Small Stress Research Articles

Discussion on the Research of GFRP Anti-floating Anchors

As a kind of anchor to deal with the anti-flotation problem of floor, anti-flotation anchors have many advantages, such as strong adaptability to stratum, high anchoring force, low cost, short construction period, small stress at single point, simple construction and low cost, compared with the traditional anchor. In recent years, it has been more and more applied to solve the problems of foundation pit supporting and foundation floor anti-floating in the construction process of buildings. In this paper, the stress and strain distribution law, load transfer characteristics and the relationship between GFRP anti-floating anchor and rock mass of GFRP anti-floating anchor are summarized, and suggestions for the future development of GFRP anti-floating anchor are put forward.

Axial Compressive Stress Dependence of Critical Current of REBCO Double-Pancake Coil

This study investigated the axial compressive stress dependence of the critical current of Rare Earth Barium-Copper-Oxide (REBCO) double-pancake coils. We measured the critical currents of REBCO coils cooled by liquid nitrogen while various axial compressive stresses from 0 MPa to 130 MPa were applied. After each stress was applied, the critical currents of the coils were also measured without the stress application to examine if the REBCO coils were irreversibly deteriorated. The experimental results showed that the REBCO coils were deteriorated at more than 100 MPa and the critical currents of the coils decreased by about 30% by applying 120 MPa to the coils. Moreover, reversible reduction of the critical currents of the coils were observed while the stresses of less than 100 MPa were applied. The reversible critical current decrease occurred even at a small stress, and the critical currents of the coils were reversibly reduced by about 15% while the stress of 100 MPa was applied. This study quantitatively clarified the dependence of the critical current of the REBCO coil on the axial compressive stress and the limitation of the axial compressive stress to prevent the deterioration of the REBCO coil.

Measuring cellular contraction: Current progress and a future in bioelectronics

Cellular contraction is a universal phenomenon that drives various processes in the body. As such, measurement of cell contractility is of great interest to the scientific community. However, contracting cells apply very small stresses, which can be difficult to monitor. Various techniques have been developed to overcome these issues, with resolutions extending to the single cell level. Despite significant progress in this field, many limitations remain, including the ability to measure contraction instantaneously and in vivo. Bioelectronics involve the application of electric fields or electrically responsive materials for measurement or stimulation in biology. Bioelectronic devices have the major potential to overcome some of the remaining challenges in monitoring cell contraction, given their ability to provide fast, non-invasive measurements. In this forward-looking perspective, we will discuss the development of contractile measurement technologies as well as new areas that require growth and the potential for application of bioelectronics in this field.

Numerical simulation on the simultaneous stress interference of parallel multiple hydraulic fractures

During horizontal well staged fracturing, there is stress interference between multiple transverse fractures in the same perforation cluster. Theoretical analysis and numerical calculation methods are applied in this study. We analysed the mechanism of induced stress interference in a single fracture under different fracture spacings and principal stress ratios. We also investigated the hydraulic fracture morphology and synchronous expansion process under different fracture spacings and principal stress ratios. The results show that the essence of induced stress is the stress increment in the area around the hydraulic fracture. Induced stress had a dual role in the fracturing process. It created favourable ground stress conditions for the diversion of hydraulic fractures and the formation of complex fracture network systems, inhibited fracture expansion in local areas, stopped hydraulic fractures, and prevented the formation of effective fractures. The curves of the maximum principal stress, minimum principal stress, and induced principal stress difference with distance under different fracture lengths, different fracture spacings, and different principal stress ratios were consistent overall. With a small fracture spacing and a small principal stress ratio, intermediate hydraulic fractures were difficult to initiate or arrest soon after initiation, fractures did not expand easily, and the expansion speed of lateral hydraulic fractures was fast. Moreover, with a smaller fracture spacing and a smaller principal stress ratio, hydraulic fractures were more prone to steering, and even new fractures were produced in the minimum principal stress direction, which was beneficial to the fracture network communication in the reservoir. When the local stress and fracture spacing were appropriate, the intermediate fracture could expand normally, which could effectively increase the reservoir permeability.

