D model of finite elements and a linearstatic analysis for the main components. Finally, a 2D axisymmetric model and a dynamic non-linear analysis were performed to validate the proposed design. The main novelty of the work consists of articulating the methodology of the mechanical design process and the conception, design, and validation of a Bulge device while solving the deficiencies found in the literature regarding the design and validation processes of this type of devices.

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Limmer, B. L. "The Theories of Inaba vs. the Bulge Theory of Cotsarella, etal." International Society of Hair Restoration Surgery 3, no. 3 (March 1993): 12.2–14. http://dx.doi.org/10.33589/3.3.0012a.

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13

Chen, Shih-Nan. "Enhancement of Alongshore Freshwater Transport in Surface-Advected River Plumes by Tides." Journal of Physical Oceanography 44, no. 11 (November 1, 2014): 2951–71. http://dx.doi.org/10.1175/jpo-d-14-0008.1.

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Abstract A recent numerical study by Isobe showed that imposing alongshore tidal forcing on buoyant coastal discharge enhances the net freshwater transport in the coastal currents. The mechanisms for this transport enhancement are studied using a three-dimensional, primitive equation ocean model [Regional Ocean Modeling System (ROMS)]. Lagrangian drifters are used to trace the freshwater transport paths. It is found that the river plume bulge circulation largely follows the rigid-body motion (i.e., constant vorticity). The buoyant fluid near the bulge’s outer edge is thinner and faster, behaving as a baroclinic jet. The bulge currents then split after impinging on the coast. The outer fluid feeds the downshelf-flowing coastal currents, while the inner fluid recirculates to form the bulge. The coastal current transport estimated from the present and prior studies corresponds well to a baroclinic jet theory, with the incident angle of bulge currents at the coast being a key parameter. Without tides, the bulge is approximately circular. The incident angle measured with respect to the cross-shore axis is small. With tides, the convergence of tidal momentum fluxes near the upshelf plume front leads to a positive pressure anomaly, which acts to compress the bulge shoreward. As a result, the incident angle increases, which in turn enhances the downshelf momentum input, thus increasing the freshwater transport in the coastal currents. Finally, the parameter space for coastal current transport in the presence of tidal forcing is explored with a conceptual model. A few observational examples are given.

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Chen, Kelin. "A general and unified theory of the kinematic relationships in bulge tests." Journal of the Mechanics and Physics of Solids 143 (October 2020): 104086. http://dx.doi.org/10.1016/j.jmps.2020.104086.

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Zhang, L., Y. Yin, M. Xue, and F. Takemasa. "Application of rigid–plastic meso-damage constitutive theory to superplastic bulge forming." Materials Science and Technology 18, no. 11 (November 2002): 1399–407. http://dx.doi.org/10.1179/026708402225007140.

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16

Watkins, David, and Ludwig Elsner. "Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem." SIAM Journal on Matrix Analysis and Applications 15, no. 3 (July 1994): 943–67. http://dx.doi.org/10.1137/s089547989122377x.

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17

Efroimsky, M. "Justification of the two-bulge method in the theory of bodily tides." Astronomy & Astrophysics 544 (August 2012): A133. http://dx.doi.org/10.1051/0004-6361/201219485.

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Chaplin, J. R., V. Heller, F. J. M. Farley, G. E. Hearn, and R. C. T. Rainey. "Laboratory testing the Anaconda." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1959 (January 28, 2012): 403–24. http://dx.doi.org/10.1098/rsta.2011.0256.

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Laboratory measurements of the performance of the Anaconda are presented, a wave energy converter comprising a submerged water-filled distensible tube aligned with the incident waves. Experiments were carried out at a scale of around 1:25 with a 250 mm diameter and 7 m long tube, constructed of rubber and fabric, terminating in a linear power take-off of adjustable impedance. The paper presents some basic theory that leads to predictions of distensibility and bulge wave speed in a pressurized compound rubber and fabric tube, including the effects of inelastic sectors in the circumference, longitudinal tension and the surrounding fluid. Results are shown to agree closely with measurements in still water. The theory is developed further to provide a model for the propagation of bulges and power conversion in the Anaconda. In the presence of external water waves, the theory identifies three distinct internal wave components and provides theoretical estimates of power capture. For the first time, these and other predictions of the behaviour of the Anaconda, a device unlike almost all other marine systems, are shown to be in remarkably close agreement with measurements.

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Delfani, M. R. "Nonlinear elasticity of monolayer hexagonal crystals: Theory and application to circular bulge test." European Journal of Mechanics - A/Solids 68 (March 2018): 117–32. http://dx.doi.org/10.1016/j.euromechsol.2017.09.012.

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Elger, D. F., D. M. Blackketter, R. S. Budwig, and K. H. Johansen. "The Influence of Shape on the Stresses in Model Abdominal Aortic Aneurysms." Journal of Biomechanical Engineering 118, no. 3 (August 1, 1996): 326–32. http://dx.doi.org/10.1115/1.2796014.

