集中载荷作用下饱和多孔Timoshenko简支梁的动力响应

基于饱和多孔弹性Timoshenko梁的动力数学模型,研究了梁中点承受突加载荷作用两端可渗透饱和多孔弹性Timoshenko简支梁的动力响应,得到了问题的解析解,给出了梁中点无量纲挠度、固相骨架弯矩和孔隙流体压力等效力偶等随无量纲时间的响应。考察了剪切和横截面转动惯性效应等对动力响应的影响,比较了饱和多孔Timoshenko、Shear、Rayleigh和Euler-Bernoulli梁的动力响应,结果表明:剪切效应使饱和多孔Timoshenko梁动力响应的幅值和周期增大,而横截面转动惯性仅增加梁动力响应的周期;固相骨架与孔隙流体的相互作用具有粘性效应,随着相互作用系数的增加,饱和多孔梁挠度和弯矩幅值减小,流体压力等效力偶幅值增大,且振幅衰减加快。同时,随着长细比的增加,饱和多孔Timoshenko梁的挠度幅值和周期逐渐减小,并最终趋于饱和多孔Euler-Bernoulli梁的挠度幅值和周期。     

埋置移动荷载作用下成层饱和地基的动力响应

利用Fourier变换和传递反射矩阵法（TRM法）研究了成层饱和地基在埋置移动荷载作用下的动力响应。土体被假设为完全饱和的多孔弹性介质并且服从Biot多孔弹性波动方程,用修正粘滞阻尼模型来描述土体的粘弹性行为,采用TRM法来考虑饱和地基的成层性,利用Fourier变换和Fourier逆变换得到了埋置移动荷载作用下饱和地基动力响应积分形式解答。当饱和成层地基退化单层饱和地基时,该文解与已有解能很好的吻合。最后,通过数值计算分析了埋置荷载深度﹑荷载速度、荷载频率及软硬夹层对动力响应的影响。     

A fully coupled finite element analysis of water‐table fluctuation and land deformation in partially saturated soils due to surface loading

A fully coupled numerical model is presented for the water‐table fluctuation and land deformation in partially saturated soils due to surface loading. This numerical model is developed based on the poroelastic governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. The numerical model is verified and validated against a one‐dimensional consolidation problem concerning surface loading on a soil column which has six different initial water‐table elevations. The numerical model is then applied to a two‐dimensional consolidation problem of surface loading on a partially saturated soil at a construction site. Results from the numerical simulations of both problems show that the water table fluctuates in the partially saturated soils, and the unsaturated zone above the water table has significant effects on the consolidation behaviour of the partially saturated soils under surface loading. Such effects are caused by the permanent absorption of a portion of the mechanical loading stress and the weak hydromechanical coupling between the solid skeleton deformation field and the groundwater flow field in the unsaturated zone due to its partial saturation. Copyright © 2000 John Wiley & Sons, Ltd.     

横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程并得到传递矩阵。进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题。数值算例表明采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的动力特性。     

饱和地基上刚性圆板的扭转振动

用解析的方法首次研究了饱和地基上刚性圆板的扭转振动特性。首先运用Hankel变换求解饱和介质动力问题的控制方程,然后按混合边值条件建立了饱和地基上刚性圆板扭转振动的对偶积分方程,并把对偶积分方程化为第二类Fredholm积分方程。文末数值算例给出了动力柔度系数和扭转角幅值随无量纲频率的变化曲线,并与单相弹性介质情况进行了对比分析。数值结果表明:与经典的弹性介质上基础的振动特性相比,水相的存在对饱和地基上刚性圆板的扭转振动特性有一定的影响,且在共振频率附近可以减弱其振动,当土体渗透性较好时更是如此。     

A complete plane strain fictitious stress boundary element method for poroelastic media

A fully coupled generalized plane strain boundary element model for determining the distribution of stress and pore pressure around underground openings in poroelastic media is developed. It is based on the indirect boundary element method of fictitious stress extended to complete plane strain analysis. New fundamental solutions for longitudinal forces were derived for the development of the model which uses elements with a constant variation of fictitious forces and sources in both space and time. As an example, the problem of a borehole drilled in an arbitrary direction in a triaxial stress field is considered. The results indicate that the fictitious stress method is an accurate and suitable means for complete plane strain poroelastic analyses of underground openings.     

