Constant Stress Model Research Articles

Adaptive outflow boundary conditions improve post-operative predictions after repair of peripheral pulmonary artery stenosis.

Peripheral pulmonary artery stenosis (PPS) is a congenital abnormality resulting in pulmonary blood flow disparity and right ventricular hypertension. Despite recent advance in catheter-based interventions, surgical reconstruction is still preferred to treat complex PPS. However optimal surgical strategies remain unclear. It would be of great benefit to be able to predict post-operative hemodynamics to assist with surgical planning toward optimizing outcomes. While image-based computational fluid dynamics has been used in cardiovascular surgical planning, most studies have focused on the impact of local geometric changes on hemodynamic performance. Previous experimental studies suggest morphological changes in the pulmonary arteries not only alter local hemodynamics but also lead to distal pulmonary adaptation. In this proof of concept study, a constant shear stress hypothesis and structured pulmonary trees are used to derive adaptive outflow boundary conditions for post-operative simulations. Patient-specific simulations showed the adaptive outflow boundary conditions by the constant shear stress model to provide better predictions of pulmonary flow distribution than the conventional strategy of maintaining outflow boundary conditions. On average, the relative difference, when compared to the gold standard clinical test, in blood flow distribution to the right lung is reduced from 20 to 4%. This suggests adaptive outflow boundary conditions should be incorporated into post-operative modeling in patients with complex PPS.

Investigation into the role of cooling/lubrication effect of cryogenic minimum quantity lubrication in machining of AISI H13 steel by three-dimensional finite element method

This article developed a three-dimensional finite element model of cryogenic minimum quantity lubrication machining in order to investigate the role of cooling/lubrication effect of cryogenic minimum quantity lubrication in machining of AISI H13 steel. In this model, the cryogenic cooling effect provided by refrigerated compressed air is modeled with a convective heat transfer coefficient. A heat transfer window with the temperature and convective heat transfer coefficient of refrigerated compressed air was defined on tool face and workpiece, respectively, which could move at the same speed as cutting tool so as to simulate continuous cryogenic cooling process of cutting zone under cryogenic minimum quantity lubrication condition. The temperature of refrigerated compressed air was set at −10 °C, −30 °C, −50 °C, −100 °C, and −140 °C to study the influence of cryogenic cooling effect of cryogenic minimum quantity lubrication. Frictional contact between tool and chip was modeled with a simple constant shear stress model. Comparative simulations were conducted under different cooling/lubrication conditions, those are, dry cutting, refrigerated compressed air, and cryogenic minimum quantity lubrication. The simulation results show that both cryogenic cooling effect and lubrication effect resulted in reduction in cutting force and tool temperature when machining AISI H13 steel under cryogenic minimum quantity lubrication condition. With a decrease in temperature of refrigerated compressed air, cutting force and tool temperature did not decrease continuously. The reduction in cutting force, maximum tool temperature, and average temperature of rake face and flank face at low and high cutting speeds was strongly attributed to the cryogenic cooling effect and lubrication effect provided by cryogenic minimum quantity lubrication, respectively. A significant reduction in cutting force and tool temperature was caused by the improvement in lubrication effect provided by cryogenic minimum quantity lubrication irrespective of the cutting speed. The trends revealed by the simulations provide helpful information for the development of this technique.

Statistical Inference for a Simple Constant Stress Model Based on Censored Sampling Data From the Kumaraswamy Weibull Distribution

In this paper, constant stress accelerated life tests are discussed based on Type I and Type II censored sampling data from Kumaraswmay Weibull distribution. The maximum likelihood estimators are derived for the unknown parameters. The log linear model is assumed as an accelerated model. In addition, confidence intervals for the model parameters are constructed. Optimum test plans, are developed to minimize the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Monte Carlo simulation is carried out to illustrate the theoretical results of the maximum likelihood estimates, confidence intervals and optimum test plans.

A reassessment of outer-rise seismicity and its implications for the mechanics of oceanic lithosphere

We use body-waveform modelling to constrain the source parameters of earthquakes occurring globally in oceanic lithosphere beneath the subduction zone outer rise and outer trench slope. These data are then used to map the stress state in the lithosphere of the downgoing plate as it bends into the subduction zone. Our results provide new constraints on the faulting of oceanic lithosphere at the outer rise, which is important for understanding the transmission of plate-driving forces through the subduction system. In all cases, shallow normal-faulting earthquakes are observed at the top of the plate, and are separated in depth from any deeper thrust-faulting earthquakes. No temporal variation associated with large thrust-faulting earthquakes on the subduction interface is seen in the depth extent of each type of faulting at the outer rise. The transition depth from trench-normal extension to compression is found to vary in agreement with models in which deformation is driven by the combination of in-plane stresses and bending stresses, resulting principally from slab pull. Combining the seismologically derived constraints on the thickness of the elastic core of the plate with estimates of the plate curvature, we place upper bounds on the strength of the lithosphere at the outer rise, which is required to be ≲300 MPa for a constant yield stress model, or governed by an effective coefficient of friction of ≲0.3.

