The undrained mechanical behavior of unsaturated completely weathered granite(CWG)is highly susceptible to alterations in the hydraulic environment,particularly under uniaxial loading conditions,due to the unique natu...The undrained mechanical behavior of unsaturated completely weathered granite(CWG)is highly susceptible to alterations in the hydraulic environment,particularly under uniaxial loading conditions,due to the unique nature of this soil type.In this study,a series of unconfined compression tests were carried out on unsaturated CWG soil in an underground engineering site,and the effects of varying the environmental variables on the main undrained mechanical properties were analyzed.Based on the experimental results,a novel constitutive model was then established using the damage mechanics theory and the undetermined coefficient method.The results demonstrate that the curves of remolded CWG specimens with different moisture contents and dry densities exhibited diverse characteristics,including brittleness,significant softening,and ductility.As a typical indicator,the unconfined compression strength of soil specimens initially increased with an increase in moisture content and then decreased.Meanwhile,an optimal moisture content of approximately 10.5%could be observed,while a critical moisture content value of 13.0%was identified,beyond which the strength of the specimen decreases sharply.Moreover,the deformation and fracture of CWG specimens were predominantly caused by shear failure,and the ultimate failure modes were primarily influenced by moisture content rather than dry density.Furthermore,by comparing several similar models and the experimental data,the proposed model could accurately replicate the undrained mechanical characteristics of unsaturated CWG soil,and quantitatively describe the key mechanical indexes.These findings offer a valuable reference point for understanding the underlying mechanisms,anticipating potential risks,and implementing effective control measures in similar underground engineering projects.展开更多
Negative Poisson ratio(NPR)steel is a new material with high strength and toughness.This study conducted tensile tests at elevated temperatures to investigate the mechanical properties of NPR steel at high temperature...Negative Poisson ratio(NPR)steel is a new material with high strength and toughness.This study conducted tensile tests at elevated temperatures to investigate the mechanical properties of NPR steel at high temperatures.The stress−strain curve,ultimate strength,yield strength,modulus of elasticity,elongation after fracture,and percentage reduction of area of NPR steel bars were measured at 9 different temperatures ranging from 20 to 800℃.The experimental results indicate that high-temperature environments significantly affect the mechanical properties of NPR steel.However,compared to other types of steel,NPR steel exhibits better resistance to deformation.When the test temperature is below 700℃,NPR steel exhibits a ductile fracture characteristic,while at 800℃,it exhibits a brittle fracture characteristic.Finally,based on the experimental findings,a constitutive model suitable for NPR steel at high temperatures is proposed.展开更多
Accurate assessment of coal brittleness is crucial in the design of coal seam drilling and underground coal mining operations.This study proposes a method for evaluating the brittleness of gas-bearing coal based on a ...Accurate assessment of coal brittleness is crucial in the design of coal seam drilling and underground coal mining operations.This study proposes a method for evaluating the brittleness of gas-bearing coal based on a statistical damage constitutive model and energy evolution mechanisms.Initially,integrating the principle of effective stress and the Hoek-Brown criterion,a statistical damage constitutive model for gas-bearing coal is established and validated through triaxial compression tests under different gas pressures to verify its accuracy and applicability.Subsequently,employing energy evolution mechanism,two energy characteristic parameters(elastic energy proportion and dissipated energy proportion)are analyzed.Based on the damage stress thresholds,the damage evolution characteristics of gas bearing coal were explored.Finally,by integrating energy characteristic parameters with damage parameters,a novel brittleness index is proposed.The results demonstrate that the theoretical curves derived from the statistical damage constitutive model closely align with the test curves,accurately reflecting the stress−strain characteristics of gas-bearing coal and revealing the stress drop and softening characteristics of coal in the post-peak stage.The shape parameter and scale parameter represent the brittleness and macroscopic strength of the coal,respectively.As gas pressure increases from 1 to 5 MPa,the shape parameter and the scale parameter decrease by 22.18%and 60.45%,respectively,indicating a reduction in both brittleness and strength of the coal.Parameters such as maximum damage rate and peak elastic energy storage limit positively correlate with coal brittleness.The brittleness index effectively captures the brittleness characteristics and reveals a decrease in brittleness and an increase in sensitivity to plastic deformation under higher gas pressure conditions.展开更多
Introducing Neutral Polymeric bonding agents(NPBA) into the Nitrate Ester Plasticized Polyether(NEPE)propellant could improve the adhesion between filler/matrix interface, thereby contributing to the development of ne...Introducing Neutral Polymeric bonding agents(NPBA) into the Nitrate Ester Plasticized Polyether(NEPE)propellant could improve the adhesion between filler/matrix interface, thereby contributing to the development of new generations of the NEPE propellant with better mechanical properties. Therefore,understanding the effects of NPBA on the deformation and damage evolution of the NEPE propellant is fundamental to material design and applications. This paper studies the uniaxial tensile and stress relaxation responses of the NEPE propellant with different amounts of NPBA. The damage evolution in terms of interface debonding is further investigated using a cohesive-zone model(CZM). Experimental results show that the initial modulus and strength of the NEPE propellant increase with the increasing amount of NPBA while the elongation decreases. Meanwhile, the relaxation rate slows down and a higher long-term equilibrium modulus is reached. Experimental and numerical analyses indicate that interface debonding and crack propagation along filler-matrix interface are the dominant damage mechanism for the samples with a low amount of NPBA, while damage localization and crack advancement through the matrix are predominant for the ones with a high amount of NPBA. Finally, crosslinking density tests and simulation results also show that the effect of the bonding agent is interfacial rather than due to the overall crosslinking density change of the binder.展开更多