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Presence of a small abdominal aortic aneurysm (AAA) often presents a difficult clinical dilemma—a reparative operation with its inherent risks versus monitoring the growth of the aneurysm, with the accompanying risk of rupture. The risk of rupture is conventionally believed to be a function of the AAA bulge diameter. In this work, we hypothesized that the risk of rupture depends on AAA shape. Because rupture is inevitably linked to stress, membrane theory was used to predict the stresses in the walls of an idealized AAA, using a model which was axisymmetric and fusiform, with the ends merged into straight open-ended tubes. When the stresses for many different shapes of model AAAs were examined, a number of conclusions became evident: (i) maximum hoop stress typically exceeded maximum meridional stress by a factor of 2 to 3 (ii) the shape of an AAA had a small effect on the meridional stresses and a rather dramatic effect on the hoop stresses, (iii) maximum stress typically occurred near the inflection point of a curve drawn coincident with the AAA wall, and (iv) the maximum stress was a function—not of the bulge diameter—but of the curvatures (i.e. shape) of the AAA wall. This last result suggested that rupture probability should be based on wall curvatures, not on AAA bulge diameter, Because curvatures are not much harder to measure than bulge diameter, this concept may be useful in a clinical setting in order to improve prediction of the likelihood of AAA rupture.

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Rees, D. W. A. "Rim and pole failures from elliptical bulging of oriented orthotropic sheet metal." Journal of Strain Analysis for Engineering Design 35, no. 2 (February 1, 2000): 109–20. http://dx.doi.org/10.1243/0309324001514062.

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Two criteria of instability are required to predict the failure in rolled sheet metal when bulged by lateral pressure through elliptical dies. The attainment of a pressure maximum is observed when the ratio of the lengths of the ellipse axes approaches unity. In nearly circular bulges this marks the onset of failure by diffuse necking under a falling pressure in the polar region. Dies with sharper elliptical apertures produce plane strain failures under a rising pressure in the region of the rim. In stretching flat sheet a local instability occurs when the rim force attains its maximum. The influence of sheet curvature upon plane strain fracture alters the limiting strain. Predictions of the critical pressure are derived for each failure and applied to an automotive aluminium alloy sheet (Alusuisse AC 120). The theory confirms experiments that show plane strain failure as a cut-off point in the plot of pressure versus height. A maximum pressure marks the start of a failure by diffuse pole thinning. In contrast, edge failures occur with uniform thinning from pole to rim along the minor axis of the ellipsoid bulge. A generalized theoretical approach accounts for each failure with an r variation in the plane of the sheet and orientation of the ellipse axes to the rolling direction. The tests reported refer to alignments between the roll direction and both axes of five elliptical dies with different aspect ratios. Pole failures provide positive forming limit strains for biaxial stress ratios between 0.5 and 1. Rim failures supply the limiting plane strains.

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22

Barrett, James H. "What caused the Viking Age?" Antiquity 82, no. 317 (September 1, 2008): 671–85. http://dx.doi.org/10.1017/s0003598x00097301.

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This paper addresses the cause of the Viking episode in the approved Viking manner – head-on, reviewing and dismissing technical, environmental, demographic, economic, political and ideological prime movers. The author develops the theory that a bulge of young males in Scandinavia set out to get treasure to underpin their chances of marriage and a separate domicile.

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Pruitt, Lesley. "Corrigendum 1: Rethinking youth bulge theory in policy and scholarship: incorporating critical gender analysis." International Affairs 97, no. 2 (March 2021): xix. http://dx.doi.org/10.1093/ia/iiab002.

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Güner, Alper, Alexander Brosius, and A. Erman Tekkaya. "Analysis of the Hydraulic Bulge Test with FEA Concerning the Accuracy of the Determined Flow Curves." Key Engineering Materials 410-411 (March 2009): 439–47. http://dx.doi.org/10.4028/www.scientific.net/kem.410-411.439.

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This work covers the finite element analysis of geometric and process parameters in hydraulic bulge tests in terms of the accuracy of the evaluated flow curve. The important parameters are identified and varied to cover the whole range of possible uses. The effects of these parameters are analyzed for three representative materials: aluminium, mid-strength steel, and high-strength steel. The flow curves of the materials for each set of parameters are calculated by using the results of the simulations and the membrane theory. It is seen that even with simulation results, it is not always possible to obtain the input flow curve, especially towards the end of the test. The dimensions of the sheet and the tooling affect the plastic strain development and geometry of the bulge, leading to errors in computed flow curves. In order to observe the effect of the material flow from the flange on the determined yield stresses, the function and position of the drawbeads are also examined. These parameters, together with the method used to calculate the radius of the bulge, determine the accuracy of the calculated flow curve. Guidelines for an accurate flow curve determination regarding the test set-up and calculation methods are given.