Exploring the Stability Landscape of Constant-Stress Pumpkin Balloon Designs

Pumpkin balloon designs such as the constant-bulge-angle design, the constant-bulge-radius design, and hybrids of the constant-bulge-angle and constant-bulge-radius schemes have been used in an attempt to achieve a cyclically symmetric pumpkinlike shape when fully inflated. A number of flight balloons that were built based on the constant-bulge-angle, constant-bulge-radius, and hybrid design strategies encountered deployment problems. In June 2006, Flight 555-NT (a hybrid design) formed an S-cleft and did not deploy. Currently, NASA's approach to superpressure balloon design uses a constant-stress model developed at NASA Goddard Space Flight Center. To fully understand the mechanism behind cleft formation in pumpkin balloons and to explore the constant-stress design space, NASA's Balloon Program Office carried out a series of inflation tests in 2007 involving four 27-meter-diameter 200-gore pumpkin balloons. One of the test vehicles was a one-third-scale mockup of the Flight 555-NT balloon. Using an inflation procedure intended to mimic ascent, the one-third-scale mockup developed an S-cleft feature that was strikingly similar to the one observed in Flight 555-NT. The remaining three 27-meter balloons tested were constant-stress designs and deployed properly. In an effort to gauge constant-stress design susceptibility to deployment problems, we carry out a number of parametric studies and assess the stability landscape of the constant-stress design space. In our studies, we examine two types of top end-fitting boundary conditions, one restrictive and one less restrictive, that help to define a cleft-free design envelope. We correlate our analytical predictions with outcomes of inflation tests involving 27-meter-diameter test vehicles and outcomes from flight 586-NT and flight 591-NT, which involved larger constant-stress designs. To study scaling effects, we consider a 14-million-cubic-foot design. Our analysis suggests that as one scales up the balloon, the size of the cleft-free envelope shrinks.

Tree allometry and crown shape of four tree species in Atlantic rain forest, south-east Brazil

The allometry of crown shape and trunk diameter with tree height were analysed for four tree species in a tropical lowland rain forest, southeast Brazil. The dimensional relationships of a subcanopy species (Garcinia gardneriana) were contrasted with those of two canopy (Chrysophyllum flexuosum and Swartzia simplex) and one emergent species (Sloanea guianensis). For all trees ≥ 1 cm dbh, we recorded dbh, total height, branching height, crown area, crown width and crown length. Observed allometric relationships indicated interspecific variation in trunk diameter and crown shape with height. All species conformed to the elastic similarity model, except the emergent one that showed thicker trunks and a scaling exponent conforming to the constant stress model. The general allometric function used to describe the overall relationship (all sizes combined) did not specify exceptional variation in crown shape between species of contrasting adult stature (emergent vs. subcanopy species). However, when allometric relationships through ontogeny were considered, different strategies of growth, maintenance and expansion of crown became evident. Crown shapes were much more variable in canopy and emergent species than in the subcanopy one, suggesting that larger-statured species might be more flexible in the relative allocation of energy to height, diameter, and crown growth than smaller-statured ones. Notwithstanding, it is suggested that it is not possible adequately to predict allometric relationships only by adult stature/canopy position. Allometric variation may be also related to size-dependent changes in demographic traits and/or different responses to light availability among tree species.

Numerical modeling of the flow in stenosed coronary artery. The relationship between main hemodynamic parameters

The severity of coronary arterial stenosis is usually measured by either simple geometrical parameters, such as percent diameter stenosis, or hemodynamically based parameters, such as the fractional flow reserve (FFR) or coronary flow reserve (CFR). The present study aimed to establish a relationship between actual hemodynamic conditions and the parameters that define stenosis severity in the clinical setting. We used a computational model of the blood flow in a vessel with a blunt stenosis and an autoregulated vascular bed to simulate a stenosed blood vessel. A key point in creating realistic simulations is to properly model arterial autoregulation. A constant flow regulation mechanism resulted in CFR and FFR values that were within the physiological range, while a constant wall-shear stress model yielded unrealistic values. The simulation tools developed in the present study may be useful in the clinical assessment of single and multiple stenoses by means of minimally invasive methods.