Nonlinear radial oscillations of micro-bubbles in a compressible UCM medium

The nonlinear oscillations of acoustically forced spherical gas bubbles in an upper-convected Maxwell (UCM) compressible fluid are investigated. The nonlinear viscoelastic model used is suitable for large-amplitude excitation of bubbles that cannot be captured by linear models. The effects of acoustic excitation are studied for compressible nonlinear viscoelastic media, which increases the complexity and nonlinearity of the behavior. The Keller–Miksis equation is used to model the dynamics of a single bubble. The constitutive equations of compressible UCM are used for viscoelastic media. These governing equations are non-dimensionalized and coupled to determine the bubble dynamic behavior. The set of derived non-dimensionalized integro-differential equations developed are numerically solved simultaneously using the fourth-order Runge–Kutta method featured by the automatic variable time step-size module. The combined effects of compressibility and viscoelasticity of the fluid on bubble radius are investigated. The results show that the combination of compressibility and nonlinear viscoelasticity for bubble radial oscillations makes forced bubble dynamics more applicable for human needs, especially for large deformations in highly non-Newtonian fluids like industrial polymers or even tissue-like media. It can be seen that compressibility controls the oscillations at higher forcing amplitudes. The relevance and importance of these bubble dynamics to biomedical ultrasound applications and light emissions by sonoluminescence and other industries are evident.     

Viscous dissipative power density function for poroelastic saturated materials at high frequencies

A viscous dissipative power density function is defined for poroelastic saturated materials at high frequencies. In the framework of Biot’s general theory of acoustics of poroelastic materials, the correction factor of the flow resistance of the fluid from low to high frequencies is derived from the power density function. For this aim the dissipative forces per unit volume are obtained from the viscous dissipative power density. The complex dynamic correction function of the viscosity is derived for the motion of a fluid limited by two parallel planes’ boundaries. It is also derived for the motion of a fluid in a cylindrical duct. Analytical solutions and impedance tube test results on air saturated porous metals are compared to validate the viscous dissipative power density up to frequencies of 6 kHz. A second comparison is performed for kerosene saturated porous metals. Finally, a validation is performed using ultrasonic experiments on water saturated bones.     

A soil damage model expressed by a double scalar and its applications

Poroelasticity refers to the study of the mechanics of porous elastic materials that are saturated with compressible or incompressible fluids. When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. The objective of this paper is to examine the problem of consolidation response of damage-susceptible poroelastic geomaterials. Firstly, a new constitutive model of soft soils expressed by isotropic double scalar damage variables is developed and incorporated into Biot’s consolidation finite element equations via EDAPD program. Then, the EDAPD program is applied to analyze a soft subgrade reinforced by surcharge preloading technology. The comparison between the numerical predictions and the experimental data shows that the isotropic double scalar damage model presented in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media.     

水下多孔吸声材料夹层板隔声分析

利用结构弯曲波法,并结合Biot理论和Bolton多层板理论,推导了水下多孔吸声材料夹层板的隔声量理论计算公式,分析了（Binding-Binding,BB）型、（Binding-Unbinding,BU）型和（Unbinding-Unbinding,UU）型三种结构的隔声性能。将入射域、辐射域和中间空腔域中的声波以相应的速度势函数形式表达,多孔吸声材料的传声过程采用Biot理论和Bolton理论描述,再结合相应模型的边界条件,即可求解出结构的理论隔声量。在BB型、BU型和UU型三种模型中,UU型的隔声性能最好,BB型的隔声性能最差。夹层板中多孔吸声材料能有效避免空腔驻波共振的发生,并能显著提高结构高频的隔声性能。多孔吸声材料厚度和空腔空气层厚度的增加,能有效地促进结构的隔声性能。     