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Price, S. F., R. A. Bindschadler, C. L. Hulbe, and I. R. Joughin. "Post-stagnation behavior in the upstream regions of Ice Stream C, West Antarctica." Journal of Glaciology 47, no. 157 (2001): 283–94. http://dx.doi.org/10.3189/172756501781832232.

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AbstractThe region where two active tributaries feed into the now stagnant Ice Stream C (ISC), West Antarctica, is thickening. In this region, we observe a correlation between faster ice flow (the tributaries) and elevated topography. We conclude that stagnation of ISC resulted in compression and thickening along the tributaries, eventually forming a “bulge” on the ice-sheet surface. Modern hydraulic potential gradients would divert basal meltwater from ISC to Ice Stream B (ISB). These gradients are primarily controlled by the bulge topography, and so likely formed subsequent to trunk stagnation. As such, we argue against “water piracy” as being the cause for ISC’s stagnation. Kinematic-wave theory suggests that thickness perturbations propagate downstream over time, but that kinematic-wave speed decreases near the stagnant trunk. This and modest diffusion rates combine to trap most of the tributary-fed ice in the bulge region. Using interfero-metric synthetic aperture radar velocity measurements, we observe that half of the ice within ISC’s southern tributary flows into ISB. That flow pattern and other observations of non-steady flow in the region likely result from stagnation-induced thickening along upper ISC combined with a longer period of thinning on upper ISB. If current trends in thickness change continue, more ice from upper ISC will be diverted to ISB.

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Clegg, R. E. S. "PN Abundances in Different Galactic Systems." Symposium - International Astronomical Union 155 (1993): 549–56. http://dx.doi.org/10.1017/s0074180900172390.

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Developments in the measurement of abundances in planetary nebulae since IAU Symposium 131 are reviewed. Present uncertainties and outstanding problems in the interpretation of emission-line measurements are discussed. Results for different samples of PN are reviewed, in terms of the galactic site. Results for the Galactic disk, Galactic Bulge, Galactic Halo, LMC & SMC, Fornax Dwarf galaxy and M31 are discussed. Attention is drawn to the importance of Magellanic Cloud samples for testing dredge-up theory, and to the strong variation of PN C/O ratios with the local site's metallicity and age. New results for carbon in Cloud PNs are presented. Important problems in the interpretation of the metallicity of Bulge PNs are highlighted. Attention is drawn to the idea that metal-rich stellar populations do not produce PNs, such stars leaving the lower AGB early.

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Kiehas, S. A., V. S. Semenov, H. K. Biernat, V. V. Ivanova, R. Nakamura, and W. Baumjohann. "Estimating the magnetic energy inside traveling compression regions." Annales Geophysicae 27, no. 5 (May 4, 2009): 1969–78. http://dx.doi.org/10.5194/angeo-27-1969-2009.

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Abstract. We investigate a series of six TCRs (traveling compression regions), appearing in the course of a small substorm on 19 September 2001. Except for two of these TCRs, all Cluster spacecraft were located in the lobe and detected the typical signatures of TCRs, i.e., compressions in |B| and bipolar Bz variations. We use these perturbations in Bz for calculations on the magnetic energy inside the TCR and compare the amount of magnetic field energy with the kinetic energy inside the underlying plasma bulge. According to results obtained from theory, the amount of magnetic energy inside TCRs is about two times higher than the kinetic plasma energy inside the accompanied plasma bulge. We verify this theoretical result by first investigations of the magnetic field energy inside TCRs. The calculations lead to a magnetic energy in the order of 1010 Joule per RE for each of the TCRs.

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Hempel, M., D. Minniti, R. Saito, P. Pietrukowicz, and P. W. Lucas. "VISTA variable survey in the Milky Way." Proceedings of the International Astronomical Union 5, S262 (August 2009): 287–90. http://dx.doi.org/10.1017/s1743921310002929.

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AbstractOver the next 5 years the VVV collaboration (Vista Variable in the Via Lactea) will conduct an extensive survey of the galactic bulge and disk in the near-IR, using the new VISTA telescope. This public survey covers a field of 520 sqr. deg, including not only regions of high star formation, but also 33 known globular clusters and ~350 open clusters. The final product will be a deep IR atlas in 5 passbands for ~109 point sources among which we expect 106 variable stars. These will be produce a 3-D map of the surveyed region using well-understood primary distance indicators such as RR Lyrae stars. The observations will be combined with data from MACHO, OGLE, EROS, VST, Spitzer, HST, Chandra, Integral, and ALMA for a complete understanding of the variable sources in the inner Milky Way. Several important implications for the history of the Milky Way, for globular cluster evolution, for the population census of the bulge and center, and for the pulsation theory will follow from this survey.

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Lin, Pao Chun, Toru Takeuchi, Ryota Matsui, and Ben Sitler. "Seismic Design of Buckling-Restrained Brace in Preventing Local Buckling Failure." Key Engineering Materials 763 (February 2018): 875–83. http://dx.doi.org/10.4028/www.scientific.net/kem.763.875.