Comparative Growth Behaviour and Leaf Nutrient Status of Native Trees Planted on Mine Spoil With and Without Nutrient Amendment

The effect of nutrient amendment on growth of nine indigenous tree species planted on coal mine spoil was studied. Greater growth in fertilized plots was accompanied by greater foliar N and P concentrations in all species. The response to fertilization varied among species and was greater in non-leguminous than in leguminous species. Furthermore, leguminous species exhibited higher growth rates compared to non-leguminous species. The log-transformed height-diameter relationships were significant for all tree species and treatments. Acacia catechu, Dalbergia sissoo, Gmelina arborea and Azadirachta indica fitted the elastic similarity model of tree growth; whereas Pongamia pinnata and Phyllanthus emblica followed the constant stress model. Tectona grandis was the only species which fitted the geometric similarity model. In Albizia lebbeck and Terminalia bellirica, the b -values (the gradients of the log-transformed height to diameter relationships) were considerably lower (<0.5), and these two species did not fit any model of tree growth. In several cases, the b -values were considerably influenced by nutrient amendment. The log-transformed crown mass and trunk mass relationships were significant for all treatments and species. The slope of the crown mass:trunk mass relationship was near unity in A. indica, D. sissoo, G. arborea, P. emblica, P. pinnata, T. grandis, and T. bellirica. However, in A. catechu and A. lebbeck, this slope was well below unity suggesting a greater allocation to non-photosynthetic tissue. Fertilizer amendment resulted in a heavier crown relative to trunk in A. indica, T. grandis and T. bellirica.

Effect of Nutrient Enrichment on Native Tropical Trees Planted on Singrauli Coalfields, India

AbstractGrowth performance of nine native tropical tree species planted on mine spoil under two levels of NPK treatment was studied by measuring height and diameter. Of the nine species, four were leguminous. All the tree species responded positively to NPK fertilization; however, the impact on leguminous species was little compared to non‐leguminous species. In general, the height/diameter ratio decreased from control to full‐dose NPK treatment, suggesting that nutrient enrichment influenced the resource allocation pattern such that the diameter growth was favored. The log‐transformed height‐diameter relationships were significant for the three treatments in all the tree species. The slopes (β) obtained were compared with three different models of tree growth (i.e., elastic similarity, geometric similarity, and constant stress). Acacia catechu, Dalbergia sissoo, Gmelina arborea, and Azadirachta indica fitted the elastic similarity model, whereas Pongamia pinnata and Phyllanthus emblica followed the constant stress model. Tectona grandis was the only species that followed the geometric similarity model. In Albizia lebbeck and Terminalia bellirica, the β values were considerably lower (i.e., below 0.5) and these two species did not fit any of the three models of tree growth. In several cases the β values were considerably influenced by nutrient enrichment.Key words: chemical fertilization, coal mine spoil, growth response, tree structure, tree volume, tropical tree species, height/diameter ratio.

Numerical study of grain rotation in polycrystalline metal during plastic deformation

When polycrystalline metals deform plastically, respective grains rotate due to crystal slips on the active slip planes and the preferred orientation is produced. In the present paper, the rate-type constitutive equation and the constant stress model of polycrystals are adopted, and the grain rotation is calculated for fcc and bcc metals. The rate sensitivity exponent in the rate-type constitutive equation is closely related to the number of active slip systems. So, the effect of the number of active slip systems on the grain rotation or the formation of texture is numerically studied and discussed.

Ontogenetic changes in size, allometry, and mechanical design of tropical rain forest trees

Size, allometry, and mechanical design were measured for trees of three canopy species in a tropical rain forest in French Guiana. Mechanical design was expressed as the safety factor, using the elastic-stability model, and the wind resistance factor, using the constant-stress model. Changes with ontogeny were described as regressions using stem diameter as the independent variable, and they were compared between species. Height, crown size, and the wind resistance factor increased with ontogeny. The safety factor decreased to a minimum and then increased continuously in thicker trees. The crown width/height ratio did not change with ontogeny. Interspecific differences in allometry and mechanical design were related to the adult stature of the species, and not to shade tolerance. The short stature species (Vouacapoua americana) was less slender (height:DBH [stem diameter at 1.3 m] ratio) and had a higher crown width/height ratio than the tall stature species (Goupia glabra and Dicorynia guianensis). Vouacapoua had a higher safety factor, but a similar wind resistance factor. The safety factors of our study species were lower than those of two temperate tree species because of a higher slenderness. Differences in safety factors between tropical and temperate trees may result from unrealistic assumptions of the elastic-stability model, and may also be related to lower light levels and-or wind rates in the tropics.