Modeling of mechanical behavior of corroded X80 steel pipeline reinforced with type-B repair sleeve

This work investigated stress response of a corroded X80 steel pipeline repaired by a type-B sleeve to internal pressure by finite element modeling. Firstly, a three-dimensional numerical model of corroded pipeline reinforced with type-B sleeve was developed, and its accuracy and reliability were verified by the burst test results and the theoretical analytical solution, respectively. Second, the von Mises stress of the pipe body, sleeve and fillet weld was simulated under various affecting factors, i.e., internal pressure, corrosion defect dimension (depth, length and width) and sleeve length. Finally, a parameter sensitivity study was conducted to determine the effects of corrosion geometry and sleeve length on the repair efficiency. The main investigation results show that the type-B sleeve repair method is effective to restore the pressure-bearing capacity of the pipeline at the corrosion defect, and the burst failure of repaired pipeline always occurs at the region far away from the defect and sleeve. At the limit state of burst, the local defective region shows the highest stress, followed by the fillet weld, and the repair sleeve has the smallest stress, thus the maximum equivalent stress of the corroded zone is suggested to be used for measuring the repair efficiency of the repaired pipe by type-B sleeve. The sleeve-repair effectiveness is affected by depth of the corrosion defect, a deep corrosion defect reduces the performance of the sleeve repair compared with a shallow defect. The effect of the corrosion defect length on sleeve repair depends on the defect depth. Furthermore, there exist a critical length of the defect that affect the repair efficiency. The corrosion defect width shows limited effect on stress level at the defect of the repaired pipe. At last, a new method based on stress analysis is proposed to optimize the sleeve length for repairing a corroded pipeline.

Springback and deformation uniformity of high-strength aluminum alloy sheet using electromagnetic forming

High-strength aluminum alloy has been widely used in aerospace and other industries. In the traditional bending process, a large springback occurs for high-strength aluminum alloy sheet due to its higher yield strength and lower elastic modulus. In the past, many scholars found that electromagnetic forming (EMF) can significantly reduce the springback effect. However, the electromagnetic-assisted bending and low-yield-strength aluminum alloy were used in the past researches. If the electromagnetic force is used to bend the high-strength aluminum alloy, what is the different of plastic deformation laws and springback effect both in electromagnetic forming and traditional bending? Those are the research interest of this paper. Thus, we have studied the influence of electromagnetic direct forming, electromagnetic drive forming, and traditional stamping on deformation uniformity and springback of high-strength aluminum alloy sheets. The deformation and stress distribution were analyzed by numerical simulations. The accuracy of the simulation was verified by experimental results. The results reveal that both electromagnetic direct forming and traditional stamping endow a large springback effect. It must also be mentioned that the high-strength aluminum alloy sheet dented on the center after electromagnetic direct forming, which reduces the sheet deformation uniformity. However, a small springback occurs on sheets due to small residual stress and the final deformed sheet has a smooth profile by electromagnetic drive forming. Thus, the electromagnetic drive forming is an effective mean to reduce springback and enhance deformation uniformity for high-strength aluminum alloy sheets.

Capturing the stress evolution in electrode materials that undergo phase transformations during electrochemical cycling

The present work sheds light on the stresses generated in a spherical particle subjected to phase transformations during ion-insertion. In order to account for the physical process that occurs during electrochemical cycling, the models used are those of small deformation and account for the effects of phase transformation, chemo-mechanical coupling and concentration-dependent material properties. The two-phase lithiation is modeled by the Cahn–Hilliard equation. It is found that the DISs arise from the inhomogeneous volume expansions resulting from Li concentration gradients and the hydrostatic stress facilitates the diffusion of Li-ions under elastic deformation while it hinders diffusion in the plastic case. When the elastic modulus is reduced the magnitude of the diffusion-induced stress decreases but the strain increases under elastic deformation whereas the opposite occurs for the plastic case. Furthermore, if the electrode is assumed to undergo strain softening during plastic deformation, smaller stresses and higher plastic strains are predicted than when strain hardening is assumed. The novelty of this work is that the proposed models highlight the importance of chemo-mechanical coupling effects, concentration-dependent material properties and plastic deformation on diffusion-induced stresses. These findings render prospective insights for designing next-generation mechanically stable phase transforming electrode materials.

