Exponential Stress Research Articles

Statistical Inference of Stress–Strength Reliability of a Parallel System with Mixed Standby Components

This paper presents the Bayesian analysis of the stress–strength reliability of a parallel system with active and mixed standby components. The Bayesian estimators of the parameters of exponential and Weibull stress–strength distributions are obtained by assuming informative and noninformative prior for the parameters of the respective distributions. The Gibbs sampling procedure is used to compute the Bayesian stress–strength reliability. The asymptotic distributions, of the maximum likelihood estimators of the parameters of the corresponding distributions, and of the respective system reliabilities are presented. The bootstrap estimate and confidence interval are also obtained. The procedures are illustrated based on certain datasets.

A linear, analytical solution to the principal stress cap, force balance equations for asymmetrical stresses in cylindrical silos

A linear, analytical solution to the principal stress cap force balance equations for asymmetrical stress in a circular silo has been derived. Principal stress relationships are linearly through gradients J1 and J2 and intercepts T1 and T2.The solution gives first-order ordinary differential equations in Z over the principal stress cap surface. The solution to the equation can either be Janssenian(stresses approach limiting values), or exponential(stresses increase exponentially with depth).Exponential stress can be caused by•reversal of the direction of vertical shear stress from upwards(positive) for Janssenian: to downwards(negative) for exponential(vertical stress reversal exponential stress).and/or•the inclination of the principal stress cap (λ-line) directing gravitational forces to the lower region of the stress cap(σ2 exponential stress).Symmetrical systems; systems with low Eccentricity; and concave systems give Janssenian stress throughout with the appropriate state of stress (passive/convex; active/concave).Exponential stress systems could cause high stresses and large variations around the perimeter of the silo, with potentially catastrophic effects.The model is relatively simple and can form a basis for the planning and design of experiments, and a base case for more sophisticated models.

Comprehensive investigation of fatigue behavior and a new strain-life model for CP-Ti under different loading conditions

This paper investigates symmetric strain, stress and asymmetric stress-controlled fatigue behavior of prestrained and non-prestrained CP-Ti. The effects of stress ratio, mean stress, prestrain on stress/strain life were carefully analyzed. Stress-life of CP-Ti shows non-monotonic variation with stress ratio, as compressive ratcheting resulted by tension-compression asymmetry accumulates under symmetric stress cycling. Stress-life can be improved by prestrain, regardless of loading condition, due to the decrease of responded strain amplitude. Stress fatigue resistance of the material is actually deteriorated by prestrain at the stress level identical to that of non-prestrained CP-Ti. Strain-life of prestrained sample shows little variation at high strain amplitude due to mean stress relaxation and significant reduction at low strain amplitude. By introducing asymmetry factor, it is further found that strain-life of the material is insensitive to prestrain if the applied mean stress level keeps constant. Finally, current strain-life models with different mean stress correction terms are discussed to evaluate their application ability in fatigue life prediction of CP-Ti under different loading conditions. Though two additional parameters are introduced into the mean stress correction term with power law form, there are still few data points beyond the scatter bounds of two. Therefore, a new strain-life model with exponential mean stress correction term is proposed and verified by fatigue life data of different materials, which has more advantage than existing strain-life models at a wide range of mean stress level.

The influence of partial hydrocarbon saturation on porosity and permeability in a palaeogene lacustrine shale-hosted oil system of the Bohai Bay Basin, Eastern China

Palaeogene calcareous (>40% carbonate) mudstones (Ro from 0.56 to 0.88%) from the Bohai Bay Basin were studied by combined petrographical, geochemical and petrophysical analysis in order to assess and quantify the pore space, pore filling and its influence on gas transport capacity.TOC contents ranged from 1.44% to 5.12% and porosities (ΦHe) determined by helium pycnometry, from 1.3% to 6.4%. Bitumen-filled porosity (ΦS1) was estimated to range between 0.3 and 2.0% based on Rock-Eval S1 values and an assumed bitumen density of 0.90 g/cm3. The “true” total porosity (Φtotal = ΦHe + ΦS1) amounts to 1.9–8.5%. The in-situ oil saturation (So) was estimated to range between 25% and 52%, with two samples (L69-1B and L69-2) having relatively high oil saturation (71% and 91%).The conductivity of the remaining “open” pore space was measured on three samples with different orientations and oil saturations from 17 to 24%. The effective Klinkenberg-corrected gas permeability coefficients range between 63 and 2000 nDarcy, and permeability is highest parallel to bedding. Upon loading from 10 to 40 MPa confining pressure the intrinsic permeability coefficients decreased by one order of magnitude, revealing a relatively high exponential stress sensitivity coefficient (0.069 MPa−1) and much lower zero stress permeability (1.416 × 10−6 mD) than most gas shales. This could be due to pore plugging by ductile bitumen.

