饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。     

变形多孔介质流固耦合模型及数值模拟研究

假定骨架、固体颗粒和水均是可压缩的,在此基础上采用两相不混溶流体的理论推导了水的连续方程,通过引入气压恒定这一假定进一步简化为水的非饱和渗流连续方程。基于广义Biot理论给出了固体骨架积分形式的平衡方程,结合非饱和渗流连续方程采用加权残值法推导了流固耦合方程组的有限元列式。通过干燥介质吸水的数值模拟来考察非饱和流固耦合模型的预测能力,数值模拟的结果表明耦合模型可以准确地反映吸水过程的规律。将耦合模型应用于水下大断面隧洞开挖的瞬态分析,可以模拟出开挖引起的EDZ区域孔隙水压力急剧升高、有效应力减小、渗透系数动态变化以及排水对洞室稳定性的影响,计算的结果与国外大型原位实验的一般性观测结论相吻合。     

多相非饱和多重孔隙介质的有效应力定律

多孔介质的有效应力定律广泛应用于流固耦合变形分析问题。该文考虑孔隙的重数、孔隙流体的相数、各向异性、非饱和、基质吸力等条件,提出了广义多相非饱和多重孔隙介质的有效应力定律。在固体相及各流体相线弹性变形的假设下,首先通过应力状态分解、边界条件叠加方法,得到了不考虑基质吸力的多相等效饱和各向异性多重孔隙介质的有效应力。考虑到非饱和多孔介质中两相界面张力引起的基质吸力,在线弹性变形基础上,叠加了基质吸力引起的变形部分,推导得到非饱和多孔介质的有效应力定律的一般形式。将所得公式根据实际需要进行简化处理,可以得到目前常用的有效应力定律的表达形式,充分说明了该文所得结论的合理性。     

温度对水饱和孔隙介质压缩波速度的影响

温度作用使孔隙介质密度、弹性模量等参数发生改变,从而影响声波传播性质。文章基于变形体能量守恒定律,考虑热机耦合和两相介质热耦合,推导水饱和孔隙介质的热传导方程;考虑孔隙水和固相孔隙介质存在的三种耦合性,基于热作用下应力应变关系分析,建立了热机耦合声波传播模型;设计温度变化沉积物样品声学测量实验,当温度由2℃增加到27℃时,压缩波速度平均增大88m·s^-1运用热机耦合声波传播模型解释了实验测量结果的上升趋势,获得理论计算值与测量值相对偏差范围为-3．03％～1．19％。     

多孔介质的一种流-固耦合动态边界理论

基于Biot理论,推导了考虑渗流作用的可变形多孔介质流-固耦合问题的基本方程,建立了本问题的渗流模型,给出了所考虑问题的流体动力弥散分布概率及系数表达式,进一步建立了多孔介质中微压液体位移场模型,讨论了流体动力弥散因素对多孔介质边界的影响,建立了描述多孔介质的动态边界方程,并分别对所建立的四种边界模拟了动态结果及算例。     

基于应变空间的碾压混凝土各向异性损伤本构模型

根据碾压混凝土材料的力学特性和损伤拉压显著不同的特点,分别在拉应变和压应变空间建立了碾压混凝土的本构关系和损伤演化方程。在拉应变空间,碾压混凝土的变形特性表现为脆弹性,考虑弹性与损伤耦合,应用正交各向异性损伤理论描述碾压混凝土的刚度退化和应变软化;在压应变空间,考虑弹塑性与损伤耦合,应用内时理论来描述碾压混凝土的弹塑性特性,正交各向异性损伤理论来描述微裂缝扩展引起的刚度退化和应变软化,内时理论没有屈服面,使模型的参数和方程大大减少,从而简化了非线性计算过程。计算结果表明,该模型能够较好地描述碾压混凝土在单轴和多轴加载下的性质。     

饱和弹性裂隙介质的混合物理论

本文首先用损伤力学的方法,按孔隙的配置及几何结构,分别定义了含各向异性分布裂隙的固体介质的二阶连续法向裂纹张量和切向裂纹张量。然后,在裂隙内充满流体时,对组分速度、组分偏应力等混合物理论的基本变量进行了各向异性修正。并用混合物理论,建立了饱和裂隙介质中各组分的质量和动量平衡方程。最后,在仅考虑裂纹的单一张开度时,针对线弹性骨架材料,得到了由不可压缩材料构成的各组分的动力学控制方程。     