46. Management of Hematocolpos in Lower Vaginal Atresia by Image-Guided Drainage with Interventional Radiology: A Case Series

<h3>Background</h3> Obstructive uterovaginal anomalies such as lower vaginal atresia (LVA), can lead to hematocolpos (HC) and subsequent pain at presentation. Definitive management of long LVA requires vaginoplasty with diligent postoperative dilation to prevent vaginal stenosis. However, many adolescents are not emotionally mature enough to adhere to this. Menstrual suppression and delayed vaginoplasty is recommended, however pain symptoms may require drainage of HC. We present a novel approach to management of symptomatic HC via image-guided percutaneous drainage by Interventional Radiology (IR). <h3>Case</h3> Case 1: 14 yo with small bladder and stress urinary incontinence presented with pelvic pain and was found to have a solitary uterus, 6 cm LVA, and a large HC on MRI. She declined vaginoplasty and opted for IR drainage. Ultrasound (US)-guided transabdominal percutaneous uterine access was obtained and tissue plasminogen activator (tPA) was infused through a drain to thin the HC fluid to allow complete aspiration. Norethindrone acetate (NAT) was initiated for menstrual suppression. Cases 2 and 3: 10 yo presented with abdominal pain and found to have a solitary uterus, 5.3 cm LVA, and a large HC on MRI. Menstrual suppression with NAT failed to control her pain; after counseling, she declined vaginoplasty and opted for IR drainage. US-guided percutaneous access was obtained, tPA infused to thin the HC, and pigtail drain placed to assist with further decompression. Cone beam CT verified the patient's anatomy and confirmed drain position. Drain was removed post-operative day 1. Symptomatic re-accumulation of HC occurred after 15 months of menstrual suppression and a repeat US-guided drainage was performed with complete decompression; GnRH agonist arm implant was placed for long-term menstrual suppression. Case 4: 15 yo with complex history including urogenital sinus, renal transplant, and urinary diversion was admitted to the hospital with pelvic pain. MRI suggested a dilated bicornuate uterus with HC and 6 cm LVA. She was counseled on management options, and elected IR drainage. US-guided, percutaneous drainage of the uterine cavity was performed with complete decompression of HC. Cone beam CT confirmed uterine anatomy after drainage. NAT was initiated for long-term menstrual suppression. Table 1 provides a detailed summary of each case. <h3>Comments</h3> We present a novel approach to management of symptomatic HC from LVA via image-guided percutaneous drainage of HC by IR. This simple outpatient procedure can successfully relieve symptoms and allow for menstrual suppression to serve as a temporizing measure until patients are mature enough to undergo definitive surgery for various obstructive uterovaginal anomalies.

From continuum to quantum mechanics study on the fracture of nanoscale notched brittle materials

The fracture of nanoscale notched brittle materials is investigated using the multi-scale analysis of cohesive zone modeling and first-principles calculations based on the notched nano-cantilever bending experiment. The fracture of nanoscale single-crystal silicon is achieved at the nano-notch tip, and the load-deflection curve is obtained during in situ TEM experiment. On the other hand, a bilinear CZM is adopted to simulate the observed fracture from the notch tip due to the stress concentration of less than 1 nm. The CZM parameters determined from one specimen, ϕn=9.78 J/m2, σmax = 13.04 GPa, and Δnc=1.5 nm, accurately predict the fracture behaviors of all other specimens regardless of specimen sizes, indicating the robust applicability of CZM for describing the fracture of nanoscale brittle materials. In addition, first-principles calculations are performed to investigate the inherent fracture properties of single-crystal silicon from atomic and electronic viewpoints. The fracture surface energy and critical bond length for the break of atomic bonds during the fracture are compared with the cohesive energy and failure length parameter, respectively, which provides the atomistic interpretation of CZM validity for the fracture of brittle materials by the extremely small stress concentration. Finally, the comparison of cohesive energy with the fracture energy obtained by fracture mechanics of nanoscale and bulk single-crystal silicon indicates that the consumed energy is an effective linkage to quantify the fracture of brittle materials at different scales.

