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1.
IntroductionConsidertheindirectcontrolsystem x =Ax Bφ(σ) , σ =CTx ρφ(σ) ,(1 )wherex∈Rn,σ ∈R ,Aisn×nstablematrix ,BandCarendimensionalvectors,thesymbolTstandsfortransposition ,ρisaconstant,function φ(σ) :R →Riscontinuousandsatisfiesconditionσφ(σ) >0   ( σ∈R ,σ≠ 0 ) . (2 )Manyspe…  相似文献   

2.
IntroductionHowtheintensionandmoduleofsteelfibrereinforcedconcrete (SFRC)dependsonitsconstituentpropertiesandcontentisaprincipalproblemtopredictmacro_mechanicspropertiesofSFRC,thekeyconsistsintheconfirmationofstressdistribution .Interfacialstresstransfe…  相似文献   

3.
EFFECTIVE STRESS LAWS FOR MULTI_POROSITY MEDIA   总被引:2,自引:0,他引:2  
Theconceptofeffectivestressisveryusefultodescribetheeffectofporefluidpressureonthemechanicalresponseofporousmedia.Terzaghifoundthefollowingfacts:1)Iftheexternalstaticpressuresσ1=σ2=σ3andtheporepressureincreasethesameamountwiththepressures,thevolumeof…  相似文献   

4.
IntroductionOneoftheprimaryproblemsingoetechnicalengineeringistoconstructasoilconstitutivemodelapplicabletogeneral 3_Dstressstates.Althoughmanytypesofconstitutivemodelshavebeenproposed ,fewcantakeproperaccountofthedirectionalchangeofstressvector (i.e .,ro…  相似文献   

5.
IntroductionTheanalysisfordynamicproblemofelasticbodieshasbeenstudiedformanyyears.Basedonthemomentlessthinshelltheory ,HuthandCole[1]studiedthestresswaveinasphericalshellproducedbypressureloadsin 1 955.Mcivor[2 ]discussedtheflexuralstressandmembranestressina…  相似文献   

6.
Considerthefollowingnonlinearcontrolsystem:·x=Ax+B(σ),σ=CTx,(1)wherex=(x1,x2,…,xn)T∈Rn,thenoteTexpressesthetransposeofmatrixandvector,A,BandCaren×n,n×mandn×mconstantmatricesrespectively,σ=(σ1,σ2,…,σm)T∈Rmand(σ)=(1(σ1),2(σ2),…,m(σm))T:Rm→Rmiscont…  相似文献   

7.
IntroductionConsiderthefollowingdelaydifferenceequationwithhigherorderxn+1=A0xp0n+ A1xp1 n- 1+… + Akxpkn-k   (n=0 ,1 ,2 ,… ) ,( 1 )whereAi,pi ∈ [0 ,∞ )   (i=0 ,1 ,2 ,…k;k∈ 1 ,2 ,… ) ( 2 )andtheinitialconditionsx-k,x-k+1,… ,x- 1,x0 arearbitrarypositivenumbers.Somespecialcasesofk=1forEq .( 1 )havebeen…  相似文献   

8.
Periodicity and strict oscillation for generalized lyness equations   总被引:1,自引:0,他引:1  
IntroductionConsiderthefollowingdelaydifferenceequationxn 1=xn(a bxn)xn- 1,  n=0 ,1 ,2 ,… ,(1 )wherea ,b∈ [0 ,∞ )witha b>0 (2 )andwheretheinitialvaluesx- 1andx0 arearbitrarypositivenumbers.Eq .(1 )isregardedasageneralizedLynessequationbyG .Ladasin [1 ] .Obviously ,undercondition (2 ) ,…  相似文献   

9.
IntroductionConsiderthefollowingperiodicboundaryvalueproblem(PBVP,forshort)forfirst_orderintegro_differentialequationofmixedtypeu′=f(t,u,T1u,T2u)  (a.e.t∈I),(1)u(0)=u(2π),(2)whereI=[0,2π],fsatisfiesCaratheodory’sconditions,T1isaVolterraintegraloperator,T2isaFredholminte…  相似文献   