Numerical Study on Yield Curves of FCC Metals Based on Rate-Dependent Crystal Slips

The macroscopic plastic deformation of polycrystalline metals, as revealed by features such as yield surface under multiaxial stress or the normality rule, is related to the microscopic slips in grains. In the present paper, a rate-type constitutive equation and a constant stress model of polycrystals are adopted and the equal-strain-rate curves under biaxial stress, which are equivalent to the yield curves in plasticity, are studied. The rate-sensitivity exponent in the rate-type constitutive equation is closely related to the number of active slip systems on the yield curves. Hence, it is possible to examine the effect of the number of active slip systems on the yield curve. The yield curves of fcc single crystals as well as fcc polycrystalline metals are calculated. The shape of the obtained yield curve is dependent on the number of active slip systems as well as the distribution of strain in polycrystals. The direction of strain rate vectors is also discussed. A new model of polycrystals called the constant maximum shear strain rate model is proposed.

Characterization of experimental composite biomaterials

A comparison was made among the elastic moduli of various combinations of dimethacrylates that may be used as matrix resins in dental restorative composite biomaterials systems. Two ceramic filler materials with contrasting shape and size were synthesized by wet chemistry; these were used to produce a range of experimental composite systems. Dynamic elastic moduli determinations were used to study the influence of filler volume, filler size/shape, use of silane coupling agents, and storage in water. The filler was varied from 0 to 59% by volume for filler A and from 0 to 48% volume for filler B. Silane treatment was found to have a significant effect on modulus. Moduli for composite materials containing silane-treated filler were higher compared to materials containing the same volume loading of non-silane-treated filler. Using a light curing resin as a matrix gave a significantly higher modulus for a filler loading of 38% by volume. Storage in water for 29 days was found to have only a slight effect on moduli for composite systems containing in excess of 20% by volume of filler. The experimental composite systems produced slightly higher values for moduli than were predicted by the theoretical Reuse constant stress model.

Delaminations at the free edge of a composite laminate

The concept of a fracture process zone where damage takes place is used to analyse the delaminations at the free edges of angle ply laminates under uniaxial tension. The use of a fracture process zone removes the singularity in the interlaminar stresses and enables the initiation and growth of delaminations to be modelled for a perfect laminate without any assumed prior defects. Two different models for the stress displacement relationship in the fracture process zone are examined: a constant stress up to critical displacement and a linear relationship. Finite element analysis shows that there is little difference in the predictions obtained from the two models. An approximate analysis is presented for the constant stress stress-displacement model which is shown to agree with a finite element solution and experimental data. Hence it is argued that the approximate method using a constant stress model for the fracture process zone is sufficient for accurate prediction of delaminations.

Fracture process zone concept and delamination of composite laminates

Delaminations occur at the free edges of composite laminates because of high interlaminar stresses, which develop due to a mismatch in elastic properties between adjacent plies and the limited toughness of the matrix. The process of delamination is modelled using the concept of a fracture process zone. A finite element analysis that can be used with a constant or linear stress-displacement relationship within the fracture process zone is presented. It is found that the simple constant stress model gives an accurate prediction of the delamination on the free edge of a tensile specimen.

Strength distribution of Carborundum polycrystalline SiC fibres as derived from the single-fibre-composite test

The single-fibre—composite (s.f.c) test, in which a fibre is embedded in an epoxy matrix and the composite tested in tension, was employed to obtain the statistical strength distribution of Carborundum SiC ceramic fibres over the range of gauge lengths from 0.5 to 20 mm. The raw s.f.c. test data was organized into three independent forms: the number of fibre breaks versus applied stress; the fibre fragment length distribution at the end of the test; and the fibre strength versus fragment length during testing. The data was interpreted using two different models of the fibre/epoxy—matrix interface, and it was found that a constant shear stress model could not self-consistently fit all of the s.f.c. data, whereas an elastic interface model provided good fits to all of the data. The applicability of the elastic interface model was supported by the absence of interfacial debonding and the rough fibre/matrix interface, which promoted mechanical interlocking. The s.f.c. test derived strength of σ0 = 1500 MPa at a gauge length of 20 mm, with a Weibull modulus of m = 9, agreed fairly well with independent tension test results obtained on 254 mm length samples. Obtaining self-consistent fits to all of the manifestations of the s.f.c. data requires careful testing and analysis, but the present work demonstrates that the s.f.c. test can be a powerful tool for the accurate and independent assessment of fibre strengths at small gauge lengths.