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When a buckling-restrained brace (BRB) is composed of a flat steel core encased in a rectangular steel tube with infill mortar, the flat steel core develops high-mode buckling waves within the spaces occupied by compressible debonding layers when BRB is in compression. The wave crests and troughs collide with mortar and then acting outward forces on restrainer. The steel tube wall may bulge out if the restrainer is too weak to sustain the outward forces and the BRB may lose its compression carrying capability. The outward force can be estimated according to steel core high-mode buckling wavelength and the debonding layer thickness. The restrainer capacity in resisting outward forces can be estimated by using the upper bound theory in plastic analysis. The results of 39 BRB tests were compared in order to evaluate the effectiveness of steel tube capacity estimation methods. 24 BRBs exhibiting local bulging failure suggested that the steel tube capacity can be estimated by assuming the bulged wall as a wedge shape with five of its boundary developing flexural strength. The proposed estimation is conservative and can be adopted for BRB design in preventing local bulging failure for severe seismic services.

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Bespalov, P. A., A. G. Demekhov, A. Grafe, and V. Yu Trakhtengerts. "On the role of collective interactions in asymmetric ring current formation." Annales Geophysicae 12, no. 5 (April 30, 1994): 422–30. http://dx.doi.org/10.1007/s00585-994-0422-8.

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Abstract. The contribution of resonant wave-particle interactions to the formation and decay of the magnetospheric ring current is analysed in the framework of a self-consistent set of equations which take into account azimuthal plasmasphere asymmetry. It is shown that the cyclotron interaction of westward drifting energetic protons with Alfven waves in the evening-side plasmaspheric bulge region leads to the formation of a ring current asymmetry located near 18:00 MLT. The time-scale of this asymmetry is determined by the proton drift time through the plasmaspheric bulge and is about 1 - 3 h. A symmetrical ring current decays mainly due to charge exchange processes. The theory is compared with known experimental data on ions and waves in the ring current and on low-latitude magnetic disturbances. New low-latitude magnetometer data on the magnetic storm of 24 - 26 July 1986 are also discussed. The model presented explains the observed localization of an asymmetrical ring current loop in the evening sector and the difference in relaxation time-scales of the asymmetry and the Dst index. It also explains measured wave turbulence levels in the evening-side plasmasphere and wave observation statistics.

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Penner, A. Raymond. "Induced energy polarization of the vacuum and the rotational curves of spiral galaxies." Canadian Journal of Physics 91, no. 8 (August 2013): 610–17. http://dx.doi.org/10.1139/cjp-2013-0060.

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The theory of an induced energy polarized vacuum is used to determine the rotational curves for modeled galaxies whose baryonic mass distribution parameters are the median values of three classes of spiral galaxies. From the theoretical curves it is found that the bulge contribution plays a dominant role in determining the behavior of the rotational curves in the inner regions (i.e., within three disc scale lengths). For the outer regions the theoretical rotational curves for all the galaxies behave similarly as they slowly fall to the asymptotic value as determined by the baryonic Tully–Fisher relationship. Overall it is found that rotational curves generated by the induced energy polarized vacuum theory can readily produce observed features in the rotational curves of spiral galaxies.

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32

Kaiser, Heather R. "Intimacy matters." Journal of Language Aggression and Conflict 6, no. 2 (November 26, 2018): 271–98. http://dx.doi.org/10.1075/jlac.00013.kai.

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Abstract This chapter analyzes conflict discourse between domestic partners/couples. The interactions, recorded in Rosario, Uruguay, were part of a larger study on the refusal behavior of Uruguayan women in various spheres of life (domains). From this corpus, 41 refusal sequences were extracted in which a female participant rejected or refused her male partner in some respect (e.g. request, offer, suggestion). Refusal sequences found in couples talk positively correlated with aggravating moves and the use of upgraders, and negatively with mitigating moves and the use of downgraders. These results are discussed in terms of Wolfson’s (1988) Bulge theory of social distance.

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Gregg, Richard. "Gogol's "Diary of a Madman": The Fallible Scribe and the Sinister Bulge." Slavic and East European Journal 43, no. 3 (1999): 439. http://dx.doi.org/10.2307/309864.

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Lee, Hunkee, Bongbu Jung, Dongseob Kim, and Hyunchul Park. "On the size effect for micro-scale structures under the plane bulge test using the modified strain gradient theory." International Journal of Precision Engineering and Manufacturing 12, no. 5 (October 2011): 865–70. http://dx.doi.org/10.1007/s12541-011-0115-7.

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Hamanaka, Shingo. "Demographic change and its social and political implications in the Middle East." Asian Journal of Comparative Politics 2, no. 1 (July 24, 2016): 70–86. http://dx.doi.org/10.1177/2057891116636490.

