926 resultados para Shear Wall
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The activity of growing living bacteria was investigated using real-time and in situ rheology-in stationary and oscillatory shear. Two different strains of the human pathogen Staphylococcus aureus-strain COL and its isogenic cell wall autolysis mutant, RUSAL9-were considered in this work. For low bacteria density, strain COL forms small clusters, while the mutant, presenting deficient cell separation, forms irregular larger aggregates. In the early stages of growth, when subjected to a stationary shear, the viscosity of the cultures of both strains increases with the population of cells. As the bacteria reach the exponential phase of growth, the viscosity of the cultures of the two strains follows different and rich behaviors, with no counterpart in the optical density or in the population's colony-forming units measurements. While the viscosity of strain COL culture keeps increasing during the exponential phase and returns close to its initial value for the late phase of growth, where the population stabilizes, the viscosity of the mutant strain culture decreases steeply, still in the exponential phase, remains constant for some time, and increases again, reaching a constant plateau at a maximum value for the late phase of growth. These complex viscoelastic behaviors, which were observed to be shear-stress-dependent, are a consequence of two coupled effects: the cell density continuous increase and its changing interacting properties. The viscous and elastic moduli of strain COL culture, obtained with oscillatory shear, exhibit power-law behaviors whose exponents are dependent on the bacteria growth stage. The viscous and elastic moduli of the mutant culture have complex behaviors, emerging from the different relaxation times that are associated with the large molecules of the medium and the self-organized structures of bacteria. Nevertheless, these behaviors reflect the bacteria growth stage.
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The Ajjanahalli gold mine is spatially associated with a Late Archean craton-scale shear zone in the eastern Chitradurga greenstone belt of the Dharwar craton, India. Gold mineralization is hosted by an similar to100-m-wide antiform in a banded iron formation. Original magnetite and siderite are replaced by a peak metamorphic alteration assemblage of chlorite, stilpnomelane, minnesotaite, sericite, ankerite, arsenopyrite, pyrite, pyrrhotite, and gold at ca. 300degrees to 350degreesC. Elements enriched in the banded iron formation include Ca, Mg, C, S, An, As, Bi. Cu, Sb, Zn, Pb, Se, Ag, and Te, whereas in the wall rocks As, Cu, Zn, Bi, Ag, and An are only slightly enriched. Strontium correlates with CaO, MgO, CO2, and As, which indicates cogenetic formation of arsenopyrite and Mg-Ca carbonates. The greater extent of alteration in the Fe-rich banded iron formation layers than in the wall rock reflects the greater reactivity of the banded iron formation layers. The ore fluids, as interpreted from their isotopic composition (delta(18)O = 6.5-8.5parts per thousand; initial Sr-87/Sr-86 = 0.7068-0.7078), formed by metamorphic devolatilization of deeper levels of the Chitradurga greenstone belt. Arsenopyrite, chalcopyrite, and pyrrhotite have delta(34)S values within a narrow range between 2.1 and 2.7 per mil, consistent with a sulfur source in Chitradurga greenstone belt lithologies. Based on spatial and temporal relationships between mineralization, local structure development, and sinistral strike-slip deformation in the shear zone at the eastern contact of the Chitradurga greenstone belt, we suggest that the Ajjanahalli gold mineralization formed by fluid infiltration into a low strain area within the first-order structure. The ore fluids were transported along this shear zone into relatively shallow crustal levels during lateral terrane accretion and a change from thrust to transcurrent tectonics. Based on this model of fluid flow, exploration should focus on similar low strain areas or potentially connected higher order splays of the first-order shear zone.