Experimental verification of the physical nature of velocity-stress relationship for isotropic porous rocks

The exponential increase of seismic velocities with effective stress has usually been explained by the presence of pores with a broad distribution of aspect ratios. More recently, a stress-related closure of soft pores with a narrow distribution of compliances (e.g., grain contacts) has been suggested to be sufficient to explain such exponential stress dependency. This theoretical interpretation has been verified here using laboratory measurements on dry sandstones. On the basis of these experimental data, linear dependency of elastic compressibility on soft porosity and exponential decay of soft porosity and elastic compressibility with effective stress up to 60 MPa is confirmed. Soft porosity, estimated from the fitting coefficients of elastic compressibilities, is on the same order of magnitude but slightly lower than obtained from strain measurements. The results confirm applicability of previously proposed stress sensitivity models and provide justification for using this approach to model stress dependency of elastic properties for isotropic and anisotropic rocks.

Stress Relaxation in Active Sarcomeres and a Hypothesized Calcium-Dependent Glass Transition

Central to the functional use of muscles is the active perturbation response that transitions between a stiff solid-like and a yielding fluid-like material depending on its neural activation. The solid-like response enables muscle to transmit stresses to tendons without stretching appreciably. A fluid-like response is essential to minimally resist being stretched during fast motions, without internal damage to the muscle. This transition manifests as a stress relaxation timescale of the perturbation response, where the muscle is solid-like for times shorter than this timescale and fluid-like for longer times. Behavioral evidence shows that muscle can dissipate stresses in less than 100ms during a fast motion such as a baseball pitch. But it can also maintain stresses for several minutes to stabilize a posture. The relaxation timescale must therefore vary by 1000-fold or more, depending on the neural input that modulates intracellular calcium concentration. We find that Huxley-based models of crossbridge mechanics, irrespective of the number of internal states, fail to capture this vast change in the relaxation timescale unless non-physiological dependence on calcium are assumed for the kinetics. Other resolutions involve either titin or stretch reflexes, and we examine the experimental evidence for each. We also posit a third crossbridge based hypothesis, namely, a calcium-dependent glass transition in population dynamics of active crossbridges. At a glass transition, the material's viscosity increases by many orders of magnitude over a small parameter change, and a characteristic of the glassy state is a slower than exponential stress relaxation for which there is no finite relaxation timescale. We hypothesize possible means by which such a transition may arise from crossbridge dynamics and suggest experiments to test the hypothesis.

Modeling R-dependence of near-threshold fatigue crack growth by combining crack closure and exponential mean stress model

A previously proposed equivalent driving force model was modified to account for crack closure for modeling stress ratio, R, dependence of fatigue crack growth in near-threshold regime. A new fatigue crack growth driving force model was established in the form of ΔK⋅f(R), where the f(R) includes both crack closure and mean stress contributions, and well informs the shift from dominance of stress intensity factor range ΔK to maximum stress intensity factor Kmax with increasing R. The model was validated widely with sound agreement between modeling results and experimental data.

On classical and Bayesian order restricted inference for multiple exponential step stress model

ABSTRACTIn this article, we consider the multiple step stress model based on the cumulative exposure model assumption. Here, it is assumed that for a given stress level, the lifetime of the experimental units follows exponential distribution and the expected lifetime decreases as the stress level increases. We mainly focus on the order restricted inference of the unknown parameters of the lifetime distributions. First we consider the order restricted maximum likelihood estimators (MLEs) of the model parameters. It is well known that the order restricted MLEs cannot be obtained in explicit forms. We propose an algorithm that stops in finite number of steps and it provides the MLEs. We further consider the Bayes estimates and the associated credible intervals under the squared error loss function. Due to the absence of explicit form of the Bayes estimates, we propose to use the importance sampling technique to compute Bayes estimates. We provide an extensive simulation study in case of three stress levels mainly to see the performance of the proposed methods. Finally the analysis of one real data set has been provided for illustrative purposes.