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This study examines the effect of the demographic trend on the breakdown of authoritarian regimes in the Middle East. Several scholars have pointed out that the combination of youth’s disproportionate share of the total population, the “youth bulge,” and high unemployment throws a society into turmoil. The demographic change determines not only how human activities are conducted but also how a society embarks on a political transition, such as a revolution, a state breakdown, or a regime change. I conduct two levels of empirical analysis of the political implications of the demographic dynamics in the Middle East. First, the macro-level analysis is based on cross-sectional data over two decades. This analysis will clarify whether the youth population had a significant effect on the Arab uprisings. Second, the micro-level analysis uses survey data from the Arab Democracy Barometer wave III to examine whether there is a significant correlation between youth and participation in protest. This analytical approach integrates the macro level with the micro level in order to avoid an ecological inference. My empirical analysis finds evidence to support Jack Goldstone’s revolution theory: it is built on demographic changes accompanied by rising food prices. The hypothesis is tested by examining the interactive effect of youth bulge and the deteriorating economic situation in the two decades following the end of the Cold War. The empirical tests at both the macro and micro levels identify a statistically significant effect.

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Zhao, Ju Mei, Guo Qing Li, Mao Hong Li, Qi Xin Yang, and Dong Min Liu. "The Deformation Analysis of Acrylic Waterproof Membrane under the Uniformly Distributed Loads." Advanced Materials Research 450-451 (January 2012): 352–55. http://dx.doi.org/10.4028/www.scientific.net/amr.450-451.352.

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The energy method was used to analysis the deformation of acrylic waterproof membrane under the uniform load and to calculate the maximum central deflection according to the clamped circular plate. Because the shape of the deformation of waterproof membrane bulge was similar to semi-ellipsoid, the curve length corresponding to the maximum central deflection was calculated by elliptic equation. According to the curve length, the deformation could be calculated under the different water pressure and membrane thickness. Comparing the deformation with the maximum elongation ratio, the water pressure and the thickness of waterproof membrane which ensure the safety could be calculated in theory. If the water pressure was known, the thickness of spray-membrane could be determined in the tunnel engineering.

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FORBES, LAWRENCE K., and GRAEME C. HOCKING. "An intrusion layer in stationary incompressible fluids Part 2: A solitary wave." European Journal of Applied Mathematics 17, no. 5 (October 2006): 577–95. http://dx.doi.org/10.1017/s0956792506006711.

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The propagation of a solitary wave in a horizontal fluid layer is studied. There is an interfacial free surface above and below this intrusion layer, which is moving at constant speed through a stationary density-stratified fluid system. A weakly nonlinear asymptotic theory is presented, leading to a Korteweg–de Vries equation in which the two fluid interfaces move oppositely. The intrusion layer solitary wave system thus forms a widening bulge that propagates without change of form. These results are confirmed and extended by a fully nonlinear solution, in which a boundary-integral formulation is used to solve the problem numerically. Limiting profiles are approached, for which a corner forms at the crest of the solitary wave, on one or both of the interfaces.

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38

Yichun, Zhou, Duan Zhuping, and Xie Bomin. "The analytical study on the laser induced reverse-plugging effect by using the classical elastic plate theory (II)?Reverse-bulge motion." Applied Mathematics and Mechanics 17, no. 7 (July 1996): 607–20. http://dx.doi.org/10.1007/bf00123105.

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Zou, Liyong, Mahamad Al-Marouf, Wan Cheng, Ravi Samtaney, Juchun Ding, and Xisheng Luo. "Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock." Journal of Fluid Mechanics 879 (September 27, 2019): 448–67. http://dx.doi.org/10.1017/jfm.2019.694.

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The Richtmyer–Meshkov (RM) instability is numerically investigated on an unperturbed interface subjected to a diffracted convergent shock created by diffracting an initially cylindrical shock over a rigid cylinder. Four gas interfaces are considered with Atwood number ranging from $-0.18$ to 0.67. Results indicate that the diffracted convergent shock increases its strength gradually and reduces its amplitude quickly when it propagates towards the convergence centre. After the strike of the diffracted convergent shock, the initially unperturbed interface deforms with a bulge structure at the centre and two interface steps at both sides, which can be ascribed to the non-uniformity of the pressure distribution behind the diffracted convergent shock. With the decrease of Atwood number, the bulge structure becomes more pronounced. Quantitatively, the interface amplitude experiences a fast but short growing stage and then enters a linear stage. A good collapse of the dimensionless amplitude is found for all cases, which indicates a weak dependence of the growth rate on Atwood number in the deformed shock-induced RM instability. Then the impulsive theory is modified by eliminating the Atwood number and considering the geometry convergence, which well predicts the amplitude growth for the deformed shock-induced RM instability. Finally, the underlying mechanism is decoupled into three parts, and it is found that both the impulsive pressure perturbation and the geometry convergence promote the growth of interface perturbation while the continuous pressure perturbation inhibits the growth. As the Atwood number decreases, the impulsive perturbation plays an increasingly important role, which suggests that the impulsive perturbation dominates the deformed shock-induced RM instability at the linear stage.