The Growth of Earthquake Clusters

Migration of hypocenters is a common attribute of induced injection seismicity and of earthquake swarms, which distinguishes them from aftershock sequences. Spreading of the triggering front is often examined by fitting the time dependence of hypocenter distances from the origin by the pore pressure diffusion model. The earthquake migration patterns however often exhibit not only spreading envelopes but also fast-growing streaks embedded in the overall migration trends. We review the observed migration patterns and show that in the case of earthquake-driven migration, where the new ruptures are triggered at the edge of previous ruptures, it is more suitable to examine the cluster growth as a function of the event index instead of time. We propose a model that relates the speed of seismicity spreading to the average rupture area and the effective magnitude of the hypocenter cluster. Application of the model to selected linearly growing clusters of the 2008 West Bohemia swarm gives an almost linear increase of the measured total rupture area with the event index, which fits the proposed model. This is confirmed by a self-similar scaling of the average rupture area with the effective magnitude for stress drops ranging from 0.1 to 1 MPa. The relatively small stress drop level indicates the presence of voids along the fault plane and a possible role of aseismic deformation.

Fracture asperity evolution during the transition from stick slip to stable sliding.

Fracture asperities interlock or break during stick slip and ride over each other during stable sliding. The evolution of fracture asperities during the transition between stick slip and stable sliding has attracted less attention, but is important to predict fracture behaviour. Here, we conduct a series of direct shear experiments on simulated fractures in homogeneous polycarbonate to examine the evolution of fracture asperities in the transition stage. Our results show that the transition stage occurs between the stick slip and stable sliding stages during the progressive reduction in normal stress on the smooth and rough fractures. Both the fractures exhibit the alternative occurrence of small and large shear stress drops followed by the deterministic chaos in the transition stage. Our data indicate that the asperity radius of curvature correlates linearly with the dimensionless contact area under a given normal stress. For the rough fracture, a bifurcation of acoustic energy release appears when the dimensionless contact area decreases in the transition stage. The evolution of fracture asperities is stress-dependent and velocity-dependent. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

A full relativistic thin disc – the physics of the plunging region and the value of the stress at the ISCO

ABSTRACT The widely used Novikov–Thorne relativistic thin disc equations are only valid down to the radius of the innermost stable circular orbit (ISCO). This leads to an undetermined boundary condition at the ISCO, known as the inner stress of the disc, which sets the luminosity of the disc at the ISCO and introduces considerable ambiguity in accurately determining the mass, spin, and accretion rate of black holes from observed spectra. We resolve this ambiguity by self-consistently extending the relativistic disc solution through the ISCO to the black hole horizon by calculating the inspiral of an average disc particle subject to turbulent disc forces, using a new particle-in-disc technique. Traditionally it has been assumed that the stress at the ISCO is zero, with material plunging approximately radially into the black hole at close to the speed of light. We demonstrate that in fact the inspiral is less severe, with several (∼4–17) orbits completed before the horizon. This leads to a small non-zero stress and luminosity at and inside the ISCO, with a local surface temperature at the ISCO between ∼0.15 and 0.3 times the maximum surface temperature of the disc, in the case where no dynamically important net magnetic field is present. For a range of disc parameters we calculate the value of the inner stress/surface temperature, which is required when fitting relativistic thin disc models to observations. We resolve a problem in relativistic slim disc models in which turbulent heating becomes inaccurate and falls to zero inside the plunging region.

Evaluation of the stress gradient of the superficial layer in ferromagnetic components based on sub-band energy of magnetic Barkhausen noise

ABSTRACT Since magnetic Barkhausen noise is very sensitive to the change of the stress or residual stress level in components, it is feasible to detect the stress or residual stress profile along the depth direction by the magnetic Barkhausen noise method. An engineering approach was used to validate a theoretical model describing the relationship between magnetic Barkhausen noise and stress magnitude. To generate stress gradients in the specimen of Q235 steel under different deflections, the four-point bending device was used. Then the detected signals obtained in the experiment were divided into different sub-bands to evaluate the stress at different depths. The testing depth was set to be around 100 μm due to the rapid exponential attenuation of the noise signals. In the experiments, the sub-band energy density showed sensitive as the loading displacement increasing. The experimental results showed that the signal energy was also sensitive to the plastic deformation of the material. Within the depth of 100 μm, the stress change was very small. The final experimental results showed that even under such small stress variations, it is sensitive and feasible to use the magnetic Barkhausen noise energy to characterise the change of stress gradients.