Vibration analysis of a poroelastic composite hollow sphere

Vibrations in a poroelastic composite hollow sphere are investigated employing Biot’s theory of wave propagation in poroelastic media. A composite hollow poroelastic sphere consists of two concentric poroelastic spherical layers both of which are made of different poroelastic materials with each poroelastic material being homogeneous and isotropic. The boundaries of the composite hollow poroelastic sphere are free from stress. The frequency equations of both radial and rotatory vibrations are obtained each for pervious and impervious surfaces. The frequency equation of vibrations of a poroelastic composite hollow sphere with rigid core is derived as a particular case. The non-dimensional frequency for propagating modes is computed as a function of ratio of thickness to inner radius of core. The results are presented graphically for two types of poroelastic composite spheres and then discussed.     

Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

The durability of concrete materials with regard to early-age volume changes and cracking phenomena depends on the evolution of the poroelastic properties of cement paste. The ability of engineers to control the uncertainty of the percolation threshold and the evolution of the elastic modulus, the Biot–Willis parameter and the skeleton Biot modulus is key for minimizing the vulnerability of concrete structures at early-age. This work presents original results on the uncertainty propagation and the sensitivity analysis of a multiscale poromechanics-hydration model applied to cement pastes of water-to-cement ratio of 0.40, 0.50 and 0.60. Notably, the proposed approach provides poroelastic properties required to model the behavior of partially saturated aging cement pastes (e.g. autogenous shrinkage) and it predicts the percolation threshold and undrained elastic modulus in good agreement with experimental data. The development of a stochastic metamodel using polynomial chaos expansions allows to propagate the uncertainties of kinetic parameters of hydration, cement phase composition, elastic moduli and morphological parameters of the microstructure. The presented results show that the propagation does not magnify the uncertainty of the single poroelastic properties although, their correlation may amplify the variability of the estimates obtained from poroelastic state equations. In order to reduce the uncertainty of the percolation threshold and that of the poroelastic properties at early-age, engineers need to assess more accurately the apparent activation energy of calcium aluminate and, later on, of the elastic modulus of low density calcium-silicate-hydrate.     

A Spherically Anisotropic Microstructure Model for Fluid-saturated Poroelastic Isotropic Materials

The microstructure model proposed in this work is an assemblage of hollow spheres saturated by a fluid. The solid phase of each sphere is linearly elastic and spherically anisotropic. On the basis of this microstructure model, the effective bulk modulus, Biot’s coefficient and porosity variation are determined. It is shown that local anisotropy has important effects on the macroscopic isotropic poroelastic properties via a dimensionless material parameter which characterizes the degree of anisotropy and exponentially affects the porosity.     

Hybrid-Trefftz displacement element for poroelastic media

The elastodynamic response of saturated poroelastic media is modelled approximating independently the solid and seepage displacements in the domain and the force and pressure components on the boundary of the element. The domain and boundary approximation bases are used to enforce on average the dynamic equilibrium and the displacement continuity conditions, respectively. The resulting solving system is Hermitian, except for the damping term, and its coefficients are defined by boundary integral expressions as a Trefftz basis is used to set up the domain approximation. This basis is taken from the solution set of the governing differential equation and models the free-field elastodynamic response of the medium. This option justifies the relatively high levels of performance that are illustrated with the time domain analysis of unbounded domains.     

高聚物粘弹性力学模型的等当性

以描述高聚物粘弹性的三元件模型之一的弹簧与沃-开氏并联单元串接的为例,通过运动方程式从而推导出应力松弛模量G(t)的表达式,用初级的数学替代就可把这个G(t)转换为另一个形式,正好对应于弹簧与麦氏串联单元并联的关系,说明弹簧与伏-开氏并联单元串接的和弹簧与麦氏串联单元并联的力学模型互为等当,它们描述的是同一个高聚物粘弹性现象。模型的这种等当性为人们提供了很大的方便,我们可以根据使用的方便而任意选择其中的任一个模型。     