Polyurea is widely employed as a protective coating in many fields because of its superior ability to improve the anti-blast and anti-impact capability of structures.In this study,the mechanical properties of polyurea...Polyurea is widely employed as a protective coating in many fields because of its superior ability to improve the anti-blast and anti-impact capability of structures.In this study,the mechanical properties of polyurea XS-350 were investigated via systematic experimentation over a wide range of strain rates(0.001-7000 s^-1)by using an MTS,Instron VHS,and split-Hopkinson bars.The stress-strain behavior of polyurea was obtained for various strain rates,and the effects of strain rate on the primary mechanical properties were analyzed.Additionally,a modified rate-dependent constitutive model is proposed based on the nine-parameter Mooney-Rivlin model.The results show that the stress-strain curves can be divided into three distinct regions:the linear-elastic stage,the highly elastic stage,and an approximate linear region terminating in fracture.The mechanical properties of the polyurea material were found to be highly dependent on the strain rate.Furthermore,a comparison between model predictions and the experimental stress-strain curves demonstrated that the proposed model can characterize the mechanical properties of polyurea over a wide range of strain rates.展开更多
The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. Accordin...The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.展开更多
According to the cutting characteristics of progressive spiral movement by rotary cutting of the disc cutter, using the broken theory of interaction of compression and shearing, the three-axis force rotary cutting mec...According to the cutting characteristics of progressive spiral movement by rotary cutting of the disc cutter, using the broken theory of interaction of compression and shearing, the three-axis force rotary cutting mechanical model of disc cutter was established and the influence of installation radius, the phase difference and the cutter space on the mechanics of disc cutter were analyzed. The results show that on the same radial line of tunneling interface, the boring distance of cutting tools installed on a different radius is not equal. The cutting radial line of tunneling interface is a polyline and its height is determined by phase angle and penetration of cutting tools. Both phase difference and the installation radius between adjacent disc cutters have little effect on the vertical force and rolling force, but increase with the increase in cutter spacing. In addition, when increasing phase difference and cutter space bilaterally, and reducing installation radius simultaneously, the lateral force would be improved. Related results have been verified onl O0 t rotary tool cutting test platform.展开更多
For the 110 mining method,it is challenging to accurately calculate the support resistance of the roadway due to the lack of understanding of the dynamic movement of the overlying strata in this method.The consequenti...For the 110 mining method,it is challenging to accurately calculate the support resistance of the roadway due to the lack of understanding of the dynamic movement of the overlying strata in this method.The consequential excessive support results in a significant increase in the cost of roadway support.The authors explored the overlying strata movement and roadway deformation of the gob-entry retaining in the 110 mining method to solve this problem.First,the typical stages of the roof-cutting gob-side entry were defined.Second,the mechanical model and calculation formula of the support resistance on the roof were explored.Then,using numerical simulation software,the starting ranges of the specific supports at different stages were verified and the feasibility of the support scheme was examined.Finally,combined with the field measurement data,the stress and the deformation of the gob roadway at different stages under the influence of two mining processes in the 110 mining method were obtained.The numerical simulation results obtained are consistent with the field test results,providing a theoretical basis for precision support at different stages by the 110 mining method.展开更多
To properly simulate hard rock with a high ratio of the uniaxial compressive strength to tensile strength(UCS/TS) and realistic strength-failure envelope,the rock deformation and mechanical characteristics were discus...To properly simulate hard rock with a high ratio of the uniaxial compressive strength to tensile strength(UCS/TS) and realistic strength-failure envelope,the rock deformation and mechanical characteristics were discussed in detail when the particle simulation method with the clump parallel-bond model(CPBM) was used to conduct a series of numerical experiments at the specimen scale.Meanwhile,the effects of the loading procedure and crack density on the mechanical behavior of a specimen,which was modeled by the particle simulation method with the CPBM,were investigated.The related numerical results have demonstrated that:1) The uniaxial compressive strength(UCS),tensile strength(TS) and elastic modulus are overestimated when the conventional loading procedure is used in the particle simulation method with the CPBM; 2) The elastic modulus,strength and UCS/TS decrease,while Poisson ratio increases with the increase of the crack density in the particle simulation method with the CPBM; 3) The particle simulation method with the CPBM can be used to reproduce a high value of UCS/TS(>10),as well as a high friction angle and reasonable cohesion strength; 4) As the confining pressure increases,both the peak strength of the simulated specimen and the number of microscopic cracks increase,but the ratio of tensile cracks number to shear cracks number decreases in the particle simulation method with the CPBM; 5) Compared with the conventional parallel-bond model,the CPBM can be used to reproduce more accurate results for simulating the rock deformation and mechanical characteristics.展开更多
