基于混合物理论的非饱和土的热-水-力耦合分析模型Ⅰ

以混合物理论为基础研究了非饱和土的热-水-力多场耦合问题.将非饱和土视为由土骨架、液态水、水蒸气、干燥气体及溶解气体共5种组分构成的混合物,在组分的质量、动量守恒方程及整体能量守恒方程的基础上,引入了37个补充方程以形成封闭方程组.其中,利用水与水蒸气的化学势改变量相同,推导了在气压力变化条件下水与水蒸气相变平衡所满足的限制方程.最终控制方程以增量形式给出,6个方程求解6个未知量(3个土骨架位移、水压力、气压力及温度),充分反映了热膨胀、热渗流、水的相变、气体溶解及土骨架变形等多种现象的耦合过程.     

微极性多组分多孔介质材料的混合物理论

将描述多组分系统的复合混合物理论与微极性连续介质力学理论相结合,建立了描述微极性多组分多孔介质材料的混合物理论.假定系统由多组分的微极性弹性固体和多组分微极性粘性流体组成.给出由混合物理论建立的系统的平衡方程.依据热力学第二定律以及本构假设建立了系统的本构方程,并使场方程闭合.为考虑固相的压缩性,在液相自由能函数中引入液相体积分数作为内变量,得到动力相容条件,用以限制固、液两相界面压力差的变化.最后,基于线性化理论得到线性化的本构方程和场方程,建立了考虑介质微极性的热-水力-力学组分输运模型.此理论框架可以运用到可变形多孔介质中污染物、药物以及农药输运等问题中,所得到的微极性多组分多孔介质系统的闭合场方程经退化后,可变为固、流相都为单一组分的多孔介质系统场方程,它与Eringen得到的结果一致.     

理想传导弹性体中能量耗散的磁-热-弹性波

广义能量耗散弹性理论(TEWED,G-NⅢ理论)广泛应用于均匀磁场作用下的时谐平面波在无限大的理想导电弹性体中传播的研究.提出了更普遍的有复杂参数的色散方程,通过运用Ieguerre 方法解决复杂条件下耦合磁-热-弹性波的问题,表明耦合磁-热-弹性波问题相当于改进的膨胀波及通过有限热波速度、热弹性耦合、热扩散率及外加磁场修正的、有限速度热波的传播问题.在G-NⅢ模型(TEWED)中,耦合磁-热-弹性波传播时发生衰减和色散,扩散的热量由热传播方程中的阻尼项考虑,而在G-N Ⅱ模型没有发生衰减和耗散.最后给出了类铜材料的数值结果.     

考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程．基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解．数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响．数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略．     

非饱和膨胀土的结构损伤模型及其在土坡多场耦合分析中的应用

针对原状膨胀土对气候变化反映敏感的特点和其具有胀缩性、裂隙性、超固结性等力学特性,以非饱和土力学和损伤力学为基础,建立了一个非饱和膨胀土的弹塑性损伤本构模型及相应的固结模型．把原状膨胀土看成是由未损部分和损伤部分的复合体,未损部分用非饱和土的非线性本构关系描述,损伤部分用损伤演化方程和两个屈服面（即,加载屈服面和剪切屈服面）描述．其中的损伤演化方程包括加载引起的损伤和干湿循环引起的损伤两个方面,用作者研制的CT-三轴试验确定．设计了相应的有限元程序UESEPDC;对非饱和膨胀土边坡进行了三相多场耦合问题的数值分析．分析分为4个阶段,得到了边坡在每一分析阶段的应力场、位移场、孔隙水压力场、孔隙气压力场、含水量场、基质吸力场、结构损伤演化场和塑性区扩展的动态图,较好地揭示了膨胀土边坡在开挖和气候变化条件下逐渐发生失稳滑动的现象及其机理．     