Uniaxial ratchetting in rate-independent plasticity laws

Summary A discussion of uniaxial ratchetting in linear viscoelasticity is given in [1]. The purpose of this paper is to analyse uniaxial ratchetting in the context of rate-independent plasticity laws. The analysis is referred to constitutive models with kinematic hardening, as well as to sawtooth input functions for stress with constant absolute value for the stress rate. For such loading histories some analytical formulas and explicit expressions concerning the model response for a sufficiently large number of cycles are derived. It turns out that an analogy can be drawn between the constitutive models of linear viscoelasticity and those of rate-independent plasticity with kinematic hardening. The analogy is established by a correspondence between the line representing the elasticity law for the equilibrium stress in viscoelasticity and the axis of kinematic hardening for the plasticity models defined in this paper.     

Strain localisation modelling and pore pressure in saturated sand samples

Dynamic strain localisation theory together with a multiphase material model is used to simulate shear band dominated processes in fully saturated sand samples. The fluid-saturated medium is viewed as multi-phase continuum consisting of a solid skeleton and pores filled by fluids. The governing equations are based on the general framework of averaging theories. A generalised plasticity constitutive model for fully saturated soils is adopted in the computational process. Both samples of medium-loose and dense sands are studied. Negative water pressures, which are important in localisation phenomena of fully saturated dilatant geomaterials, are obtained for dense sands, while positive water pressures result for medium-loose sands.     

On the Fractional Order Model of Viscoelasticity

Fractional order models of viscoelasticity have proven to be very useful for modeling of polymers. Time domain responses as stress relaxation and creep as well as frequency domain responses are well represented. The drawback of fractional order models is that the fractional order operators are difficult to handle numerically. This is in particular true for fractional derivative operators. Here we propose a formulation based on internal variables of stress kind. The corresponding rate equations then involves a fractional integral which means that they can be identified as Volterra integral equations of the second kind. The kernel of a fractional integral is integrable and positive definite. By using this, we show that a unique solution exists to the rate equation. A motivation for using fractional operators in viscoelasticity is that a whole spectrum of damping mechanisms can be included in a single internal variable. This is further motivated here. By a suitable choice of material parameters for the classical viscoelastic model, we observe both numerically and analytically that the classical model with a large number of internal variables (each representing a specific damping mechanism) converges to the fractional order model with a single internal variable. Finally, we show that the fractional order viscoelastic model satisfies the Clausius–Duhem inequality (CDI).     

Flexural vibrations of poroelastic plates

Summary The governing equations of flexural vibrations of thin, fluid-saturated poroelastic plates are derived in detail. The plate material obeys Biot's theory of poroelasticity with one degree of porosity, while the plate theory employed is the one due to Kirchhoff. These governing equations are compared with the corresponding ones for thermoelastic plates and a poroelastic-thermoelastic analogy for flexural plate dynamics is established in the frequency domain. The dynamic response of a rectangular, simply supported, poroelastic plate to harmonic load is obtained analytically-numerically and the effects of inertia as well as of porosity and permeability on the response is assessed.     

复合材料固化相关黏弹性性能演化及残余应力分析

通过对复合材料固化度和温度相关黏弹性本构方程的分析,定义一个能综合反映固化度和温度等对复合材料黏弹性性能影响的无量纲参数De_m。当参数De_m都大于10~2时,复合材料基体处于流动状态;当参数De_m都小于10~(-2)时,复合材料为弹性状态;仅当部分参数De_m小于10~2而大于10~(-2)时,复合材料处于黏弹性状态。以AS4纤维/3501-6树脂复合材料为例,基于对其参数De_m在典型固化工艺过程中的演化,研究该复合材料黏弹性性能的发展过程,发现基于参数De_m分析得到的凝胶点时间与实验结果一致。根据复合材料黏弹性性能对残余应力发展的影响,将复合材料残余应力计算分为流动阶段和黏弹性阶段,并建立了相应的状态相关黏弹性本构模型。最后通过与原始模型预测结果的比较验证了提出的本构模型,表明本文提出的计算方法与原始黏弹性本构模型计算结果一致,但大大降低了计算所需的时间和存储空间。