The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete elem...The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.展开更多
A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been deve...A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.展开更多
A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forwar...A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.展开更多
Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coa...Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of展开更多
A complete quantum mechanical model for GaAs?AlGaAs quantum well infrared photodetectors(QWIPs) is presented here. The model consisted of four parts: (1) Starting with the description of the electromagnetic field of t...A complete quantum mechanical model for GaAs?AlGaAs quantum well infrared photodetectors(QWIPs) is presented here. The model consisted of four parts: (1) Starting with the description of the electromagnetic field of the infrared radiation in the QWIP, effective component of the vector potential <| A z |> along the QWIP growth direction ( z axis) due to the optical diffraction grating was calculated. (2) From the wave transmissions and the occupations of the electronic states, it was discussed that the dark current in the QWIP is determined by the drift diffusion current of carriers thermally excited from the ground sublevel in the quantum well to extended states above the barrier. (3) The photocurrent was investigated by the optical transition (absorption coefficient between the ground state to excited states due to the nonzero <| A z |> ). (4) By studying the inter diffusion of the Al atoms across the GaAs?AlGaAs heterointerfaces,the mobility of the drift diffusion carriers in the excited states was calculated, so the measurement results of the dark current and photocurrent spectra can be explained theoretically. With the complete quantum mechanical descriptions of (1 4), QWIP device design and optimization are possible.展开更多
Based on fluid mechanics, thermodynamics and damage mechanics, thermal-hydro-mechanical （THM） coupling damage model of brittle rock is established by analyzing THM coupling mechanism, where THM coupling damage varia...Based on fluid mechanics, thermodynamics and damage mechanics, thermal-hydro-mechanical （THM） coupling damage model of brittle rock is established by analyzing THM coupling mechanism, where THM coupling damage variable DTHM is dominated by TH coupling damage variable DTH, TM coupling damage variable DTM and HM coupling damage variable DHM, and DTH is firstly expressed in term of dimensionless total thermal conductivity of the water Nu. Permeability test, uni-axial compression test and THM coupling test are conducted to measure the permeability, elastic modulus and THM coupling stress-strain curves of brittle rock. The tested values of THM coupling elastic modulus E＇HM are in good agreement with the predicted values of THM coupling elastic modulus ETHM, which can verify the newly established THM coupling damage model.展开更多
The deformation fracture and stability of mountain under the earthquake action is an important issue that arouses concern of researchers in the field of engineering geology.The authors,from 2000 to 2006, selected the ...The deformation fracture and stability of mountain under the earthquake action is an important issue that arouses concern of researchers in the field of engineering geology.The authors,from 2000 to 2006, selected the 1933 earthquake in Diexi zone as a typical study site to carry out the genetic mechanism research of mountain deformation-fracture caused by earthquake; in order to have comparability,the breadth展开更多
Background The mechanical properties are related with many biological functions of cells. Accurate quantification of the mechanical properties of living cells require the combined use of experimental techniques and th...Background The mechanical properties are related with many biological functions of cells. Accurate quantification of the mechanical properties of living cells require the combined use of experimental techniques and theoretical models. Micropipette aspiration (MPA) is one of common techniques in determining mechanical properties of the living cells. The halfspace model (HSM) is employed in MPA technique. However,in the conditions of linear constitutive relations and small deformations,the HSM is inadequate for characterizing the MPA of a spherical cell in two respects. Firstly,the cell size is fairly finite other than semi-infinite to the inner radius of a micropipette;Secondly,cells are compressible,with a Poisson’s ratioνvarying from 0. 2 to 0. 4 (23-25) instead of incompressible (ν=0. 5). Thus,a more accurate model is necessary.In this study,the viscoelastic expressions were derived from our previous MPA test. Then,a sphere model (SM) employed to analyze mechanical properties of rabbit chondrocytes combined with the experimental data. Differences in mechanical properties estimated by different mechanical models were evaluated.Methods A sphere model (SM) was employed. The relative dimension of cell to micropipette and the compressibility of the cell were taken into account,as shown in Fig. 1a.■Fig.1 Sphere model of the MPA of a single cell employing different constitutive relationships The approximate expression for the aspirated length was obtained from our previous study as follows:■Furthermore,assuming that the cell behaves as a homogeneous and isotropic standard linear solid (Fig. 1b),two viscoelastic creep expressions of the aspirated length for incompressible sphere model (ICSM) and for compressible sphere model (CSM) were derived by elastic-viscoelastic correspondence principle and integral transformation as Eqs.(2) and (3)respectively.■Results(1) Comparisons of models The elastic modulus from the ICSM was 47. 4%higher than that of the half-space model (HSM)(P<0. 001). For the CSM,the percentage increase in E over the value for the HSM was 87. 7%,78. 9%,and 64. 9%when the Poisson’s ratio was set to 0. 2,0. 3,and 0. 4,respectively.For the viscoelasticity,the parameters for the ICSM and CSM were significantly larger than those of the HSM (P <0. 001). The k1,k2,andμfor the ICSM were 37. 8%,37. 9%,and 39. 0%higher,respectively,than those of the HSM. For the CSM,the viscoelastic parameters decreased with the increase ofν. Whenν=0. 