损伤材料本构关系的一种内蕴时间理论

在评述了现有的连续介质损伤力学(CDM)的严重缺陷之后,基于所提出的损伤对本构关系影响的物理机制和模型及在ε_(T_qD)空间中对损伤材料不可逆过程的热力学描述,本文提出了一组新型的弹塑性损伤本构方程。该方程符合本文第一作者所提出的耗散型材料本构方程形式不变性定律的条件,以及Lemaitre,Valanis的本构方程和经典塑性理论的主要结果可由它在简化条件下推出的属性。文中还简略提到了损伤演化方程、有限元算法、材料函数确定方法及其在弹塑性损伤场分析中的初步应用。文末强调了内蕴表征时间z*和φ在ε_TD与ε_Tq)子空间中分析复杂的损伤与非弹性变形耦合问题时的重要价值;并将本文所提出的模型推广得到了纤维增强复合材料的损伤本构方程。     

有限变形下的混凝土动态本构关系研究

讨论有限变形和小变形假设下本构关系的区别,并将其运用于混凝土的弹-粘塑性本构关系研究,提出了一个应变率相关的动态力学模型．模型基于Ottosen的4参数屈服准则,分别考虑混凝土在硬化阶段和软化阶段加载面的不同变化规律,建立冲击荷载下的混凝土本构关系．该模型可以应用于冲击载荷下混凝土材料响应的模拟．引进Green-Naghdi客观率建立有限变形的混凝土模型．根据大量实验结果对应变率和材料强度的关系提出合理假设,使模型可以反映混凝土大变形的动态力学行为,为相关工程问题的研究提供有益的思路和有效的工具．     

热-力耦合原子-连续关联模型的框架及其算法

对热-力耦合的原子-连续关联模型进行了系统研究,给出了计及热-力耦合行为的金属微-纳米构件内材料的瞬态弹性常数,应力、应变、比热容等物理量的具体计算公式及其算法.利用原子运动中的“结构形变”部分来研究微-纳米尺度下多晶原子团簇的非均匀结构变形.将原子团簇晶格结构的变形与连续体的变形关联起来,在准简谐近似假设下,推导出依赖于微观结构变形和热振动的自由能密度、熵密度、内能密度表达式,从而给出了微-纳米尺度下的瞬态热-力学参数.     

多相固体弹塑性本构方程的同类性

本文以复合材料为背景,讨论多相固体即混合物的等效弹塑性本构方程.按照所提出的等效本构方程的定义,文章证明,由服从广义正交法则的多种均匀的弹塑性介质组成的混合物具有与它的组分介质同类的、也服从广义正交法则的等效本构方程.     

论非线性连续介质热-力耦合系统中的动力裂纹传播

在许多工程问题中,热-力耦合是重要的,而不能加以忽略.核反应堆工程就是这样的一个例子.本文讨论非线性连续介质的热-力耦合系统中的裂纹传播问题.各种的非线性介质,包括非线性弹性、弹塑性介质,被加以考虑,并且给出了相应情况下的各种路径无关积分.为了解释这些积分的物理含义,通过考虑一个缺口试件的裂纹传播,证明热-力耦合系统中的动力裂纹扩展力就等于这一路径无关积分.因此,就可利用这些积分来构作热-力耦合系统断裂动力学的非线性断裂准则.     

A continuum model for transport phenomena in convective flow of solid–liquid phase change material suspensions

Heat and mass transport is modeled in convective flow of a dilute binary mixture of a continuous fluid with mono-dispersed particles (PCM suspensions), in which solid–liquid phase change can take place. The model is based on the mixture continuum approach together with an approximate enthalpy formulation, in which the temporal and spatial variations of phase change fraction in the particles are considered explicitly. Derivations are given for a set of equations governing conservation of mass, momentum, species, and energy of the suspensions, as well as the evolution of phase change fraction of the dispersed particles.     

Coupled fluid-solid thermal interaction modeling for efficient transient simulation of biphasic water-steam energy systems

This paper proposes a fluid-solid coupled finite element formulation for the transient simulation of water-steam energy systems with phase change due to boiling and condensation. As it is commonly assumed in the study of thermal systems, the transient effects considered are exclusively originated by heat transfer processes. A homogeneous mixture model is adopted for the analysis of biphasic flow, resulting in a nonlinear transient advection-diffusion-reaction energy equation and an integral form for mass conservation in the fluid, coupled to the linear transient heat conduction equation for the solid. The conservation equations are approximated applying a stabilized Petrov-Galerkin FEM formulation, providing a set of coupled nonlinear equations for mass and energy conservation. This numerical model, combined with experimental heat transfer coefficients, provides a comprehensive simulation tool for the coupled analysis of boiling and condensation processes. For the treatment of enthalpy discontinuities traveling with the flow, a novel explicit-implicit time integration method based on Crank-Nicolson scheme is proposed, analyzing its accuracy and stability properties. To reduce problem size and enhance numerical efficiency, a modal superposition method with balanced truncation is applied to the solid equations. Finally, different example problems are solved to demonstrate the capabilities, flexibility and accuracy of the proposed formulation.     