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Park, J. J., S. I. Oh, and T. Altan. "Analyses of Axisymmetric Sheet Forming Processes by Rigid-Viscoplastic Finite Element Method." Journal of Engineering for Industry 109, no. 4 (November 1, 1987): 347–54. http://dx.doi.org/10.1115/1.3187138.

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Two types of sheet forming processes are analyzed by rigid-viscoplastic FEM (Finite Element Method): axisymmetric punch stretching and hydrostatic bulge forming. The present formulations, based on the membrane theory and the Hill’s anisotropic flow rule, include the rate sensitivity which is a key factor in controlling the forming of superplastic materials. Normal anisotropy is taken into account and Coulomb friction is assumed at the interface between punch and sheet. Nonsteady-state deformation processes, investigated in this study, were quasi-statically and incrementally analyzed. An FEM code was developed, using two-node linear elements with two degrees of freedom at each node, and applied to solve four categories of problems: (1) A.K. steel punch stretching, (2) hydrostatic bulging of a rate-insensitive material, (3) hydrostatic bulging of rate-sensitive materials, and (4) hydrostatic bulging of a superplastic material (Ti-6-4). Strain distributions and shape changes predicted in the first two problems were compared with experiments and results of other analyses. The results of the third problem could not be compared with experiments; however, the results showed that the rate sensitivity affects the deformation as expected. The fourth problem is the main theme of this paper. To maintain the superplasticity in forming processes and to produce sound products, the control of the strain-rate is a key factor. A hydrostatic bulge forming process, which is often used for manufacturing structural aerospace parts, was analyzed and discussed. Further, an optimum pressure curve (pressure versus time), which maintains the desired strain-rate in the deformed material, was obtained and compared with the results of an analytical prediction, available in the literature.

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Davari, Zahra, and Sohrab Rahvar. "Testing MOdified Gravity (MOG) theory and dark matter model in Milky Way using the local observables." Monthly Notices of the Royal Astronomical Society 496, no. 3 (June 12, 2020): 3502–11. http://dx.doi.org/10.1093/mnras/staa1660.

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ABSTRACT In this paper, we have investigated one of the alternative theories to dark matter named MOdified Gravity (MOG) by testing its ability to describe the local dynamics of the Milky Way (MW) in vertical and transverse directions with the baryonic matter. MOG is designed to interpret the dynamics of galaxies and cluster of galaxies without the need for dark matter. We use local observational data such as the vertical dispersion, rotation curve, surface density, and number density of stars in the Milky Way to obtain the parameters of MOG and the baryonic component of MW by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method. We compare our results with the dark matter model of MW. The two models of MOG and cold dark matter are able to describe equally well the rotation curve and the vertical dynamics of stars in the local MW. The best values for the free parameters of MOG in this analysis are obtained as α = 8.99 ± 0.02 and μ = 0.054 ± 0.005 kpc−1. Also, we obtain the parameters of the generalized gNFW model in the dark matter model. Our best value of bulge mass from MOG is $(1.06 \pm 0.26)\times 10^{10}\, \rm M_{\odot }$, which is consistent with the estimations form the microlensing observations.

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Zhang, Hua, Guangshuai Peng, Chao Shen, and Yewen Wu. "A new perspective and explanation for the formation of plasmaspheric shoulder structures." Annales Geophysicae 39, no. 4 (July 20, 2021): 701–7. http://dx.doi.org/10.5194/angeo-39-701-2021.

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Abstract. Over the hours of 05:00–09:00 UT on 8 June 2001, the extreme ultraviolet (EUV) instrument on board the IMAGE satellite observed a shoulder-like formation in the morning sector and a post-noon plume-like structure. The plasmapause formation is simulated using the test particle model (TPM), based on a drift motion theory, which reproduces various plasmapause structures and evolution of the shoulder feature. The analysis indicates that the shoulder is created by sharp reduction and spatial non-uniformity in the dawn–dusk convection electric field intensity. The TPM-modeled event is found to develop an initial pre-dawn asymmetric bulge that becomes a shoulder as a result of increased “corotation” rate with an increasing L-shell that is preceded by localized outward convection. The shoulder structure rotates sunward and develops into a single- or double-plume structure during an active time period in simulation.

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POLLOCK, M. D. "ON THE RELAXATION OF SUPERSTRING AXION MINI-CLUSTERS." Modern Physics Letters A 18, no. 14 (May 10, 2003): 947–53. http://dx.doi.org/10.1142/s0217732303010703.