Development of microcellular thermoplastic polyurethane honeycombs with tailored elasticity and energy absorption via CO2 foaming

In this study, thermoplastic polyurethane (TPU) honeycombs with ordered macrostructure and microcellular lattice structure was fabricated via the integration of fused deposition modelling (FDM) and solid-state CO2 foaming. The physical foaming induced and introduced the microcellular structure with cell size of about 2.77-12.27 mm into TPU honeycombs. The influences of microcellular structure on the mechanical property, energy absorption and elastic recovery behavior of TPU honeycombs were systematically investigated. Foamed TPU honeycombs had a maximum energy absorption efficiency of 0.40, which was larger than that of the corresponded unfoamed honeycombs (0.32-0.38) owing to having the microcellular structure. The effects of lateral and vertical directions on elastic and energy absorption behaviors were discussed because of the obvious anisotropy of microcellular TPU honeycombs. The advantages of lightweight, soft touching and anisotropic characteristics make microcellular TPU honeycombs have great prospects in small stress and high stress sensitive applications.

Experimental Study on Immersion Effects of Pressure Water on the Tensile Characteristics of Sandstone Samples

In this study, Brazilian splitting tests were conducted on sandstone samples subjected to drying and immersing at water pressures of 0, 1, and 3 MPa (immersion duration of 120 h). Investigation of the immersion effects of pressure water on the tensile characteristics of the samples revealed that their tensile strengths decreased with the immersion water pressure. Relative to a sandstone sample subjected to drying alone, immersing at water pressures of 0, 1, and 3 MPa reduced the tensile strength by 12.96%, 19.03%, and 30.16%, respectively. Although the immersed samples experienced splitting failure indicative of obvious brittle failure characteristics, decreases in the postpeak stress reduction rate with immersion water pressure revealed that the intensity of brittle failure weakened with pressure. Based on the obtained data, the deformation evolution process of the sandstone samples could be divided into five stages: deformation adjustment, formation of local deformation zones, local deformation zone propagation, failure surface formation, and sample failure. The water pressure aggravated the physicochemical reactions between water and the hydrophilic minerals in the sandstone, promoting argillisation, dissolution, and loss of hydrophilic minerals and interparticle cementitious materials. As a result of these immersion micromechanisms, the deterioration of the sandstone samples increased with the immersion water pressure, with the average porosities of the fracture surfaces at 0, 1, and 3 MPa increasing by 142.86%, 368.37%, and 593.88%, respectively, relative to the dried sample. As a result of these morphological changes, the sandstone samples subjected to water pressure immersion failed at small axial stresses with low levels of applied mechanical energy.

Surrounding Rock Failure Characteristics and Water Inrush Mechanism of Roadway above the Aquifer in Nonuniform Stress Field

The expansion of the roadway surrounding rock failure zone may connect the floor aquifer and cause the roadway water inrush. In order to reveal the mechanism of the roadway water inrush above confined water, we established the force model of the roadway surrounding rock above confined water in nonuniform stress field and studied the shape characteristics and expansion law of the roadway surrounding rock plastic zone. The results show that the roadway surrounding rock will form three kinds of plastic zone under different lateral pressure coefficients: circular, elliptical, and butterfly; when the shape of plastic zone is circular or elliptic, the maximum radius increases linearly with the increase of regional stress; when the shape is butterfly, the maximum radius increases exponentially with the increase of stress. Under the condition of a larger bidirectional stress ratio, the surrounding rock of the roadway will show butterfly-shaped failure, and small stress change will cause malignant expansion of the plastic zone; when the plastic zone is connected with the underlying aquifer, confined water of floor will enter the rock mass from the water diversion point and eventually flood into the roadway, causing floor water inrush.

A new isotropic hyper-elasticity model for enhancing the rate of convergence of Mohr-Coulomb-like constitutive models and application to shallow foundations and trapdoors

A new hyper-elastic formulation is proposed for improving the convergence of Mohr–Coulomb-like constitutive models at small stresses, when the convergence problems come from the vicinity to the apex of the yield surface and the elastic predictor can lay in a region in which the yield surface is not defined. The proposed hyper-elastic formulation avoids stress states with tensile mean pressures and provides shear and bulk stiffnesses increasing with the square root of mean stress, as typically occurs in granular soil. The new model is applied to two typical engineering problems: a centred-loaded, superficial foundation and the active and passive trapdoor problem. The numerical results are compared with upper and lower bound solutions, showing the reliability of FEM results. In addition, FEM analyses highlight some peculiar aspects of soil-foundation interaction which are usually neglected in the current engineering practice of foundation design.