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Objective: Saphenous vein graft bypass remains the salvage option when¦endovascular procedure has failed or was contraindicated due to extensive¦occlusive lesions. However, pathological wall remodeling leading leading to¦graft failure is one of the most limiting factors of this therapy. Therefore, the¦understanding of this remodeling process of human vein is essential to the design¦of future effective therapeutics and it requires an adapted model of ex-vivo vein¦perfusion.¦Methods: We have developed an ex vivo vein support system (EVVSS), which¦uses standardized and controlled hemodynamic parameters for the pulsatile¦perfusion of saphenous vein segments. The morphological and molecular¦parameters involved in the remodeling process under an arterial shear stress¦associated to low (7 mm Hg) or high (70 mm Hg) pressure conditions can be¦analyzed.¦Results: Histomorphometric analysis showed that the vein segments perfused¦during 7 days under high pressure undergo a significant neointima development¦compared to veins exposed to low pressure conditions. The application of an¦arterial shear stress in the vein under low pressure induced an elevation of the¦MMP-2 and MMP-9 expression, activity and transcription. The application of¦higher pressure is associated to increased MMP2 expression and transcription¦and MMP9 transcription. TIMP1 expression and transcription were initiated by¦the application of an arterial shear stress but not modified by the modification¦of the pressure. However, TIMP2 expression was increased under high¦pressure conditions but its transcription was inhibited by arterial shear stress,¦independently of the pressure. The values of transcription and expression of¦PAI-1 were not modified by high pressure. Eph-B4 transcription and expression¦were significantly decreased under arterial shear stress.¦Conclusion: These data show that our EVVSS is a valuable setting to study¦ex vivo remodeling of human saphenous veins submitted to arterial conditions.¦The intimal hyperplasia as well as MMP 2, 9 and TIMP 2 seem to be influenced¦by the pressure.
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Results of a field and microstructural study between the northern and the central bodies of the Lanzo plagioclase peridotite massif (NW Italy) indicate that the spatial distribution of deformation is asymmetric across kilometre-scale mantle shear zones. The southwestern part of the shear zone (footwall) shows a gradually increasing degree of deformation from porphyroclastic peridotites to mylonite, whereas the northeastern part (hanging wall) quickly grades into weakly deformed peridotites. Discordant gabbroic and basaltic dykes are asymmetrically distributed and far more abundant in the footwall of the shear zone. The porphyroclastic peridotite displays porphyroclastic zones and domains of igneous crystallization whereas mylonites are characterized by elongated porphyroclasts, embedded between fine-grained, polycrystalline bands of olivine, plagioclase, clinopyroxene, orthopyroxene, spinel, rare titanian pargasite, and domains of recrystallized olivine. Two types of melt impregnation textures have been found: (1) clinopyroxene porphyroclasts incongruently reacted with migrating melt to form orthopyroxene plagioclase; (2) olivine porphyroclasts are partially replaced by interstitial orthopyroxene. The meltrock reaction textures tend to disappear in the mylonites, indicating that deformation in the mylonite continued under subsolidus conditions. The pyroxene chemistry is correlated with grain size. High-Al pyroxene cores indicate high temperatures (11001030C), whereas low-Al neoblasts display lower final equilibration temperatures (860C). The spinel Cr-number [molar Cr/(Cr Al)] and TiO2 concentrations show extreme variability covering almost the entire range known from abyssal peridotites. The spinel compositions of porphyroclastic peridotites from the central body are more variable than spinel from mylonite, mylonite with ultra-mylonite bands, and porphyroclastic rocks of the northern body. The spinel compositions probably indicate disequilibrium and would favour rapid cooling, and a faster exhumation of the central peridotite body, relative to the northern one. Our results indicate that melt migration and high-temperature deformation are juxtaposed both in time and space. Meltrock reaction may have caused grain-size reduction, which in turn led to localization of deformation. It is likely that melt-lubricated, actively deforming peridotites acted as melt focusing zones, with permeabilities higher than the surrounding, less deformed peridotites. Later, under subsolidus conditions, pinning in polycrystalline bands in the mylonites inhibited substantial grain growth and led to permanent weak zones in the upper mantle peridotite, with a permeability that is lower than in the weakly deformed peridotites. Such an inversion in permeability might explain why actively deforming, fine-grained peridotite mylonite acted as a permeability barrier and why ascending mafic melts might terminate and crystallize as gabbros along actively deforming shear zones. Melt-lubricated mantle shear zones provide a mechanism for explaining the discontinuous distribution of gabbros in oceancontinent transition zones, oceanic core complexes and ultraslow-spreading ridges.