3,k1,k2,andμincreased by 71. 0%,200%,and 157%,respectively,compared to those of the ICSM (P<0. 001);For the cases ofν=0. 2 andν=0. 4,the above parameters were respectively 102%,243%,and 209%and 35. 3%,97. 5%,and 79%higher than those of the ICSM.(2) Predictions for the relative errors of mechanical parameters caused by HSM e is defined as the relative change of elastic moduli (or relative error) between the HSM and SM. As shown in Fig. 2,when Poisson’s ratioνis 0. 3,in order to let the e less than 30%,relative dimension between the cell and the micropipetteξneeds to be at least 5. 0. Whenνequals 0. 5 (ICSM),ξis about 3. 3 to make the e reach 20%. However,ξis rarely larger than 5. 0 in general MPA experiments,thus the relative error of modulus will exceed 30%. The above results are independent of cell types,thus they are applicable to other spherical solid-like cells.■Fig.2 Thresholds ofξvarying withνwhen e was 10%,20%,and 30%,respectively Another parameter VR was introduced to represent the relative errors of viscoelastic parameters between HSM and SM.With regard to ICSM (Fig. 3a),whenξis 3,VRis nearly 22%. If theξis larger than 8. 0,the relative error will be reduced to less than 10%. For the CSM,the viscoelastic parameters of a typical chondrocyte varying withξandνwere obtained,as shown from Figs. 3b to 3d. Whenνtends to 0. 5,the parameters tend to those of ICSM. When theξexceeds 10,each parameter changes very little. For a certain Poisson’s ratio (ν=0. 3),whenξis 3,the VR of k1,k2,andμare 47. 1%,70. 8%,and 68. 2%,respectively. Whenξequals 5 and 10,the above values are 42. 3%,68. 8%,65%,and 38. 4%,66. 0%,63. 2%,respectively. For a givenξ(ξ=3),whenνis 0. 2,the VR of k1,k2,andμare 53. 6%,73. 3%,and 75. 0%,respectively.Whenνis taken as 0. 3 and 0. 4,the above errors are 47. 7%,71. 1%,68. 2%,and 38. 4%,58. 8%,54. 8%,respectively.Thus,the VR also decreases with the increase ofξandν.Conclusions The effects of the relative dimension between the cell,and micropipette and the Poisson’s ratio of cell were remarkable and should be taken into consideration in the pursuit of more accurate mechanical parameters of cells.展开更多
To understand the high strain rate deformation mechanism and determine the grain size,strain rate and porosity dependent yield strength of nanocrystalline materials,a new mechanical model based on the deformation mech...To understand the high strain rate deformation mechanism and determine the grain size,strain rate and porosity dependent yield strength of nanocrystalline materials,a new mechanical model based on the deformation mechanism of nanocrystalline materials under high strain rate loading was developed.As a first step of the research,the yield behavior of the nanocrystalline materials under high strain rate loading was mainly concerned in the model and uniform deformation was assumed for simplification.Nanocrystalline materials were treated as composites consisting of grain interior phase and grain boundary phase,and grain interior and grain boundary deformation mechanisms under high strain rate loading were analyzed,then Voigt model was applied to coupling grain boundary constitutive relation with mechanical model for grain interior phase to describe the overall yield mechanical behavior of nanocrystalline materials.The predictions by the developed model on the yield strength of nanocrysatlline materials at high strain rates show good agreements with various experimental data.Further discussion was presented for calculation results and relative experimental observations.展开更多
Bone modeling and remodeling are governed by distinct biochemical processes that may hold unique opportunities for optimizing bone mass[1,2].Remodeling refers to the coupled resorption and subsequent formation on the ...Bone modeling and remodeling are governed by distinct biochemical processes that may hold unique opportunities for optimizing bone mass[1,2].Remodeling refers to the coupled resorption and subsequent formation on the bone surface,while modeling represents uncoupled formation or resorption.Mechanical loading is known to improve bone mass,though whether this occurs through modeling or remodeling(or by some combination)is unclear.Dynamic in vivo morphometry utilizing high resolution micro-CT and image registration has only recently become feasible and thus holds an untapped and expanding potential for understanding bone metabolism by quantifying and localizing formation/resorption and modeling/remodeling events.16-week-old mice were given 2 baseline weekly micro-CT scans of both tibiae prior to the initiation of daily unilateral loading(contralateral limb for nonloaded control).Weekly scanning and daily loading continued for 5 weeks.Registered images for each mouse in a global coordinate system revealed the time course of each voxel,and changes in bone mass were quantified as modeling or remodeling starting at the onset of loading.In cortical bone,after an initial response to loading in both regimes,modeling emerged as the dominant response.Loading effects were largest in areas of mechanical significance.For example,anabolic modeling on the periosteal surface of the half of the tibia in compression under axial load presented a strong effect of loading,whereas the same measure on the endosteal surface in the area in tension showed no difference.Similarly,in trabecular bone anabolic modeling was significantly increased with loading on trabecular plates but not rods(plates have been shown to be the major contributor to overall bone strength).The catabolic modeling response on the endosteal surface showed an interesting transition over time.Loading initially led to a significant suppression of catabolic modeling,but over time increased it to levels significantly beyond that of nonloaded controls.展开更多
This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume e...This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.展开更多
基金Project(42202318)supported by the National Natural Science Foundation of ChinaProject(252300421199)supported by the Natural Science Foundation of Henan Province,ChinaProject(2024JJ6219)supported by the Hunan Provincial Natural Science Foundation of China。