Nonlocal electrothermomechanical instability of temperature-dependent FGM nanopanels with piezoelectric facesheets

Within the framework of a novel shear deformation panel theory based on exponential shear stress distribution, the nonlocal continuum theory is utilized to establish an efficient size-dependent panel model to anticipate the nonlinear instability characteristics of nanoscaled panels subjected to combination of axial compressive load, lateral electric field and through-thickness heat conduction and corresponding to both the temperature-dependent (TD) and temperature-independent cases. The nanopanels contain a substrate made of functionally graded material (FGM) and surface-bonded piezoelectric nanolayers with temperature-dependent material properties. To eliminate the stretching-bending coupling terms, the physical neutral plane position related to the FGM substrate of nanopanels is taken into consideration. The nonlocal nonlinear governing equations are deduced to boundary layer-type ones and then solved via a perturbation-based solving process which results in explicit expressions for nonlocal temperature-dependent equilibrium curves. It is found that in the TD case, by heating the outer surface of nanopanel, the reductions in the values of buckling load and minimum postbuckling load are more considerable for nonlocal hybrid FGM nanopanel than those of local one.

Uniaxial ratcheting behavior and fatigue life models of commercial pure titanium

AbstractThe uniaxial fatigue and ratcheting behavior of commercial pure titanium (CP‐Ti) was investigated by asymmetric cyclic stress‐controlled experiments at room temperature. The effects of mean stress, stress amplitude, stress ratio, and peak stress on ratcheting behavior and fatigue life were discussed. It was found that increasing mean stress, stress amplitude, and peak stress or decreasing stress ratio reduced fatigue life and promoted ratcheting behavior. The applicability of different fatigue life models was analyzed, and a new stress ratio‐related failure model was proposed based on the exponential increase of fatigue life with stress ratio. Among all the models investigated in this study, the exponential stress ratio‐related model has more advantage in fatigue life predictions for CP‐Ti under ratcheting‐fatigue interaction.

Experimental study on the influence of slickwater on shale permeability

There are two diametrically opposite views of the influence of slickwater on shale permeability among scholars at home and abroad. We used the shale outcrops rock samples from the Lower Silurian Longmaxi Formation in Sichuan Basin. The permeability of these dry samples before and after immersion in different solution systems were tested by pulse attenuation method. The experimental results show that the impregnation of different slickwater components and standard salt solution can promote the increase of the permeability of shale samples. The stress sensitivity of shale samples after liquid immersion is medium weak to weak. The sample stress sensitivity is weak after soaked by the synergist solution and Drag reducing agent solution, and the sensitivity of the sample stress is medium weak after immersed by the standard saline solution, defoamer solution and antiswelling solution; The Ki/K0 of the shale sample after liquid immersion on σi/σ0 is consistent with the exponential stress sensitive evaluation model. With the increase of soaking time, the increase of sample permeability increases first and then decreases.

Exam Stress in MBBS Students and the Methods Used for its Alleviation

<p><strong>Background:</strong> Stress is a state of mental or emotional strain or tension resulting from adverse or demanding circumstances. Stress level in all aspects of life is growing at an exponential rate but stress level in students, especially MBBS students is alarming.</p><p><strong>Objective:</strong> To find out the level of stress and relieving methods used by medical students before examination.</p><p><strong>Material and Methods:</strong> Observational, Cross sectional study was conducted on 600 medical students using questionnaire. Responses of the students were recorded on Likert’s scale just after the examination. Data was tabulated and analyzed statistically.</p><p><strong>Results:</strong> The mean age of 600 medical students were 20.1±0.9. 143(23.8%) students always felt stressed, 161(26.8%) often, 211(35.2%) sometimes, 37(6.2%) rarely and 48(8%) never felt stressed before examination. 252(42%) reported that this level of stress did not affect their performance in examination while decrease in performance was reported by 198(33%). 150(25%) said that their performance was improved during examination due to stress. 145(24.2%) felt no anxiety during examination, 432(72%) felt healthy anxiety and 23(3.8%) felt unhealthy anxiety level.</p><p><strong>Conclusion:</strong> Majority of the medical students experiences some level of anxiety during exams and used various coping mechanisms to deal with stress. Although some degree of stress is accepted as a normal part of medical training and can be a motivator for some individuals, not all students find the stress manageable.</p>