求解饱和多孔介质圆柱壳动力学问题的一种半解析方法

基于弹性薄壳理论,结合Biot理论中流体和固体骨架的运动方程及本构关系,得到饱和多孔介质圆柱薄壳在谐激励作用下的一阶矩阵常微分控制方程。结合齐次扩容精细积分法和精细元法,建立了分析该类结构振动问题的半解析方法。该方法充分考虑了多孔介质圆柱薄壳骨架与流体的耦合作用,具有广泛的适应性,弥补了现有计算模型和等效媒质法的不足。基于该方法,还讨论了孔隙率对饱和多孔介质圆柱薄壳的频响特性的影响。     

三重介质油藏有限导流垂直裂缝井的流-固耦合模型

考虑了三重介质油藏介质变形与垂直裂缝井闭合的影响,推广了Cinco-Ley H的有限导流垂直裂缝井的双线性渗流理论,将流体在垂直裂缝井与地层中形成的渗流划分为两个区域:三重介质油藏中的非线性流动区域和垂直裂缝井内的非线性流动区域;由此建立了三重介质油藏有限导流垂直裂缝井的流-固耦合模型。鉴于该模型的强非线性,采用稳定的有限差分格式求得其数值解,并将数值结果绘制成试井样板曲线。将数值结果与不考虑介质变形或垂直裂缝闭合的模型进行对比验证了该文模型研究的必要性。另外,还讨论了垂直裂缝井渗透率模量、窜流系数、基岩弹性储容比、井筒储集系数对无因次井底压力及压力导数的敏感性影响。     

煤与瓦斯突出的固─流耦合失稳理论及数值分析

本文在多相介质力学的理论基础上,提出了煤体有限变形下煤与瓦斯突出的耦合失稳理论。从热力学第二定律出发,以应力的二阶功最小原理作为突出发生的准则,建立了煤与瓦斯突出的固─流两相介质耦合失稳的数学模型,给出了两相介质耦合失稳问题的非线性有限元方程并进行了数值模拟。     

A numerical contact algorithm in saturated porous media with the extended finite element method

In this paper, a coupled hydro-mechanical formulation is developed for deformable porous media subjected to crack interfaces in the framework of extended finite element method. Governing equations of the porous medium consist of the momentum balance of the bulk together with the momentum balance and continuity equations of the fluid phase, known as formulation. The discontinuity in fractured porous medium is modeled for both opening and closing modes that results in the fluid flow within the fracture, and/or contact behavior at the crack edges. The fluid flow through the fracture is assumed to be viscous and is modeled by employing the Darcy law in which the permeability of fracture is obtained using the cubic law. The contact condition in fractured porous medium is handled by taking the advantage from two different algorithms of LATIN method and penalty algorithm. The effect of contact on fluid phase is employed by considering no leak-off from/into the porous medium. The nonlinearity of coupled equations produced due to opening and closing modes is carried out using an iterative algorithm in the Newton–Raphson procedure. Finally, several numerical examples are solved to illustrate the performance of proposed X-FEM method for hydro-mechanical behavior of fractured porous media with opening and closing modes.     

复杂多孔介质多重介质模型的表征单元体

裂缝性岩体及缝洞型碳酸盐岩储层属于复杂多孔介质,岩体内部空隙为从纳米或微米级的微孔隙到数十厘米以上的大裂缝和溶蚀孔洞,空隙尺度跨越的范围很大。对于很多实际问题,由于单重介质模型计算不准确,且又不可能对复杂空隙空间结构在微观水平上进行精确描述,因此只能应用多重连续介质方法研究复杂多孔介质中的输运问题。该文给出了多重介质模型表征单元体的定义。在所研究问题的尺度范围内,这一多重介质模型表征单元体存在,复杂多孔介质的多重连续介质理论才能够成立。还以孔隙度和渗透率作为相关状态变量进行分析,研究了单重介质模型表征单元体和多重介质模型表征单元体间的联系,给出了复杂多孔介质多重介质模型的建立方法。     