文摘The undrained mechanical behavior of unsaturated completely weathered granite(CWG)is highly susceptible to alterations in the hydraulic environment,particularly under uniaxial loading conditions,due to the unique nature of this soil type.In this study,a series of unconfined compression tests were carried out on unsaturated CWG soil in an underground engineering site,and the effects of varying the environmental variables on the main undrained mechanical properties were analyzed.Based on the experimental results,a novel constitutive model was then established using the damage mechanics theory and the undetermined coefficient method.The results demonstrate that the curves of remolded CWG specimens with different moisture contents and dry densities exhibited diverse characteristics,including brittleness,significant softening,and ductility.As a typical indicator,the unconfined compression strength of soil specimens initially increased with an increase in moisture content and then decreased.Meanwhile,an optimal moisture content of approximately 10.5%could be observed,while a critical moisture content value of 13.0%was identified,beyond which the strength of the specimen decreases sharply.Moreover,the deformation and fracture of CWG specimens were predominantly caused by shear failure,and the ultimate failure modes were primarily influenced by moisture content rather than dry density.Furthermore,by comparing several similar models and the experimental data,the proposed model could accurately replicate the undrained mechanical characteristics of unsaturated CWG soil,and quantitatively describe the key mechanical indexes.These findings offer a valuable reference point for understanding the underlying mechanisms,anticipating potential risks,and implementing effective control measures in similar underground engineering projects.
基金Projects(41702320,52104125)supported by the National Natural Science Foundation of ChinaProject(ZR2021MD005)+2 种基金supported by the Natural Science Foundation of Shandong Province,ChinaProject(TMduracon2022002)supported by the Engineering Research Center of Marine Environmental Concrete Technology,Ministry of Education,China。
文摘Negative Poisson ratio(NPR)steel is a new material with high strength and toughness.This study conducted tensile tests at elevated temperatures to investigate the mechanical properties of NPR steel at high temperatures.The stress−strain curve,ultimate strength,yield strength,modulus of elasticity,elongation after fracture,and percentage reduction of area of NPR steel bars were measured at 9 different temperatures ranging from 20 to 800℃.The experimental results indicate that high-temperature environments significantly affect the mechanical properties of NPR steel.However,compared to other types of steel,NPR steel exhibits better resistance to deformation.When the test temperature is below 700℃,NPR steel exhibits a ductile fracture characteristic,while at 800℃,it exhibits a brittle fracture characteristic.Finally,based on the experimental findings,a constitutive model suitable for NPR steel at high temperatures is proposed.
基金Project(52274096)supported by the National Natural Science Foundation of ChinaProject(WS2023A03)supported by the State Key Laboratory Cultivation Base for Gas Geology and Gas Control,China。
文摘Accurate assessment of coal brittleness is crucial in the design of coal seam drilling and underground coal mining operations.This study proposes a method for evaluating the brittleness of gas-bearing coal based on a statistical damage constitutive model and energy evolution mechanisms.Initially,integrating the principle of effective stress and the Hoek-Brown criterion,a statistical damage constitutive model for gas-bearing coal is established and validated through triaxial compression tests under different gas pressures to verify its accuracy and applicability.Subsequently,employing energy evolution mechanism,two energy characteristic parameters(elastic energy proportion and dissipated energy proportion)are analyzed.Based on the damage stress thresholds,the damage evolution characteristics of gas bearing coal were explored.Finally,by integrating energy characteristic parameters with damage parameters,a novel brittleness index is proposed.The results demonstrate that the theoretical curves derived from the statistical damage constitutive model closely align with the test curves,accurately reflecting the stress−strain characteristics of gas-bearing coal and revealing the stress drop and softening characteristics of coal in the post-peak stage.The shape parameter and scale parameter represent the brittleness and macroscopic strength of the coal,respectively.As gas pressure increases from 1 to 5 MPa,the shape parameter and the scale parameter decrease by 22.18%and 60.45%,respectively,indicating a reduction in both brittleness and strength of the coal.Parameters such as maximum damage rate and peak elastic energy storage limit positively correlate with coal brittleness.The brittleness index effectively captures the brittleness characteristics and reveals a decrease in brittleness and an increase in sensitivity to plastic deformation under higher gas pressure conditions.
基金National Natural Science Foundation of China(U22B20131)for supporting this project.
文摘Introducing Neutral Polymeric bonding agents(NPBA) into the Nitrate Ester Plasticized Polyether(NEPE)propellant could improve the adhesion between filler/matrix interface, thereby contributing to the development of new generations of the NEPE propellant with better mechanical properties. Therefore,understanding the effects of NPBA on the deformation and damage evolution of the NEPE propellant is fundamental to material design and applications. This paper studies the uniaxial tensile and stress relaxation responses of the NEPE propellant with different amounts of NPBA. The damage evolution in terms of interface debonding is further investigated using a cohesive-zone model(CZM). Experimental results show that the initial modulus and strength of the NEPE propellant increase with the increasing amount of NPBA while the elongation decreases. Meanwhile, the relaxation rate slows down and a higher long-term equilibrium modulus is reached. Experimental and numerical analyses indicate that interface debonding and crack propagation along filler-matrix interface are the dominant damage mechanism for the samples with a low amount of NPBA, while damage localization and crack advancement through the matrix are predominant for the ones with a high amount of NPBA. Finally, crosslinking density tests and simulation results also show that the effect of the bonding agent is interfacial rather than due to the overall crosslinking density change of the binder.