10.
IntroductionTheboundaryelementmethod(BEM)providesanattractivealternativefortheanalysisofengineeringproblems.Itsmainadvantagesareeconomicalandparticularlyconvenientforunboundeddomainandstressconcentrationproblems.Theboundaryintegralequation(BIE)isthe…  相似文献   

11.
Theoretical analysis and finite element (FE) simulation have been carried out for a constant specific load rate (CSLR) indentation creep test. Analytical results indicate that both the representative stress and the indentation strain rate become constant after a transient period. Moreover, the FE simulation reveals that both the contours of equivalent stress and equivalent plastic strain rate underneath the indenter evolve with geometrical self-similarity. This suggests that pseudo-steady indentation creep occurs in the region beneath the indenter. The representative points in the region are defined as the ones with the equivalent stress equal to the representative stress. In addition, it is revealed that the proportionality between indentation strain rate and equivalent plastic strain rate holds at the representative points during the pseudo-steady indentation creep of a power law material. A control volume (CV) beneath the indenter, which governs the indenter velocity, is identified. The size of the CV at the indented surface is approximately 2.5 times the size of the impression. The stress exponent for creep can be obtained from the pseudosteady indentation creep data. These results demonstrate that the CSLR testing technique can be used to evaluate creep parameters with the same accuracy as conventional uniaxial creep tests.  相似文献   

12.
蠕变压痕实验的计算机模拟   总被引:2,自引:0,他引:2  
采用有限元的方法对双相材料的蠕变压痕实验进行了数值模拟,在有限元数值解的基础上,定义了相应于传统单轴蠕变实验的“等效应力”和“等效应变”,建立了蠕变压痕实验同传统单轴蠕变实验之间的关系,给出了确定薄膜蠕变应力指数和蠕变常数的方法;同时数值解的结果表明,实验中通过控制压痕深度不超过薄膜厚度的 5%~10%,忽略基体的硬化指数对确定薄膜性能的影响存在一定的误差,但基体的弹性模量对确定薄膜的蠕变性能影响不大。  相似文献   

13.
An expanding cavity model (ECM) for determining indentation hardness of elastic strain-hardening plastic materials is developed. The derivation is based on a strain gradient plasticity solution for an internally pressurized thick-walled spherical shell of an elastic power-law hardening material. Closed-form formulas are provided for both conical and spherical indentations. The indentation radius enters these formulas with its own dimensional identity, unlike that in classical plasticity based ECMs where indentation geometrical parameters appear only in non-dimensional forms. As a result, the newly developed ECM can capture the indentation size effect. The formulas explicitly show that indentation hardness depends on Young’s modulus, yield stress, strain-hardening exponent and strain gradient coefficient of the indented material as well as on the geometry of the indenter. The new model reduces to existing classical plasticity based ECMs (including Johnson’s ECM for elastic–perfectly plastic materials) when the strain gradient effect is not considered. The numerical results obtained using the newly developed model reveal that the hardness is indeed indentation size dependent when the indentation radius is very small: the smaller the indentation, the larger the hardness. Also, the indentation hardness is seen to increase with the Young’s modulus and strain-hardening level of the indented material for both conical and spherical indentations. The strain-hardening effect on the hardness is observed to be significant for materials having strong strain-hardening characteristics. In addition, it is found that the indentation hardness increases with decreasing cone angle of the conical indenter or decreasing radius of the spherical indenter. These trends agree with existing experimental observations and model predictions.  相似文献   

