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。     

饱和多孔介质一维瞬态波动问题的解析分析

采用基于混合物理论的多孔介质模型,提出了饱和多孔介质一维动力响应的初边值问题。利用拉氏变换和卷积定理,分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。几种典型的数值算例同时给出了两类边界条件下瞬态波动过程中多孔固体的位移场、应力场和孔隙流体的速度场、压力场。结果表明,饱和多孔介质的波动过程是多孔固体和孔隙流体中以同一速度传播的两种波动的耦合过程,时效特性分析也揭示了饱和多孔介质固有的表观粘弹性性质。     

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。     

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。     

树脂基三维编织复合材料粘弹性能的数值预报

建立了基于三细胞模型数值预报三维编织复合材料粘弹性能的方法。首先构造了三维编织复合材料的三细胞模型并施加周期性边界条件,随后利用标准线性固体模型模拟树脂基体的粘弹性能,导出基体的松弛模量,再通过有限元计算及Prony级数拟合,得到三种胞元的粘弹性参数。然后根据三种胞元的体积分数和粘弹性参数,利用三个标准线性固体模型并联,模拟得到三维编织复合材料沿编织方向的粘弹性参数和蠕变本构关系。最后,分析了编织角和纤维体积含量对粘弹性能的影响。     

含液饱和多孔波阻板的地基振动控制研究

基于含液饱和多孔介质中的流-固耦合作用,提出了以含液饱和多孔材料作为隔振屏障的一类新型的地基振动控制体系。考虑在弹性地基内部设置饱和多孔波阻板,基于线弹性理论和Biot多孔介质模型,采用Fourier级数展开的方法,分别建立了地基表面和内部受到条形简谐荷载作用下地基动力响应的计算列式。通过数值算例,与传统的单相固体波阻板的隔振效果进行了比较,并且分析了多孔材料波阻板中固相材料性质、孔隙率、孔隙流体性质等物理力学参数对地基隔振性能的影响规律。结果表明,相对于单相固体波阻板隔振体系,基于含液饱和多孔波阻板的地基隔振体系更加具有优越性,并且更具有可设计性。     

微极饱和土波动分析中的变分原理

主要给出饱和多孔微极介质波动方程变分所对应的泛函表达式和有限元离散化方程。首先对u-U形式的饱和多孔微极介质波动方程和边界条件进行Laplace 变换,形成力学中的非齐次边值问题,然后构造变分后满足波动方程和边界条件的泛函,最后将有限元插值形式代入泛函表达式得到单元体的有限元离散方程。此方程对微极饱和多孔介质的动力固结问题数值分析具有重要意义。     

饱和多孔介质不同动力耦合形式数值分析EI北大核心CSCD

Biot饱和多孔介质波动行为的数值模拟在众多工程领域中具有重要的意义和作用,由于固相与液相耦合方程难以解耦,使该问题的数值模拟难度较大。针对饱和多孔介质中部分耦合u-p及全耦合u-p-U方程形式的特征,推导了相应动力耦合控制方程的有限元弱形式,并引入不同耦合形式的饱和多孔介质时域黏性边界,综合利用Comsol Multiphysics提供的偏微分方程应用模式进行二次开发求解,通过一维饱和多孔介质动力响应的解析解和数值解验证了模型求解技术的合理性和可行性,基于u-p-U耦合形式探讨了冲击荷载作用下干砂饱和砂地基动力固结中应力波传播特性。计算结果表明慢纵波对动力固结的影响比较显著,合理的冲击荷载持续时间有利于固结效果的改善。     