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The cosmological axion theory leads to the prediction of axionic mini-clusters of mass M ~ 10-9M⊙, which form at the time t e of equipartition of matter and radiation. By applying the two-body relaxation formula of Spitzer and Hart, we show, for the heterotic superstring theory of Gross et al., that these mini-clusters, considered as point masses, themselves cluster into axion mini-stars of mass [Formula: see text] within the age of the Universe t0 only if they are located within a distance R ~ 0.1 pc of the Galactic Center. Here, λ ≡ fB/fA is the ratio of the second to model-independent axion decay constants, assuming the QCD decay constant to be in the range [Formula: see text], and [Formula: see text] is the strong-interaction coupling parameter. Thus, if axion mini-stars are to explain the microlensing observations by the EROS and MACHO groups towards the Galactic Bulge and the Large and Small Magellanic Clouds, then a collisionless relaxation mechanism is required, as proposed by Seidel and Suen (essentially the violent relaxation of Lynden–Bell), or the four-axion self-interaction effect considered by Tkachev.

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Machado, G., D. Favier, and G. Chagnon. "Membrane Curvatures and Stress-strain Full Fields of Axisymmetric Bulge Tests from 3D-DIC Measurements. Theory and Validation on Virtual and Experimental results." Experimental Mechanics 52, no. 7 (December 3, 2011): 865–80. http://dx.doi.org/10.1007/s11340-011-9571-3.

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45

Lian, Yong-Sheng, Jun-Yi Sun, Zhi-Hang Zhao, Shou-Zhen Li, and Zhou-Lian Zheng. "A Refined Theory for Characterizing Adhesion of Elastic Coatings on Rigid Substrates Based on Pressurized Blister Test Methods: Closed-Form Solution and Energy Release Rate." Polymers 12, no. 8 (August 10, 2020): 1788. http://dx.doi.org/10.3390/polym12081788.

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Adhesion between coatings and substrates is an important parameter determining the integrity and reliability of film/substrate systems. In this paper, a new and more refined theory for characterizing adhesion between elastic coatings and rigid substrates is developed based on a previously proposed pressurized blister method. A compressed air driven by liquid potential energy is applied to the suspended circular coating film through a circular hole in the substrate, forcing the suspended film to bulge, and then to debond slowly from the edge of the hole as the air pressure intensifies, and finally to form a blister with a certain circular delamination area. The problem from the initially flat coating to the stable blistering film under a prescribed pressure is simplified as a problem of axisymmetric deformation of peripherally fixed and transversely uniformly loaded circular membranes. The adhesion strength depends on the delamination area and is quantified in terms of the energy released on per unit delamination area, the so-called energy release rate. In the present work, the problem of axisymmetric deformation is reformulated with out-of-plane and in-plane equilibrium equations and geometric equations, simultaneously improved, and a new closed-form solution is presented, resulting in the new and more refined adhesion characterization theory.

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Deliduman, Cemsinan, Oğuzhan Kaşıkçı, and Barış Yapışkan. "Astrophysics with Weyl gravity." International Journal of Modern Physics A 33, no. 34 (December 10, 2018): 1845011. http://dx.doi.org/10.1142/s0217751x18450112.

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We aim to explain some astrophysical phenomena in low density astronomical regions without invoking dark matter. We propose that the effective theory of gravity could have individual terms which become dominant in respective regions, and effectively describe the gravitational phenomena there. In the outer region of galaxies, the effective theory of gravity could be the Weyl gravity, which is the unique local scale symmetric metric theory. Inside the bulge, however, general relativity is the effective description of gravity. Hence, we propose the Einstein–Weyl gravity as a scale-dependent effective description of the gravitational phenomena. At high densities or high curvature regions, the effective description for gravity is provided by Einstein’s general relativity, whereas in the low density regions it is provided by the Weyl gravity. We then solve the field equations of Weyl gravity in the outer region of galaxies and determine the geometry in which stars move with the same rotational velocity independent of their distance from the center of the galaxy. We then utilize this metric solution to calculate the deflection angle of light from a distant source by a galaxy cluster. The deflection angle calculated in Schwarzschild–de Sitter-like space includes contributions from both the cosmological constant [Formula: see text] and the Mannheim–Kazanas parameter [Formula: see text]. There are conflicting results on the deflection angle for light in Weyl gravity in the literature. Our result agrees with some and disagrees with many. We point out possible reasons for this discrepancy.

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Son, G., and V. K. Dhir. "Numerical Simulation of Saturated Film Boiling on a Horizontal Surface." Journal of Heat Transfer 119, no. 3 (August 1, 1997): 525–33. http://dx.doi.org/10.1115/1.2824132.

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The past efforts in applying linear Taylor instability theory to the prediction of heat transfer during film boiling on a horizontal surface have suffered from the fact that empirical correlations must be used to define the shape of vapor-liquid interfaces and to determine the transport of mass and heat across these interfaces. The objective of this study is to clarify the physics of film boiling and to predict heat transfer coefficients through complete numerical simulation of the evolving interface between superposed layers of immiscible fluids. A coordinate transformation technique supplemented by a numerical grid generation method and a second-order projection method are combined to solve for the flow and temperature fields associated with an evolving interface. From the numerical simulation, the film thickness and, in turn, the heat transfer coefficient are found to vary both spatially and temporally. Increased wall superheat not only thickens the vapor film in the valley but also enlarges the vapor bulge. The effect of increased system pressure is to slow down the growth of the interface.