14.
Two expanding cavity models (ECMs) are developed for describing indentation deformations of elastic power-law hardening and elastic linear-hardening materials. The derivations are based on two elastic–plastic solutions for internally pressurized thick-walled spherical shells of strain-hardening materials. Closed-form formulas are provided for both conical and spherical indentations, which explicitly show that for a given indenter geometry indentation hardness depends on Young’s modulus, yield stress and strain-hardening index of the indented material. The two new models reduce to Johnson’s ECM for elastic-perfectly plastic materials when the strain-hardening effect is not considered. The sample numerical results obtained using the two newly developed models reveal that the indentation hardness increases with the Young’s modulus and strain-hardening level of the indented material. For conical indentations the values of the indentation hardness are found to depend on the sharpness of the indenter: the sharper the indenter, the larger the hardness. For spherical indentations it is shown that the hardness is significantly affected by the strain-hardening level when the indented material is stiff (i.e., with a large ratio of Young’s modulus to yield stress) and/or the indentation depth is large. When the indentation depth is small such that little or no plastic deformation is induced by the spherical indenter, the hardness appears to be independent of the strain-hardening level. These predicted trends for spherical indentations are in fairly good agreement with the recent finite element results of Park and Pharr.  相似文献   

15.
The aim of indentation analysis is to link indentation data, typically an indentation force vs. indentation depth curve, Ph, to meaningful mechanical properties of the indented material. While well established for time independent behavior, the presence of a time dependent behavior can strongly affect both the loading and the unloading responses. The paper presents a framework of viscoelastic indentation analysis based on the method of functional equations, developed by Lee and Radok [1960, The contact problem for viscoelastic bodies, J. Appl. Mech. 27, 438–444]. While the method is restricted to monotonically increasing contact areas, we show that it remains valid at the very beginning of the unloading phase as well. Based on this result, it is possible to derive closed form solutions following the classical procedure of functional formulations of viscoelasticity: (1) the identification of the indentation creep function, which is the indentation response to a Heaviside load; and (2) a convolution integral of the load history over the indentation creep function. This is shown here for a trapezoidal loading by a conical indenter on three linear isotropic viscoelastic materials with deviator creep: the 3-parameter Maxwell model, the 4-parameter Kelvin–Voigt model and the 5-parameter combined Kelvin–Voigt–Maxwell model. For these models, we derive closed form solutions that can be employed for the back-analysis of indentation results from the loading and holding period and for the definition of unloading time criteria that ensure that viscous effects are negligible in the unloading response.  相似文献   

16.
Asphalt binders are common construction materials, however due to time- and temperature- dependence, their mechanical properties are often difficult to characterize. Several standard tests methods exist to describe their complex behavior. This paper presents an exploratory feasibility study of a flat-tip indentation testing to analyze the linear viscoelastic properties of asphalt binders. Depth-sensing indentation testing has been extensively used to characterize the properties of many engineering materials, however the applications to asphalt binders are very limited. This paper presents a simple solution for the creep compliance in tension derived for flat-tipped indenter. This solution was verified with the Finite Element Analysis and then applied to the experimental results from the indentation testing performed on one typical unmodified asphalt binder. The testing was conducted at three different low temperatures and under three different creep load levels to verity the linearity of the response, and to evaluate the robustness and applicability of the indentation method. Furthermore, the creep compliance functions determined from the indentation testing were compared with a more traditional 3-point bending experiments. The results show that there is a non-uniform discrepancy between the two testing methods, most likely due to nonlinear behavior of the asphalt binder at higher temperatures and micro-damage of the binder samples at lower temperatures. Other possible sources of error between indentation and 3-point bending are problems determining the initial tip-specimen contact surface and possible tip-specimen adhesion. It is concluded that flat-tipped indentation at low temperatures should be performed at lower load levels to avoid excessive stress concentrations that leads to micro-damage and nonlinear response of asphalt binders. Alternatively, asphalt binders at low temperatures could be evaluated using different indenter geometries, such as spherical or pyramidal, using corresponding parameter interpretation procedures.  相似文献   