Misorientation effect of twist grain boundaries on crack nucleation from molecular dynamics

Grain boundaries (GBs) have profound effects on the dislocation motion in materials so as to cause crack nucleation. However, the experimental observation on how the misorientation of twist GBs affects the crack nucleation is scarce. In this paper, we proposed a theoretical model to quantify the dislocation energy per unit length. With it, the critical resolved shear stress at GBs was calculated to assess the crack nucleation. It was found that crack nucleation is significantly influenced by the surface energy, grain boundary energy, system potential energy, boundary stress and misorientation. With the increase of the twist angle, high-angle GBs are more favorable for crack nucleation as general. Interestingly, some specific low-angle GBs possess comparable small critical resolved shear stress as the high-angle GBs and they are favorable for crack nucleation as well. Through the analysis of the resolved shear stress distribution of GBs, it is revealed that the crack nucleation mechanism of these specific low-angle GBs is similar to that of general high-angle GBs. It is inferred that the special low-angle GB systems could generate a crack under a relatively low resolved shear stress.

Laboratory Investigation on Particle Breakage Characteristics of Calcareous Sands

Many studies have demonstrated the fragility of calcareous sands even under small stresses. This bears an adverse influence on their engineering properties. A series of laboratory tests were carried out on poor‐graded calcareous sands to investigate the crushability mechanism. Einav’s relative breakage and fractal dimension were used as the particle breakage indices. The results show that the particles broke into smaller fragments at the low‐stress level by attrition which was caused by friction and slip between particles. In contrast, particles broke in the form of crushing at the relatively higher stresses. The evolution of the particle size was reflected by the variation in Einav’s relative breakage and fractal dimension. As testing commenced, the breakage index rapidly increased. When the stress was increased to 400 kPa, the rate of increase in the breakage index was retarded. As the stress was further increased beyond 800 kPa, the rate of increase in the fractal index became much smaller. This elucidated that the well‐graded calcareous sands could resist crushing depending on the range of applied stresses. Based on the test findings, a new breakage law is proposed.

Experimental study of the evolution of pore water pressure and total stresses during and after the deposition of slurried backfill

Mining backfill is increasingly used in underground mines to fill stopes. Its successful application depends on the stability of barricades built to retain the backfill in stopes. The design of barricades requires a good estimation of pore water pressure (PWP) and total stresses during and after the deposition. On this regard, a large number of works have been published on analytical and numerical solutions. There are however very few experimental results with simultaneous measurements of PWP as well as horizontal and vertical total stresses that can be used to validate or calibrate the analytical and numerical solutions. For a specific project, field measurements are interesting in terms of representativeness to field conditions, but the results are very difficult to be correctly interpreted because the treated problem can involve a large number of uncertainties and the obtained results are due to combined effects of several influencing factors. Laboratory tests with simplified and well-controlled conditions are thus preferred. Until now, however, the most previous laboratory tests were conducted with dry backfill or with a tailings slurry instantaneously poured in a confining structure without simultaneous measurements of PWP as well as horizontal and vertical total stresses. Studies on the effects of filling rate and solid content of backfill on the variation of PWP and total stresses during the filling operation are absent. To fill these gaps, a series of column backfilling tests were conducted with simultaneous measurements of PWP as well as vertical and horizontal total stresses during and after the deposition of slurried backfill. When the filling rate is high, the test results showed that the PWP, horizontal and vertical total stresses increase at the same rate and equal to the iso-geostatic overburden pressure during the deposition of backfill slurry. Their peak values appear at the end of deposition. The backfill thus behaves like a liquid with little generation of effective stresses during the deposition. High filling rate and/or high solid content lead to high PWP and horizontal total stresses at the end of deposition. When the filling rate is small, the PWP and total stresses exhibit also peak values at the end of filling operation, but the vertical total stress at the center can continue increasing with time after the end of deposition due to the suspended sensor and occurrence of a phenomenon known as stress shielding effect. The results also showed that the settlement of settled backfill after the end of slurry deposition can generally exhibits a fast evolution rate stage, followed by a slow evolution rate stage. The duration of the fast evolution rate stage and the final settlement of the settled backfill increase as the solid content decreases. The final settlement after the end of slurry deposition is related to the solid content, not to the filling rate.