可变形孔隙介质中热、水耦合力学问题的代数多格子分析方法

研究了孔隙介质中包括热和质量传递的全耦合多相流问题的代数多格子分析方法。数学模型包括质量、线性矩、能量平衡方程和本构方程,以位移、毛细压力、汽压和温度为基本变量,模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑相变、热传导、对流和潜热交换(汽化-冷凝),气相是由易混合的干空气和水蒸气组成,视为理想气体。考题显示出较高的计算效率。     

重建极性连续统理论的基本定律和原理(Ⅱ)——微态连续统理论和偶应力理论

重建微态连续统理论和偶应力理论的动量和动量矩均衡定律以及能量守恒定律,并由这些定律自然地推导出相应的局部和非局部均衡方程。这些结果可由耦合型微极连续统理论过渡和归结而得到。把推导出的结果和传统的质量和微惯性守恒定律以及熵不等式结合在一起就构成微态连续统理论和偶应力理论的基本均衡定律和方程体系。还弄清了以前的各种连续统理论的不完整性层次。最后,给出了几种特殊情形。     

Phase transition processes of pore fluids in porous materials

Taking a closer look on, e. g., storage processes of greenhouse gases in deep geological aquifers or pressure decreases in dilatant shear bands, the observation can be made that pressure and temperature changes in porous materials can induce phase transition processes of the respective pore fluids. For a numerical simulation of this behaviour, a continuum mechanical model based on a multiphasic formulation embedded in the well-founded framework of the Theory of Porous Media (TPM) is presented in this contribution. The single phases are an elasto-viscoplastic solid skeleton, a materially compressible pore gas consisting of the components air and gaseous pore water (water vapour) and a materially incompressible pore liquid, i. e., liquid pore water. The numerical treatment is based on the weak formulations of the governing equations, whereas the primary variables are the temperature of the mixture, the displacement of the solid skeleton and the effective pressures of the pore fluids. An initial boundary-value problem is discussed in detail, where the resulting system of strongly coupled differential-algebraic equations is solved by the FE tool PANDAS. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An existence result for nonisothermal immiscible incompressible 2‐phase flow in heterogeneous porous media

In the present article, we study the temperature effects on two‐phase immiscible incompressible flow through a porous medium. The mathematical model is given by a coupled system of 2‐phase flow equations and an energy balance equation. The model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy‐Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation; ie, the saturation of one phase, the pressure of the second phase, and the temperature are primary unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we show the existence of weak solutions with the help of an appropriate regularization and a time discretization. We use suitable test functions to obtain a priori estimates. We prove a new compactness result to pass to the limit in nonlinear terms.     

Mechanical Balance Laws for Boussinesq Models of Surface Water Waves

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of these quantities are not known. This work presents a systematic derivation of mass, momentum and energy densities and fluxes associated with a general family of Boussinesq systems. The derivation is based on a reconstruction of the velocity field and the pressure in the fluid column below the free surface, and the derivation of differential balance equations which are of the same asymptotic validity as the evolution equations. It is shown that all these mechanical quantities can be expressed in terms of the principal dependent variables of the Boussinesq system: the surface excursion ?? and the horizontal velocity w at a given level in the fluid.     

重建极性连续统理论的基本定律和原理(Ⅶ)——增率型

目的是建立微极连续统增率型的较为完整的运动方程,边界条件和能率方程.为此,先给出较为完整的变形梯度及其逆的定义.接着推导出各种应力率和偶应力率间的新关系式.最后,作为一种特殊情形得到连续统力学的耦合的增率型运动方程、边界条件和能率方程.