Atomistic–continuum model for probing the biomechanical properties of human erythrocyte membrane under extreme conditions

A precise first attempt is performed to quantify the biomechanical properties of human erythrocyte membrane subjects to extreme temperature and loading conditions. An improved three-dimensional (3D) atomistic–continuum model based on the Cauchy–Born rule is proposed to investigate the elastic properties and biomechanical responses of the erythrocyte membrane. A membrane rigidity model is developed to estimate the membrane elastic properties over an extreme temperature range. Our computational results reveal that the membrane is able to sustain large strains up to a certain limit; beyond which, mechanically induced hemolysis may occur as exponential stress increment, fluctuations and multiple peaks were observed in the stress–strain curves. Additionally, we found that the overall deformability of the erythrocyte membrane significantly decreases as temperature increases. It is concluded that the observed increase in membrane rigidity may be attributed to the denaturation, structural remodeling and cross-linking of membrane cytoskeletal proteins.

Preferential hydration fully controls the renaturation dynamics of collagen in water-glycerol solvents.

Glycerol is one of the additives which stabilize collagen, as well as globular proteins, against thermally induced denaturation --an effect explained by preferential hydration, i.e. by the formation, in water/glycerol solvents, of a hydration layer whose entropic cost favors the more compact triple-helix native structure against the denatured one, gelatin. Quenching gelatin solutions promotes renaturation which, however, remains incomplete, as the formation of a gel network gives rise to growing topological constraints. So, gelatin gels exhibit glass-like dynamical features such as slow aging of their shear modulus and stretched exponential stress relaxation, the study of which gives us access to the re(de)naturation dynamics of collagen. We show that this dynamics is independent of the bulk solvent viscosity and controlled by a single parameter, the undercooling [Formula: see text] below the glycerol-concentration-dependent denaturation temperature. This provides direct proof of i) the presence of a nanometer thick, glycerol-free hydration layer, ii) the high locality of the kinetically limiting process governing renaturation.

Stress impact on elastic anisotropy of triclinic porous and fractured rocks

AbstractUnderstanding the stress dependence of elastic properties of rocks is important for reservoir characterization and seismic‐hazard monitoring. Several known approaches describing this dependence are the following: the nonlinear elasticity theory, effective‐medium theories for fractured rocks with stress‐dependent crack densities, and the piezosensitivity approach (also called the porosity deformation approach). Here I propose a generalization of the piezosensitivity approach to triclinic rocks. I assume the isotropy of the tensor describing sensitivity of elasticity to small strains of the pore space, and generalize known linear and exponential stress dependencies of compliances. This generalization is capable of describing the effect of loads on elastic properties of anisotropic rocks when the principal stresses are not necessarily aligned with the symmetrical axes of the unstressed anisotropic material. For example, the generalization describes how monoclinic anisotropy changes under isostatic stress or pore pressure, and how tilted transverse isotropy changes to monoclinic anisotropy due to a pseudo‐triaxial (or a uniaxial) load. The results are expected to be valid up to several hundred megapascals. This theory is closely related to the two other approaches mentioned above. On the one hand, for unloaded rocks, the theory is consistent with the noninteracting scalar‐crack approximation. On the other hand, the theory's predictions of mutual relations between isotropic third‐order elastic moduli is in good agreement with literature data on corresponding laboratory measurements. Thus, using the piezosensitivity approach, the physical nonlinearity of rocks can quantitatively be rather well explained by the strain of compliant pores.

A generalized layered global-local beam theory for elasto-plastic analysis of thin-walled members

Based on a generalized layered global-local beam (GLGB) theory, a computationally low cost finite element model is presented for the elasto-plastic analysis of thin-walled beams. In the employed GLGB theory, the cross-section of the thin-walled beam is replaced with an equivalent layered composite one. For describing the displacement fields of the equivalent layered composite beam, the double superposition hypothesis in conjugate with an exponential shear stress function is employed. In contrast to the most of available advanced one-dimensional (1D) models proposed for thin-walled structures, the effects of the transverse normal stress and transverse flexibility are considered in the present GLGB theory. The proposed GLGB theory does not need the incorporation of any shear correction factor and it has only one general unknown parameter more than Timoshenko's beam theory. For plasticity modeling, von Mises yield criterion is employed. The non-linear 1D finite element formulations are solved using Newton-Raphson algorithm. The proposed nonlinear finite element model is validated through comparison with the three-dimensional (3D) finite element and other similar theoretical models available in the literature.