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48

Holmes, Janet. "Apologies in New Zealand English." Language in Society 19, no. 2 (June 1990): 155–99. http://dx.doi.org/10.1017/s0047404500014366.

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ABSTRACTThe function of apologies is discussed within the context of a model of interaction with two intersecting dimensions – affective and referential meaning. Apologies are defined as primarily social acts conveying affective meaning. The syntactic, semantic, and sociolinguistic features of apologies are described, based on a corpus of 183 apologies. While apology exchanges divided equally between those which used a combination of strategies and those where a single strategy sufficed, almost all apology exchanges involved an explicit apology. An account is provided of the kinds of social relationships and the range of offenses which elicited apologies in this New Zealand corpus.Apologies are politeness strategies, and an attempt is made to relate the relative “weightiness” of the offense (assessed using the factors identified as significant in Brown and Levinson's model of politeness) to features of the apology strategies used to remedy it. Though some support is provided for Brown and Levinson's model, it is suggested that Wolf-son's “bulge” theory more adequately accounts for a number of patterns in the data. In particular, the functions of apologies between friends may be more complex than a simple linear model suggests. (Apologies, politeness, speech functions, New Zealand English, sociolinguistics, pragmatics)

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Das, Susmita, Shashi M. Kanbur, Earl P. Bellinger, Anupam Bhardwaj, Harinder P. Singh, Brett Meerdink, Nicholas Proietti, Anthony Chalmers, and Ryan Jordan. "The stellar photosphere–hydrogen ionization front interaction in classical pulsators: a theoretical explanation for observed period–colour relations." Monthly Notices of the Royal Astronomical Society 493, no. 1 (January 22, 2020): 29–47. http://dx.doi.org/10.1093/mnras/staa182.

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ABSTRACT Period–colour and amplitude–colour (PCAC) relations can be used to probe both the hydrodynamics of outer envelope structure and evolutionary status of Cepheids and RR Lyraes. In this work, we incorporate the PCAC relations for RR Lyraes, BL Her, W Vir, and classical Cepheids in a single unifying theory that involves the interaction of the hydrogen ionization front (HIF) and stellar photosphere and the theory of stellar evolution. PC relations for RR Lyraes and classical Cepheids using the Optical Gravitational Lensing Experiment (OGLE-IV) data are found to be consistent with this theory: RR Lyraes have shallow/sloped relations at minimum/maximum light, whilst long-period (P > 10 d) Cepheids exhibit sloped/flat PC relations at minimum/maximum light. The differences in the PC relations for Cepheids and RR Lyraes can be explained based on the relative location of the HIF and stellar photosphere which changes depending on their position on the Hertzsprung–Russell diagram. We also extend our analysis of PCAC relations for type II Cepheids in the Galactic bulge, Large and Small Magellanic Clouds using OGLE-IV data. We find that BL Her stars have sloped PC relations at maximum and minimum light similar to short-period (P < 10 d) classical Cepheids. W Vir stars exhibit sloped/flat PC relation at minimum/maximum light similar to long-period classical Cepheids. We also compute state-of-the-art 1D radiation hydrodynamic models of RR Lyraes, BL Her and classical Cepheids using the radial stellar pulsation code in mesa to further test these ideas theoretically and find that the models are generally consistent with this picture. We are thus able to explain PC relations at maximum and minimum light across a broad spectrum of variable star types.

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Panich, Sansot, and Vitoon Uthaisangsuk. "Effects of Anisotropic Yield Functions on Prediction of Forming Limit Diagram for AHS Steel." Key Engineering Materials 622-623 (September 2014): 257–64. http://dx.doi.org/10.4028/www.scientific.net/kem.622-623.257.

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In this study, experimental and numerical analyses of Forming Limit Diagram (FLD) for Advanced High Strength (AHS) steel grade 980 were performed. Forming limit curve was first determined by means of the Nakazima stretch-forming test. Then, analytical calculations of the FLD based on the Marciniak-Kuczynski (M-K) model were carried out. Different yield criteria, namely, Hill’48 (r-value and stress-based), Yld89 (r-value and stress-based) and Barlat2000 (Yld2000-2d) were investigated. The strain hardening law according to Swift was applied. To identify parameters of each model, uniaxial tension, balanced bi-axial bulge test and in-plane biaxial tension test were performed. As a result, predicted plastic flow stresses and plastic anisotropies of the AHS steel by various directions were evaluated. In addition, effects of the anisotropic yield functions, strain rate sensitivities, imperfection values and work hardening coefficient on the predicted FLD were studied and discussed. It was found that the FLD based on the Yld2000-2d yield criterion was in better agreement with the experimental curve. Accuracy of the FLD predictions based on the M-K theory, especially in the biaxial state of stress, significantly depended on the applied yield criteria, for which yield stresses and r-values of different loading directions were required.

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Journal articles on the topic 'Bulge Theory'

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