基金the Provincial Basic Research Program of China(NO.2016209A003,NO·2016602B003)
文摘Polyurea is widely employed as a protective coating in many fields because of its superior ability to improve the anti-blast and anti-impact capability of structures.In this study,the mechanical properties of polyurea XS-350 were investigated via systematic experimentation over a wide range of strain rates(0.001-7000 s^-1)by using an MTS,Instron VHS,and split-Hopkinson bars.The stress-strain behavior of polyurea was obtained for various strain rates,and the effects of strain rate on the primary mechanical properties were analyzed.Additionally,a modified rate-dependent constitutive model is proposed based on the nine-parameter Mooney-Rivlin model.The results show that the stress-strain curves can be divided into three distinct regions:the linear-elastic stage,the highly elastic stage,and an approximate linear region terminating in fracture.The mechanical properties of the polyurea material were found to be highly dependent on the strain rate.Furthermore,a comparison between model predictions and the experimental stress-strain curves demonstrated that the proposed model can characterize the mechanical properties of polyurea over a wide range of strain rates.
基金Project(2013CB036004) supported by the National Basic Research Program of ChinaProject(51178468) supported by the National Natural Science Foundation of ChinaProject(2013zzts235) supported by Innovation Fund of Central South University of China
文摘The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.
基金Project(2007CB714002) supported by the National Basic Research Program of ChinaProject(51074180) supported by the National Natural Science Foundation of ChinaProject(2010FJ1002) supported by Hunan Municipal Science and Technology Program,China
文摘According to the cutting characteristics of progressive spiral movement by rotary cutting of the disc cutter, using the broken theory of interaction of compression and shearing, the three-axis force rotary cutting mechanical model of disc cutter was established and the influence of installation radius, the phase difference and the cutter space on the mechanics of disc cutter were analyzed. The results show that on the same radial line of tunneling interface, the boring distance of cutting tools installed on a different radius is not equal. The cutting radial line of tunneling interface is a polyline and its height is determined by phase angle and penetration of cutting tools. Both phase difference and the installation radius between adjacent disc cutters have little effect on the vertical force and rolling force, but increase with the increase in cutter spacing. In addition, when increasing phase difference and cutter space bilaterally, and reducing installation radius simultaneously, the lateral force would be improved. Related results have been verified onl O0 t rotary tool cutting test platform.
基金Project(51674265) supported by the National Natural Science Foundation of ChinaProjects(2018YFC0603705,2016YFC0600901) supported by the State Key Research Development Program of ChinaProject supported by the Yueqi Outstanding Scholar Award Program of China University of Mining&Technology,Beijing,China。
文摘For the 110 mining method,it is challenging to accurately calculate the support resistance of the roadway due to the lack of understanding of the dynamic movement of the overlying strata in this method.The consequential excessive support results in a significant increase in the cost of roadway support.The authors explored the overlying strata movement and roadway deformation of the gob-entry retaining in the 110 mining method to solve this problem.First,the typical stages of the roof-cutting gob-side entry were defined.Second,the mechanical model and calculation formula of the support resistance on the roof were explored.Then,using numerical simulation software,the starting ranges of the specific supports at different stages were verified and the feasibility of the support scheme was examined.Finally,combined with the field measurement data,the stress and the deformation of the gob roadway at different stages under the influence of two mining processes in the 110 mining method were obtained.The numerical simulation results obtained are consistent with the field test results,providing a theoretical basis for precision support at different stages by the 110 mining method.
基金Project(11272359) supported by the National Natural Science Foundation of China
文摘To properly simulate hard rock with a high ratio of the uniaxial compressive strength to tensile strength(UCS/TS) and realistic strength-failure envelope,the rock deformation and mechanical characteristics were discussed in detail when the particle simulation method with the clump parallel-bond model(CPBM) was used to conduct a series of numerical experiments at the specimen scale.Meanwhile,the effects of the loading procedure and crack density on the mechanical behavior of a specimen,which was modeled by the particle simulation method with the CPBM,were investigated.The related numerical results have demonstrated that:1) The uniaxial compressive strength(UCS),tensile strength(TS) and elastic modulus are overestimated when the conventional loading procedure is used in the particle simulation method with the CPBM; 2) The elastic modulus,strength and UCS/TS decrease,while Poisson ratio increases with the increase of the crack density in the particle simulation method with the CPBM; 3) The particle simulation method with the CPBM can be used to reproduce a high value of UCS/TS(>10),as well as a high friction angle and reasonable cohesion strength; 4) As the confining pressure increases,both the peak strength of the simulated specimen and the number of microscopic cracks increase,but the ratio of tensile cracks number to shear cracks number decreases in the particle simulation method with the CPBM; 5) Compared with the conventional parallel-bond model,the CPBM can be used to reproduce more accurate results for simulating the rock deformation and mechanical characteristics.