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Purpose: Atheromatic plaque progression is affected, among others phenomena, by biomechanical, biochemical, and physiological factors. In this paper, the authors introduce a novel framework able to provide both morphological (vessel radius, plaque thickness, and type) and biomechanical (wall shear stress and Von Mises stress) indices of coronary arteries. Methods: First, the approach reconstructs the three-dimensional morphology of the vessel from intravascular ultrasound(IVUS) and Angiographic sequences, requiring minimal user interaction. Then, a computational pipeline allows to automatically assess fluid-dynamic and mechanical indices. Ten coronary arteries are analyzed illustrating the capabilities of the tool and confirming previous technical and clinical observations. Results: The relations between the arterial indices obtained by IVUS measurement and simulations have been quantitatively analyzed along the whole surface of the artery, extending the analysis of the coronary arteries shown in previous state of the art studies. Additionally, for the first time in the literature, the framework allows the computation of the membrane stresses using a simplified mechanical model of the arterial wall. Conclusions: Circumferentially (within a given frame), statistical analysis shows an inverse relation between the wall shear stress and the plaque thickness. At the global level (comparing a frame within the entire vessel), it is observed that heavy plaque accumulations are in general calcified and are located in the areas of the vessel having high wall shear stress. Finally, in their experiments the inverse proportionality between fluid and structural stresses is observed.
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The geologic structures and metamorphic zonation of the northwestern Indian Himalaya contrast significantly with those in the central and eastern parts of the range, where the high-grade metamorphic rocks of the High Himalayan Crystalline (HHC) thrust southward over the weakly metamorphosed sediments of the Lesser Himalaya along the Main Central Thrust (MCT). Indeed, the hanging wall of the MCT in the NW Himalaya mainly consists of the greenschist facies metasediments of the Chamba zone, whereas HHC high-grade rocks are exposed more internally in the range as a large-scale dome called the Gianbul dome. This Gianbul dome is bounded by two oppositely directed shear zones, the NE-dipping Zanskar Shear Zone (ZSZ) on the northern flank and the SW-dipping Miyar Shear Zone (MSZ) on the southern limb. Current models for the emplacement of the HHC in NW India as a dome structure differ mainly in terms of the roles played by both the ZSZ and the MSZ during the tectonothermal evolution of the HHC. In both the channel flow model and wedge extrusion model, the ZSZ acts as a backstop normal fault along which the high-grade metamorphic rocks of the HHC of Zanskar are exhumed. In contrast, the recently proposed tectonic wedging model argues that the ZSZ and the MSZ correspond to one single detachment system that operates as a subhorizontal backthrust off of the MCT. Thus, the kinematic evolution of the two shear zones, the ZSZ and the MSZ, and their structural, metamorphic and chronological relations appear to be diagnostic features for discriminating the different models. In this paper, structural, metamorphic and geochronological data demonstrate that the MSZ and the ZSZ experienced two distinct kinematic evolutions. As such, the data presented in this paper rule out the hypothesis that the MSZ and the ZSZ constitute one single detachment system, as postulated by the tectonic wedging model. Structural, metamorphic and geochronological data are used to present an alternative tectonic model for the large-scale doming in the NW Indian Himalaya involving early NE-directed tectonics, weakness in the upper crust, reduced erosion at the orogenic front and rapid exhumation along both the ZSZ and the MSZ.
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Purpose: Atheromatic plaque progression is affected, among others phenomena, by biomechanical, biochemical, and physiological factors. In this paper, the authors introduce a novel framework able to provide both morphological (vessel radius, plaque thickness, and type) and biomechanical (wall shear stress and Von Mises stress) indices of coronary arteries. Methods: First, the approach reconstructs the three-dimensional morphology of the vessel from intravascular ultrasound(IVUS) and Angiographic sequences, requiring minimal user interaction. Then, a computational pipeline allows to automatically assess fluid-dynamic and mechanical indices. Ten coronary arteries are analyzed illustrating the capabilities of the tool and confirming previous technical and clinical observations. Results: The relations between the arterial indices obtained by IVUS measurement and simulations have been quantitatively analyzed along the whole surface of the artery, extending the analysis of the coronary arteries shown in previous state of the art studies. Additionally, for the first time in the literature, the framework allows the computation of the membrane stresses using a simplified mechanical model of the arterial wall. Conclusions: Circumferentially (within a given frame), statistical analysis shows an inverse relation between the wall shear stress and the plaque thickness. At the global level (comparing a frame within the entire vessel), it is observed that heavy plaque accumulations are in general calcified and are located in the areas of the vessel having high wall shear stress. Finally, in their experiments the inverse proportionality between fluid and structural stresses is observed.