Ontogenetic Scaling and Mechanical Behaviour of the Tibiae of the African Desert Locust (Schistocerca Gregaria)

ABSTRACT Current models for scaling of skeletal morphology were examined to test their applicability to the ontogenetic growth of an exoskeletal animal, the African desert locust ( Schistocerca gregaria). It was found that the tibial leg segments of both the mesothoracic (i.e. non-jumping) and the metathoracic (jumping) legs scaled in a manner that produced relatively longer, more slender skeletal elements as the animal grew. Metathoracic tibial length scaled to tibial diameter raised to the power 1.21. This result deviates both from isometric (i.e. geometric similarity) and distortive (constant stress, elastic similarity) allometric models. The mechanical properties of the metathoracic tibiae were measured using a dynamic, three-point bending technique. The flexural stiffness of metathoracic tibiae scaled to body mass raised to the power 1.53. This was intermediate to the predictions made by constant stress and elastic similarity models. Thus, the mechanical properties scaled as predicted by mechanical scaling expectations in spite of the morphological developmental programme. It may be that the thin-walled skeleton developed in the exoskeletal body plan has allowed a finer control over the distribution of load-bearing material in the leg. Such a distribution may be responsible for the observed increase in mechanical stiffness of legs that exhibit an unexpectedly spindly morphology. The rationale for the observed morphological programme may be a design that takes advantage of the inherent deformability of long, slender beams. Thus, it may be that the tibiae, which have been treated as rigid levers, are in fact flexible springs. Calculations indicate that the energy stored in the substantial deflection of the adult, metathoracic tibiae during a jump may be as high as 10% of the total kinetic energy of the jump.

Influence of leaf area and canopy structure on size-density relations in even-aged lodgepole pine stands

The hypothesis that size-density relationships result from the distribution of constant amounts of population leaf area among varying numbers of trees per unit area, was modified to include the influence of population density on canopy structure. The modification was made possible with the constant-stress model of stem formation. The modified hypothesis was tested in unmanaged, even-aged stands of lodgepole pine ( Pinus contorta var. latifolia Engelm.) in northern Utah. Using mean leaf area per tree, mean live-crown length, and mean live-crown ratio, the constant-stress model was used to calculate hypothetical values of mean quadratic diameter ( D q) for those stands with equilibrium levels of leaf area. Linear regression showed that the hypothetical and measured values of D q were not significantly different ( P=0.29). Consequently, the modified hypothesis duplicated the observed relationship between D q and number of trees per hectare ( N) for these stands. Using the modified hypothesis, canopy structure is shown to be responsible for the curvilinear relationship between the log of D q and the log of N observed for these stands.

速度依存性構成式によるＢＣＣ結晶のすべりと回転の検討

Crystal grains in polycrystalline metals rotate during the plastic deformation by crystal slips, which results in the deformation textures of polycrystalline metals. In the present paper, the rotation of crystal due to slips was calculated adopting the constant stress model of polycrystals. The rate dependent type constitutive laws for crystalline materials that deform plastically by slips was used.Namely, a power law used by Hutchinson and an exponential type law proposed by Bodner were adopted as a relation between shear stress and shear strain-rate on the slip plane. It was pointed out that the parameters in the rate-type constitutive equations are related to the number of active slip systems. The relation between the rotation of crystals and these parameters, that is, the number of the active slip systems was clarified. A method was proposed to change the constant stress polycrystalline model toward the constant strain model by changing the parameter in the constitutive equation.

High-temperature fracture of composite materials

The high-temperature fracture of composite materials containing strong particles is discussed on the basis of micromechanical models in which the recovery effect by diffusion of atoms is taken into account. The results of the calculations are compared with experimental results on 21Cr-4Ni-9Mn steels which consist of equiaxed grains containing rod-like M23 C6 carbide particles. The internal stresses acting in the particles and the grains are calculated on the basis of the model. The fracture mode of the material changes from transgranular to grain boundary fracture with increasing temperature, and the elongation of the material increases as a result. These experimental observations can be interpreted in terms of the calculation results of the constant stress model in which non-uniform distribution of plastic strain is assumed, but the calculated results of the constant strain model cannot explain the experimental results.