斜入射下水下地基场地地震输入的一维化时域方法

地震波斜入射下水下地基场地地震动输入问题,是涉及水层、饱和多孔介质和基岩三种不同性质介质耦合的复杂问题,目前理论成果还很匮乏。该文在现有的成层饱和多孔介质平面波斜入射的一维化时域方法的基础上,建立了水下地基场地的一维化时域计算方法。该计算方法依据Snell定理,将地震波斜入射下水层波动的空间二维问题转化为简单的一维问题,通过考虑水层与饱和多孔介质层交界面、不同饱和多孔介质交界面以及基岩与饱和多孔介质层交界面的边界条件,将已有的成层饱和土的一维化有限元方程与水层的一维化有限元方程组装,采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,形成了水下地基场地的整体有限元方程,借助于中心差分法和Newmark法相结合的时步积分法,推导了地震波斜入射下水下地基场地各节点动力响应时程的显式表达式。通过与傅里叶变换得到的理论解和现有的文献进行了对比,初步验证了该文时域算法的有效性和精度,为地震波斜入射下水下地基场地地震动输入提供了一种新型高效的研究方法。     

饱和多孔介质不同动力耦合形式数值分析

Biot饱和多孔介质波动行为的数值模拟在众多工程领域中具有重要的意义和作用,由于固相与液相耦合方程难以解耦,使该问题的数值模拟难度较大。针对饱和多孔介质中部分耦合u-p及全耦合u-p-U方程形式的特征,推导了相应动力耦合控制方程的有限元弱形式,并引入不同耦合形式的饱和多孔介质时域黏性边界,综合利用Comsol Multiphysics提供的偏微分方程应用模式进行二次开发求解,通过一维饱和多孔介质动力响应的解析解和数值解验证了模型求解技术的合理性和可行性,基于u-p-U耦合形式探讨了冲击荷载作用下干砂饱和砂地基动力固结中应力波传播特性。计算结果表明慢纵波对动力固结的影响比较显著,合理的冲击荷载持续时间有利于固结效果的改善。     

Parallel 3-d simulations for porous media models in soil mechanics

 Numerical simulations in 3-d for porous media models in soil mechanics are a difficult task for the engineering modelling as well as for the numerical realization. Here, we present a general numerical scheme for the simulation of two-phase models in combination with an abstract material model via the stress response with a specialized parallel saddle point solver. Therefore, we give a brief introduction into the theoretical background of the Theory of Porous Media and constitute a two-phase model consisting of a porous solid skeleton saturated by a viscous pore-fluid. The material behaviour of the skeleton is assumed to be elasto-viscoplastic. The governing equations are transfered to a weak formulation suitable for the application of the finite element method. Introducing an abstract formulation in terms of the stress response, we define a clear interface between the assembling process and the parallel solver modules. We demonstrate the efficiency of this approach by challenging numerical experiments realized on the Linux Cluster in Chemnitz. Received 15 February 2002 / Accepted 12 April 2002     

Thermo-plasticity of metal foams

The thermo-mechanical behaviour of a fluid-filled metal foam is influenced by the characteristics of the solid skeleton and the pore-fluid. During the deformation process both constituents exchange momentum and energy. Based on the theory of porous media a fluid-filled foam is modeled as a binary mixture consisting of a metal skeleton and a pore-gas. The porous solid skeleton is assumed to behave thermo-elasto-plastically. The pore-gas is considered as an ideal gas. For both constituents different phase temperatures and thermo-mechanical coupling mechanisms are taken into account. The resulting system of differential equations is solved using the finite element method. An example demonstrates the applicability and validity of this approach.     

A coupled discrete element‐finite difference approach for modeling mechanical response of fluid‐saturated porous materials

A model of fluid‐saturated poroelastic medium was developed based on a combination of the discrete element method and grid method. The developed model adequately accounts for the deformation, fracture, and multiscale internal structure of a porous solid skeleton. The multiscale porous structure is taken into account implicitly by assigning the porosity and permeability values for the enclosing skeleton, which determine the rate of filtration of a fluid. Macroscopic pores and voids are taken into account explicitly by specifying the computational domain geometry. The relationship between the stress–strain state of the solid skeleton and pore fluid pressure is described in the approximations of simply deformable discrete element and Biot's model of poroelasticity. The developed model was applied to study the mechanical response of fluid‐saturated samples of brittle material. Based on simulation results, we constructed a generalized logistic dependence of uniaxial compressive strength on loading rate, mechanical properties of fluid and enclosing skeleton, and on sample dimensions. The logistic form of the generalized dependence of strength of fluid‐saturated elastic–brittle porous materials is due to the competition of two interrelated processes, such as pore fluid pressure increase under solid skeleton compression and fluid outflow from the enclosing skeleton to the environment. Copyright © 2015 John Wiley & Sons, Ltd.     