基于VOF/PLIC界面追踪方法的RTM工艺充模过程数值模拟

针对基于Darcy定律的树脂传递模塑(RTM)工艺的充模过程数值模拟的局限性,将纤维预制体内的充填流动作为两相流(树脂相和空气相)处理,在动量方程中考虑了惯性项和粘性项,采用有限体积方法(FVM)离散控制方程,并与VOF/PLIC界面追踪方法相结合,发展了求解树脂在纤维预制体内非稳态流动问题的数值模拟方法.在此基础上开发了RTM工艺的充模过程数值模拟程序,其算例的数值模拟结果与解析解或实验结果吻合良好,验证了此数值模拟方法的有效性和可靠性.     

Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows

Correct modeling of resin flow in liquid composite molding (LCM) processes is important for accurate simulation of the mold-filling process. Recent experiments indicate that the physics of resin flow in woven (also stitched or braided) fiber mats is very different from the flow in random fiber mats. The dual length-scale porous media created by the former leads to the formation of a sink term in the equation of continuity; such an equation in combination with the Darcy's law successfully replicate the drooping inlet pressure history, and the region of partial saturation behind the flow-front, for the woven mats. In this paper, the mathematically rigorous volume averaging method is adapted to derive the averaged form of mass and momentum balance equations for unsaturated flow in LCM. The two phases used in the volume averaging method are the dense bundle of fibers called tows, and the surrounding gap present in the woven fiber mats. Averaging the mass balance equation yields a macroscopic equation of continuity which is similar to the conventional continuity equation for a single-phase flow except for a negative sink term on the right-hand side of the equation. This sink term is due to the delayed impregnation of fiber tows and is equal to the rate of liquid absorbed per unit volume. Similar averaging of the momentum balance equation is accomplished for the dual-scale porous medium. During the averaging process, the dynamic interaction of the gap flow with the tow walls is lumped together as the drag force. A representation theorem and dimensional analysis are used to replace this drag force with a linear function of an average of the relative velocity of the gap fluid with respect to the tow matrix for both the isotropic and anisotropic media. Averaging of the shear stress term of the Navier–Stokes equation gives rise to a new quantity named the interfacial kinetic effects tensor which includes the effects of liquid absorption by the tows, and the presence of slip velocity on their surface. Though the gradient of the tensor contributes a finite force in the final momentum balance equation, a scaling analysis leads to its rejection in the fibrous dual-scale porous medium if the permeability of flow through the gaps is small. For such a porous medium, the momentum equation reduces to the Darcy's law for single-phase flow.     

Magnetoelectric interaction phenomena in materials

Following the phenomenological approach of Landau and Lifshitz the existence of linear magnetoelectric effect in antiferromagnetic Cr₂O₃ was predicted by Dzyaloshinskii which was later experimentally confirmed by Astrov and Folenet al. Magnetoelectric phenomenon has been observed in several single-phase materials in which simultaneous electric and magnetic ordering coexists and in two-phase composites in which the participating phases are the ferroelectric and magnetic. The author’s group has recently undertaken a systematic study of the preparation, characterization and detection of the (ME) _H output in a few single-phase materials and two-phase composites. This article describes the magnetoelectric phenomenon in general and recent work carried out in the author’s group.     

On the Relationship Between Microstructure of the Cortical Bone and its Overall Elastic Properties

The relationship between microstructure of the cortical bone and its effective elastic properties is discussed. We utilize results of Kachanov et al (1994) on materials with cracks/pores of diverse shapes. Bone's microstructure is modeled using available micrographs. The calculated anisotropic elastic constants for porous cortical bone are compared with available experimental data. For Young's moduli and shear moduli the agreement is good, whereas Poisson's ratios differ significantly. Possible reasons for this difference are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Third-order bound of nonlinear composites and porous media under hydrostatic deformation

In this study the third-order variational bound is explicitly derived for nonlinear composites subject to hydrostatic deformation. By formulating the stochastic extreme principle for nonlinear boundary value problems, the third-order upper bound of the potential is derived for nonlinear two-phase composites, which is further explicitly specialized to porous media. Examples of application are provided by applying the derived bound to various cases of composites and porous media characterized with power law nonlinearity.