含有序孔洞的多孔氧化铝薄膜的力学性能测量和数值模拟

高纯铝箔在特定的溶液下经过电化学阳极氧化腐蚀,可在其表面生成一层多孔的非晶氧化铝层,其孔径分布非常均匀,孔大致呈六方密排布。由于此类薄膜具有规则的纳米级孔径,大的比表面积,良好的自组织排列性,所以其日益受到人们的关注。然而,到目前为止,对于此类薄膜力学性能的研究还很少,所以在一定程度上限制其功能的开发和应用。为了获得此类多孔膜的弹性常数,本文首先由实验出发,通过光力学检测(双光束散斑干涉)的方法得到薄膜拉伸时的整体表观弹性模量。然后对薄膜建立二维有限元模型,运用均匀化理论反推出其基体(无孔结构)的弹性模量,同时考察了不同的基体泊松比对模型整体表观模量的影响,并且用一般有限元方法验证了沿特定方向拉伸时均匀化模型计算的有效性。     

Method of homogenization applied to dispersion in porous media

The theory of homogenization which is a rigorous method of averaging by multiple scale expansions, is applied here to the transport of a solute in a porous medium. The main assumption is that the matrix has a periodic pore structure on the local scale. Starting from the pores with the Navier-Stokes equations for the fluid motion and the usual convective-diffusion equation for the solute, we give an alternative derivation of the three-dimensional macroscale dispersion tensor for solute concentration. The original result was first found by Brenner by extending Brownian motion theory. The method of homogenization is an expedient approach based on conventional continuum equations and the technique of multiple-scale expansions, and can be extended to more complex media involving three or more contrasting scales with periodicity in every but the largest scale.     

Higher-order analysis of near-tip fields around an interfacial crack between two dissimilar power law hardening materials

By means of an asymptotic expansion method of a regular series, an exact higher-order analysis has been carried out for the near-tip fields of an interfacial crack between two different elastic-plastic materials. The condition of plane strain is invoked. Two group of solutions have been obtained for the crack surface conditions: (1) traction free and (2) frictionless contact, respectively. It is found that along the interface ahead of crack tip the stress fields are co-order continuous while the displacement fields are cross-order continuous. The zone of dominance of the asymptotic solutions has been estimated. The project supported by the National Natural Science Foundation of China     

Non-gaussian diffusion modeling in composite porous media by homogenization: Tail effect

In the paper anomalous diffusion appearing in a porous medium composed of two porous components of considerably different diffusion characteristics is examined. The differences in diffusivities are supposed to result either from two medium types being present or from variations in pore size (double porosity media). The long-tail effect is predicted using the homogenization approach based on the application of multiple scale asymptotic developments. It is shown that, if the ratio of effective diffusion coefficients of two porous media is of the order of magnitude smaller or equal O( ²), where is a homogenization parameter, then the macroscopic behaviour of the composite may be affected by the presence of tail-effect. The results of the theoretical analysis were applied to a problem of diffusion in a bilaminate composite. Analytical calculations were performed to show the presence of the long-tail effect in two particular cases.Notations c _i the concentration of chemical species in water within the medium i - D _i the effective diffusion coefficient for the medium i - D _ij ^eff the macroscopic (or effective) diffusion tensor in the composite - ERV the elementary representative volume - h the thickness of the period - l a chracteristic length of the ERV or the periodic cell - L a characteristic macroscopic length - n the volumetric fraction of the material 2 - 1–n the volumetric fraction of the material 1 - N the unit vector normal to - t the time variable - x the macroscopic (or slow) space variable - y the microscopic (or fast) space variable - c _1c ,C _2c ,D _1c ,D _2c the characteristic quantities - T,T _1L ,T _2L ,T _1l ,T _2l the characteristic times - c ₁ ^* ,c ₂ ^* ,D ₁ ^* ,D ₂ ^* ,t ^* the non-dimensional variables - the homogenization parameter - ₁ the domain occupied by the material 1 - ₂ the domain occupied by the material 2 - the interface between the domains 1 and 2 - the total volume of the periodic cell - /x_i the gradient operator - the gradient operator     

Derivation of the Forchheimer Law Via Matched Asymptotic Expansions

Matched asymptotics are used formally in the linearized Navier–Stokes equations, the so-called Oseen approximation, to derive a nonlinear law for the flow of a single-phase, incompressible Newtonian fluid through a rigid porous medium. A suitable choice of the linear term gives, to order a Forchheimer-type law.     

Asymptotic Solution of the Problem of Heat Transfer between Two Plates and a Uniform Fluid Flow

For low Peclet numbers, analytic expressions are obtained for three highest terms of the asymptotic expansion of the solution of the convective heat-transfer problem for a system consisting of two parallel plates with identical lengths identical and constant surface temperatures and an infinite uniform fluid flow with a low Prandtl number.     

SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition :　　　　εx″(t) =f(t,x(t) ,x(t-ε) ,ε) ,　　t∈(0 ,1 ) ,(1 )　　　　x(t) =φ(t,ε) ,　t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse…     

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.     

岩土材料应变局部化的有限元分析方法

采用有限单元法分析岩土材料的应变局部化时经常会遇到单元尺寸敏感性问题和网格锁定问题。自适应网格技术能够有效地解决网格锁定问题,但仍然无法克服计算结果对单元尺寸的依赖性,尽管在一维情况下被证明是可行的。复合体理论(均匀化理论)和弱非连续有限元方法可以成功地解决岩土材料的单元尺寸敏感性问题,在一维情况下两类方法实际上是一致的。本文针对岩土材料应变局部化的有限元新技术所存在的若干问题进行了详细的讨论,并给出了有关算例。