Exponentially harmonic maps, exponential stress energy and stability

We study the exponential stress energy associated to an exponentially harmonic map between Riemannian manifolds. We prove three equivalent statements for a horizontally weakly conformal exponentially harmonic map between Riemannian manifolds. We also investigate the stability of exponentially harmonic maps.

Surface properties and exponential stress relaxations of mammalian meibum films

The surface properties of meibomian secretion (MGS), the major constituent of the tear film (TF) lipid layer, are of key importance for TF stability. The interfacial properties of canine, cMGS, and feline, fMGS, meibum films were studied using a Langmuir surface balance. These species were selected because they have blinking frequency and TF stability similar to those of humans. The sample's performance during dynamic area changes was evaluated by surface pressure (π)-area (A) isocycles and the layer structure was monitored with Brewster angle microscopy. The films' dilatational rheology was probed via the stress-relaxation technique. The animal MGS showed similar behavior both between each other and with human MGS (studied previously). They form reversible, non-collapsible, multilayer thick films. The relaxations of canine, feline, and human MGS films were well described by double exponential decay reflecting the presence of two processes: (1) fast elastic process, with characteristic time τ<10s and (2) slow viscous process, with τ>100s-emphasizing the meibum layers viscoelasticity. The temperature decrease from 35 to 25°C resulted in decreased thickness and lateral expansion of all MGS layers accompanied with increase of the π/A hysteresis and of the elastic process contribution to π relaxation transients. Thus, MGS films of mammals with similar blinking frequency and TF stability have similar surface properties and stress relaxations unaltered by the interspecies MGS compositional variations. Such knowledge may impact the selection of animal mimics of human MGS and on a better understanding of lipid classes' impact on meibum functionality.

PREDICTION OF SOIL SETTLEMENT BASED ON CONSTANT PLASTIC INDEX METHOD

The development of Constant Plastic Index (CPI) method is an approach model based on the theory of consolidation. The objective behind the development CPI method is to predicts critical state settlement whereby CPI is to achieved secondary settlement and reduced time of consolidation. The development CPI has been derived base on the ultimate soil settlement where soils are classified accordingly using initial void ratio, final void ratio and thickness of soil layers. The linear and non linear soil was developed by the relationship between an exponential stress - void ratio and the parabolic permeability - void ratio. The external forces is normally consolidated soil layers and develop Stratum index factor (SIF) and Void ratio function(VRF) which is composed of such a soil varies non- linearly in deposition. Development of CPI will used to predicts critical state settlement, using Eurelian method By combination of these elements, the Potential Instability of settlement was develop and integrate CS- Rating makes concerted effort to produce CS- statement guidelines and better design strategy for geo -mechanics engineer to involve in soil development settlement analysis. Finally, modification of CPI method can be determine soil settlement by using CS- Rating. © 2016, Int. J. of GEOMATE.

Near-exponential relationship between effective stress and permeability of porous rocks revealed in Gangi's phenomenological models and application to gas shales

A number of theoretical models, as well as empirical equations obtained by fitting specific experimental data, have been developed to describe the relationship between effective stress and permeability of intact and fractured porous rocks. It has been found that most experimental data can be fitted using exponential equations. In this study the modified power law equations by Gangi for intact and fractured rocks are revisited to evaluate their applicability for modeling experimental permeability data which display exponential or near-exponential effective stress dependency. It has been shown that Gangi's power law equations for both intact and fractured rocks can be approximated, over the range of effective stresses of practical interest, by exponential equations with compressibilities that are related to the physical properties of the rock. The significance of this work is that it has provided further theoretical evidence for the apparent exponential relationship between effective stress and permeability. Moreover, it allows for more vigorous theoretical equations to be applied with the easiness of empirical exponential equations. This is demonstrated by applying the models to the experimental permeability data for six gas shales reported recently.