基金Project(51378006) supported by National Natural Science Foundation of ChinaProject(141076) supported by Huoyingdong Foundation of the Ministry of Education of China+1 种基金Project(2242015R30027) supported by Excellent Young Teacher Program of Southeast University,ChinaProject(BK20140109) supported by the Natural Science Foundation of Jiangsu Province,China
文摘The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.
基金Projects(41674080,41674079)supported by the National Natural Science Foundation of China
文摘A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.
基金Project(60672042) supported by the National Natural Science Foundation of China
文摘A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.
文摘Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of
文摘A complete quantum mechanical model for GaAs?AlGaAs quantum well infrared photodetectors(QWIPs) is presented here. The model consisted of four parts: (1) Starting with the description of the electromagnetic field of the infrared radiation in the QWIP, effective component of the vector potential <| A z |> along the QWIP growth direction ( z axis) due to the optical diffraction grating was calculated. (2) From the wave transmissions and the occupations of the electronic states, it was discussed that the dark current in the QWIP is determined by the drift diffusion current of carriers thermally excited from the ground sublevel in the quantum well to extended states above the barrier. (3) The photocurrent was investigated by the optical transition (absorption coefficient between the ground state to excited states due to the nonzero <| A z |> ). (4) By studying the inter diffusion of the Al atoms across the GaAs?AlGaAs heterointerfaces,the mobility of the drift diffusion carriers in the excited states was calculated, so the measurement results of the dark current and photocurrent spectra can be explained theoretically. With the complete quantum mechanical descriptions of (1 4), QWIP device design and optimization are possible.
基金Project(11072269) supported by the National Natural Science Foundation of ChinaProject(20090162110066) supported by the Research Fund for the Doctoral Program of Higher Education of China
文摘Based on fluid mechanics, thermodynamics and damage mechanics, thermal-hydro-mechanical （THM） coupling damage model of brittle rock is established by analyzing THM coupling mechanism, where THM coupling damage variable DTHM is dominated by TH coupling damage variable DTH, TM coupling damage variable DTM and HM coupling damage variable DHM, and DTH is firstly expressed in term of dimensionless total thermal conductivity of the water Nu. Permeability test, uni-axial compression test and THM coupling test are conducted to measure the permeability, elastic modulus and THM coupling stress-strain curves of brittle rock. The tested values of THM coupling elastic modulus E＇HM are in good agreement with the predicted values of THM coupling elastic modulus ETHM, which can verify the newly established THM coupling damage model.
文摘The deformation fracture and stability of mountain under the earthquake action is an important issue that arouses concern of researchers in the field of engineering geology.The authors,from 2000 to 2006, selected the 1933 earthquake in Diexi zone as a typical study site to carry out the genetic mechanism research of mountain deformation-fracture caused by earthquake; in order to have comparability,the breadth
文摘Background The mechanical properties are related with many biological functions of cells. Accurate quantification of the mechanical properties of living cells require the combined use of experimental techniques and theoretical models. Micropipette aspiration (MPA) is one of common techniques in determining mechanical properties of the living cells. The halfspace model (HSM) is employed in MPA technique. However,in the conditions of linear constitutive relations and small deformations,the HSM is inadequate for characterizing the MPA of a spherical cell in two respects. Firstly,the cell size is fairly finite other than semi-infinite to the inner radius of a micropipette;Secondly,cells are compressible,with a Poisson’s ratioνvarying from 0. 2 to 0. 4 (23-25) instead of incompressible (ν=0. 5). Thus,a more accurate model is necessary.In this study,the viscoelastic expressions were derived from our previous MPA test. Then,a sphere model (SM) employed to analyze mechanical properties of rabbit chondrocytes combined with the experimental data. Differences in mechanical properties estimated by different mechanical models were evaluated.Methods A sphere model (SM) was employed. The relative dimension of cell to micropipette and the compressibility of the cell were taken into account,as shown in Fig. 1a.■Fig.1 Sphere model of the MPA of a single cell employing different constitutive relationships The approximate expression for the aspirated length was obtained from our previous study as follows:■Furthermore,assuming that the cell behaves as a homogeneous and isotropic standard linear solid (Fig. 1b),two viscoelastic creep expressions of the aspirated length for incompressible sphere model (ICSM) and for compressible sphere model (CSM) were derived by elastic-viscoelastic correspondence principle and integral transformation as Eqs.(2) and (3)respectively.■Results(1) Comparisons of models The elastic modulus from the ICSM was 47. 4%higher than that of the half-space model (HSM)(P<0. 001). For the CSM,the percentage increase in E over the value for the HSM was 87. 7%,78. 9%,and 64. 9%when the Poisson’s ratio was set to 0. 2,0. 3,and 0. 4,respectively.For the viscoelasticity,the parameters for the ICSM and CSM were significantly larger than those of the HSM (P <0. 001). The k1,k2,andμfor the ICSM were 37. 8%,37. 9%,and 39. 