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The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.
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The changes that occur with age in the distribution of atherosclerotic lesions around arterial branch points challenge accepted theories relating disease to haemodynamic stresses. We investigated whether flow near branch points changes with age in a way that can account for the different lesion distributions. Flow around 20 branches from immature and mature aortas was investigated by examining the length:width ratio and orientation of endothelial nuclei; these properties depend on the magnitude and direction of near-wall flows, respectively. There were significant changes in the pattern of nuclear shape with age, consistent with a reversal in the pattern of shear around branches. In control regions away from branches, there were no such changes. The role of haemodynamic stresses in atherogenesis may require re-evaluation in the light of these results. (C) 2003 Elsevier Ireland Ltd. All rights reserved.
Resumo:
The changes that occur with age in the distribution of atherosclerotic lesions around arterial branch points challenge accepted theories relating disease to haemodynamic stresses. We investigated whether flow near branch points changes with age in a way that can account for the different lesion distributions. Flow around 20 branches from immature and mature aortas was investigated by examining the length:width ratio and orientation of endothelial nuclei; these properties depend on the magnitude and direction of near-wall flows, respectively. There were significant changes in the pattern of nuclear shape with age, consistent with a reversal in the pattern of shear around branches. In control regions away from branches, there were no such changes. The role of haemodynamic stresses in atherogenesis may require re-evaluation in the light of these results.
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The rapid-distortion model of Hunt & Graham (1978) for the initial distortion of turbulence by a flat boundary is extended to account fully for viscous processes. Two types of boundary are considered: a solid wall and a free surface. The model is shown to be formally valid provided two conditions are satisfied. The first condition is that time is short compared with the decorrelation time of the energy-containing eddies, so that nonlinear processes can be neglected. The second condition is that the viscous layer near the boundary, where tangential motions adjust to the boundary condition, is thin compared with the scales of the smallest eddies. The viscous layer can then be treated using thin-boundary-layer methods. Given these conditions, the distorted turbulence near the boundary is related to the undistorted turbulence, and thence profiles of turbulence dissipation rate near the two types of boundary are calculated and shown to agree extremely well with profiles obtained by Perot & Moin (1993) by direct numerical simulation. The dissipation rates are higher near a solid wall than in the bulk of the flow because the no-slip boundary condition leads to large velocity gradients across the viscous layer. In contrast, the weaker constraint of no stress at a free surface leads to the dissipation rate close to a free surface actually being smaller than in the bulk of the flow. This explains why tangential velocity fluctuations parallel to a free surface are so large. In addition we show that it is the adjustment of the large energy-containing eddies across the viscous layer that controls the dissipation rate, which explains why rapid-distortion theory can give quantitatively accurate values for the dissipation rate. We also find that the dissipation rate obtained from the model evaluated at the time when the model is expected to fail actually yields useful estimates of the dissipation obtained from the direct numerical simulation at times when the nonlinear processes are significant. We conclude that the main role of nonlinear processes is to arrest growth by linear processes of the viscous layer after about one large-eddy turnover time.
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For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.
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The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.
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The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.
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Bending shear was observed to produce nearly vertical shear bands in a calving ice wall standing on dry land on Deception Island (Iat. 63.0 oS., long. 60.6 W.), and slabs calved straight downward when shear rupture occurred along these shear bands (Hughes, 1989). A formula for the calving rate was developed from the Deception Island data, and we have attempted to justify generalizing this formula to include ice walls standing along beaches or in water. These are environments in which a wave-washed groove develops along the base of the ice wall or along a water line above the base. The rate of wave erosion provides an alternative mechanism for controlling the calving rate in these environments. We have determined that the rate at which bending creep produces nearly vertical shear bands, along which shear r upture occurs, controls the calving rate in all environments. Shear rupture occurs at a calving shear stress of about I bar. Our results justify using the calving formula to compute the calving rate of ice walls in computer models of ice-sheet dynamics. This is especially important in simulating retreat of Northern Hemisphere ice sheets during the last deglaciation, when marine and lacustrine environments were common along retreating ice margins. These margins would have been ice walls standing along beaches or in water, because floating ice shelves are not expected in the ablation zone of retreating ice sheets.