A stabilized finite element formulation for monolithic thermo‐hydro‐mechanical simulations at finite strain

An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo‐hydro‐mechanical behavior of porous media undergoing large deformation. We first formulate a finite‐deformation thermo‐hydro‐mechanics field theory for non‐isothermal porous media. Projection‐based stabilization procedure is derived to eliminate spurious pore pressure and temperature modes due to the lack of the two‐fold inf‐sup condition of the equal‐order finite element. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non‐isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this thermo‐hydro‐mechanical model. Copyright © 2015 John Wiley & Sons, Ltd.     

A phase field model for the freezing saturated porous medium

In terms of the mixture theory and phase field theory, a phase field model is developed for the saturated porous medium undergoing phase transition. In the proposed model, it is postulated that during the phase transition of the porous medium, both the solid skeleton and pore fluid will undergo phase transition. The phase states of the solid skeleton and pore fluid are characterized by respective order parameters. To simplify the proposed phase field model, the temperatures and order parameters of the solid skeleton and pore fluid are assumed to be equal. The balance laws of the porous medium are given by the conventional mixture theory. The order parameter and the porosity of the porous medium are considered as internal variables and their evolution equations are determined by the entropy inequality of the porous medium. The constitutive representations for the stresses, entropies, heat fluxes, drag force and the evolution equations for the order parameter and porosity are derived by exploitation of the entropy inequality. To illustrate the proposed model, a concrete phase field model for the freezing porous medium is established in the paper. In the model, the memory effect associated with phase transition of the porous medium is taken into account by assuming Stieltjes integral for the strain energy of the porous medium. The constitutive representations for the above variables are then derived according to the proposed free energy expression for the porous medium. Finally, the boundary condition associated with the proposed model and the determination of some parameters involved in our model are discussed in the paper briefly.     

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot’s Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy.     

A thermodynamic-consistent model describing growth and remodeling phenomena

In the following contribution we present a continuum-mechanical model describing erosion/deposition, growth/atrophy and remodeling phenomena, based on the thermodynamically consistent theory of porous media (TPM). The specific model considered in this paper is based on three constituents, namely an incompressible solid skeleton, a viscous pore fluid and a third constituent containing fluidized particles. The balance equations are formulated in a general setting within the material space. Restrictions on the model with respect to the constitutive equations are obtained by evaluating the entropy balance following the standard proposal of Coleman and Noll [Arch. Rat. Mech. Anal. 13 (1963) 167].     

Energy focusing and the shapes of wave fronts in anisotropic fluid-saturated porous media

Summary The purpose of this paper is to investigate the energy focusing pattern evolution in the parameter space while the wave fronts propagate in the anisotropic fluid-saturated porous media. Firstly, the bifurcation conditions for a general anisotropic fluid-saturated porous material are deduced. Then, by choosing the material parameters as control variables, the influence of the anisotropy of the solid skeleton and pore fluid parameters on the development characteristics of energy focusing patterns is discussed, and the three-dimensional configurations for the focusing structures are explored. The results indicate that the energy focusing also exists on the wave fronts of the slow waves, which is a particular propagation characteristic for the slow waves in anisotropic fluid-saturated porous media. The distinct trends for the slow wave energy focusing are revealed. This has significant meaning in further understanding the roles of the fluid phase in the dynamic response of the fluid-saturated porous media.