0%higher,respectively,than those of the HSM. For the CSM,the viscoelastic parameters decreased with the increase ofν. Whenν=0. 3,k1,k2,andμincreased by 71. 0%,200%,and 157%,respectively,compared to those of the ICSM (P<0. 001);For the cases ofν=0. 2 andν=0. 4,the above parameters were respectively 102%,243%,and 209%and 35. 3%,97. 5%,and 79%higher than those of the ICSM.(2) Predictions for the relative errors of mechanical parameters caused by HSM e is defined as the relative change of elastic moduli (or relative error) between the HSM and SM. As shown in Fig. 2,when Poisson’s ratioνis 0. 3,in order to let the e less than 30%,relative dimension between the cell and the micropipetteξneeds to be at least 5. 0. Whenνequals 0. 5 (ICSM),ξis about 3. 3 to make the e reach 20%. However,ξis rarely larger than 5. 0 in general MPA experiments,thus the relative error of modulus will exceed 30%. The above results are independent of cell types,thus they are applicable to other spherical solid-like cells.■Fig.2 Thresholds ofξvarying withνwhen e was 10%,20%,and 30%,respectively Another parameter VR was introduced to represent the relative errors of viscoelastic parameters between HSM and SM.With regard to ICSM (Fig. 3a),whenξis 3,VRis nearly 22%. If theξis larger than 8. 0,the relative error will be reduced to less than 10%. For the CSM,the viscoelastic parameters of a typical chondrocyte varying withξandνwere obtained,as shown from Figs. 3b to 3d. Whenνtends to 0. 5,the parameters tend to those of ICSM. When theξexceeds 10,each parameter changes very little. For a certain Poisson’s ratio (ν=0. 3),whenξis 3,the VR of k1,k2,andμare 47. 1%,70. 8%,and 68. 2%,respectively. Whenξequals 5 and 10,the above values are 42. 3%,68. 8%,65%,and 38. 4%,66. 0%,63. 2%,respectively. For a givenξ(ξ=3),whenνis 0. 2,the VR of k1,k2,andμare 53. 6%,73. 3%,and 75. 0%,respectively.Whenνis taken as 0. 3 and 0. 4,the above errors are 47. 7%,71. 1%,68. 2%,and 38. 4%,58. 8%,54. 8%,respectively.Thus,the VR also decreases with the increase ofξandν.Conclusions The effects of the relative dimension between the cell,and micropipette and the Poisson’s ratio of cell were remarkable and should be taken into consideration in the pursuit of more accurate mechanical parameters of cells.
基金Project(10502025) supported by the National Natural Science Foundation of ChinaProject(101005) supported by Fok Ying Tong Education FoundationProject(BK2007528) supported by the Natural Science Foundation of Jiangsu Province,China
文摘To understand the high strain rate deformation mechanism and determine the grain size,strain rate and porosity dependent yield strength of nanocrystalline materials,a new mechanical model based on the deformation mechanism of nanocrystalline materials under high strain rate loading was developed.As a first step of the research,the yield behavior of the nanocrystalline materials under high strain rate loading was mainly concerned in the model and uniform deformation was assumed for simplification.Nanocrystalline materials were treated as composites consisting of grain interior phase and grain boundary phase,and grain interior and grain boundary deformation mechanisms under high strain rate loading were analyzed,then Voigt model was applied to coupling grain boundary constitutive relation with mechanical model for grain interior phase to describe the overall yield mechanical behavior of nanocrystalline materials.The predictions by the developed model on the yield strength of nanocrysatlline materials at high strain rates show good agreements with various experimental data.Further discussion was presented for calculation results and relative experimental observations.
基金supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases ( R01 AR069148)
文摘Bone modeling and remodeling are governed by distinct biochemical processes that may hold unique opportunities for optimizing bone mass[1,2].Remodeling refers to the coupled resorption and subsequent formation on the bone surface,while modeling represents uncoupled formation or resorption.Mechanical loading is known to improve bone mass,though whether this occurs through modeling or remodeling(or by some combination)is unclear.Dynamic in vivo morphometry utilizing high resolution micro-CT and image registration has only recently become feasible and thus holds an untapped and expanding potential for understanding bone metabolism by quantifying and localizing formation/resorption and modeling/remodeling events.16-week-old mice were given 2 baseline weekly micro-CT scans of both tibiae prior to the initiation of daily unilateral loading(contralateral limb for nonloaded control).Weekly scanning and daily loading continued for 5 weeks.Registered images for each mouse in a global coordinate system revealed the time course of each voxel,and changes in bone mass were quantified as modeling or remodeling starting at the onset of loading.In cortical bone,after an initial response to loading in both regimes,modeling emerged as the dominant response.Loading effects were largest in areas of mechanical significance.For example,anabolic modeling on the periosteal surface of the half of the tibia in compression under axial load presented a strong effect of loading,whereas the same measure on the endosteal surface in the area in tension showed no difference.Similarly,in trabecular bone anabolic modeling was significantly increased with loading on trabecular plates but not rods(plates have been shown to be the major contributor to overall bone strength).The catabolic modeling response on the endosteal surface showed an interesting transition over time.Loading initially led to a significant suppression of catabolic modeling,but over time increased it to levels significantly beyond that of nonloaded controls.
文摘This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.