17.
纳米压痕过程的三维有限元数值试验研究   总被引:18,自引:3,他引:15  
采用有限元方法模拟了纳米压痕仪的加、卸载过程,三维有限元模型考虑了纳米压痕仪的标准Berkovich压头.介绍了有限元模型的几何参数、边界条件、材料特性与加载方式,讨论了摩擦、滑动机制、试件模型的大小对计算结果的影响,进行了计算结果与标准试样实验结果的比较,证实了模拟的可靠性.在此基础上,重点研究了压头尖端曲率半径对纳米压痕实验数据的影响.对比分析了尖端曲率半径r=0与r=100nm两种压头的材料压痕载荷—位移曲线.结果表明,当压头尖端曲率半径r≠0时,基于经典的均匀连续介质力学本构理论、传统的实验手段与数据处理方法,压痕硬度值会随着压痕深度的减小而升高.  相似文献   

18.
The introduction of controlled gradients in plastic properties is known to influence the resistance to damage and cracking at contact surfaces in many tribological applications. In order to assess potentially beneficial effects of plastic property gradients in tribological applications, it is essential first to develop a comprehensive and quantitative understanding of the effects of yield strength and strain hardening exponent on contact deformation under the most fundamental contact condition: normal indentation. To date, however, systematic and quantitative studies of plasticity gradient effects on indentation response have not been completed. A comprehensive parametric study of the mechanics of normal indentation of plastically graded materials was therefore undertaken in this work by recourse to finite element method (FEM) computations. On the basis of a large number of computational simulations, a general methodology for assessing instrumented indentation response of plastically graded materials is formulated so that quantitative interpretations of depth-sensing indentation experiments could be performed. The specific case of linear variation in yield strength with depth below the indented surface is explored in detail. Universal dimensionless functions are extracted from FEM simulations so as to predict the indentation load versus depth of penetration curves for a wide variety of plastically graded engineering metals and alloys for interpretation of, and comparisons with, experimental results. Furthermore, the effect of plasticity gradient on the residual indentation pile-up profile is systematically studied. The computations reveal that pile-up of the graded alloy around the indenter, for indentation with increasing yield strength beneath the surface, is noticeably higher than that for the two homogeneous reference materials that constitute the bounding conditions for the graded material. Pile-up is also found to be an increasing function of yield strength gradient and a decreasing function of frictional coefficient. The stress and plastic strain distributions under the indenter tip with and without plasticity gradient are also examined to rationalize the predicted trends. In Part II of this paper, we compare the predictions of depth-sensing indentation and pile-up response with experiments on a specially made, graded model Ni-W alloy with controlled gradients in nanocrystalline grain size.  相似文献   

19.
IntroductionThecreepbehaviorofshortfiberreinforceMetalMatrixComposites (MMCs)dependsonthefollowingfactors,suchasthecreeppropertyofthematrix ,elasticandfracturespropertiesofthefiber,geometricparametersofthefibers,arrangementofthefibersandthepropertyofthef…  相似文献   

20.
We propose a dual indentation technique for the assessment of the cohesion and friction angle of cohesive-frictional materials of the Mohr–Coulomb type. The technique is based on a computational implementation of the yield design theorems applied to conical indentation tests with different apex angles. The upper bound solutions are found to be very close to flat indentation solutions available for cohesive-frictional materials. On this basis we derive fundamental hardness-to-cohesion solutions in function of the friction angle and the apex angle. By studying the property of these dimensionless relations, we show that the ratio of two hardness measurements obtained from indentation tests with different apex angles, allows one to determine the friction angle. This dual indentation method is applied to Berkovich and Corner Cube indenter assimilated to equivalent cones of different apex angle. The method is validated for a ‘model’ material, metallic glass, which has recently been identified as a cohesive-frictional materials. The only input to the method are two hardness values which we obtain by microindentation on metallic glass. The outcome are values of the cohesion and friction angle, which are found to be in excellent agreement with reported cohesion and friction angle values of metallic glass obtained by macroscopic triaxial testing and comprehensive finite-element backanalysis of indentation curves.  相似文献   

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