Penalty finite element method for nonlinear dynamic response of viscous fluid-saturated biphase porous media

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｏｒｏｕｓｍｅｄｉａｍｏｄｅｌｓｄｅｄｕｃｅｄｆｒｏｍｍｉｘｔｕｒｅｔｈｅｏｒｙａｒｅａｔｔｒａｃｔｉｎｇａｔｔｅｎｔｉｏｎｏｆｍｏｒｅａｎｄｍｏｒｅｒｅｓｅａｒｃｈｅｒｓｂｅｃａｕｓｅｉｔｉｓｂａｓｅｄｏｎｔｈｅｆｒａｍｅｏｆｃｏｎｔｉｎｕｕｍｍｅｃｈａｎｉｃｓ[1]ａｎｄｗｅｒｅｓｕｃｃｅｓｓｆｕｌｌｙｕｓｅｄｔｏｄｅｐｉｃｔｔｈｅｍｅｃｈａｎｉｃａｌｂｅｈａｖｉｏｒｓｏｆｓｏｉｌｓａｎｄｂｉｏｌｏｇｉｃａｌｓｏｆｔｔｉｓｓｕｅｓ[2 ,3].Ｗｉｔｈｔｈｉｓｔｙｐｅｏ…     

Three-dimensional modeling of the mechanical property of linearly elastic open cell foams

Three-dimensional Voronoi models are developed to investigate the mechanical behavior of linearly elastic open cell foams. Dependence of the Young’s modulus, Poisson’s ratio and bulk modulus of the foams on the relative density is evaluated through finite element analysis. Obtained results show that in the low density regime the Young’s modulus and bulk modulus of random Voronoi foams can be well represented by those of Kelvin foams, and are sensitive to the geometric imperfections inherent in the microstructure of foams. In contrast, the compressive plateau stress of the foams is less sensitive to the imperfections. Failure surface of the foams subject to multi-axial compression is determined and is found to comply with the maximum compressive principal stress criterion, consistent with available experimental observations on polymer foams. Numerical results also show that elastic buckling of cell edges at microscopic level is the dominant mechanism responsible for the compressive failure of elastic open cell foams.     

A thermodynamical gradient theory for deformation and strain localization of porous media

In this work, a thermodynamically consistent gradient formulation for partially saturated cohesive-frictional porous media is proposed. The constitutive model includes a classical or local hardening law and a softening formulation with state parameters of non-local character based on gradient theory. Internal characteristic length in softening regime accounts for the strong shear band width sensitivity of partially saturated porous media regarding both governing stress state and hydraulic conditions. In this way the variation of the transition point (TP) of brittle-ductile failure mode can be realistically described depending on current confinement condition and saturation level. After describing the thermodynamically consistent gradient theory the paper focuses on its extension to the case of partially saturated porous media and, moreover, on the formulation of the gradient-based characteristic length in terms of stress and hydraulic conditions. Then the localization indicator for discontinuous bifurcation is formulated for both drained and undrained conditions.     

A linear dynamic model for a saturated porous medium

A linear isothermal dynamic model for a porous medium saturated by a Newtonian fluid is developed in the paper. In contrast to the mixture theory, the assumption of phase separation is avoided by introducing a single constitutive energy function for the porous medium. An important advantage of the proposed model is it can account for the couplings between the solid skeleton and the pore fluid. The mass and momentum balance equations are obtained according to the generalized mixture theory. Constitutive relations for the stress, the pore pressure are derived from the total free energy accounting for inter-phase interaction. In order to describe the momentum interaction between the fluid and the solid, a frequency independent Biot-type drag force model is introduced. A temporal variable porosity model with relaxation accounting for additional attenuation is introduced for the first time. The details of parameter estimation are discussed in the paper. It is demonstrated that all the material parameters in our model can be estimated from directly measurable phenomenological parameters. In terms of the equations of motion in the frequency domain, the wave velocities and the attenuations for the two P waves and one S wave are calculated. The influences of the porosity relaxation coefficient on the velocities and attenuation coefficients of the three waves of the porous medium are discussed in a numerical example.     

Basic features of the time finite element approach for dynamics

Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated. To this aim, significant parallels with elastostatics are emphasized. Paper presented at the ‘International Technical Specialists' Meeting on Rotorcraft Basic Research’, March 25–27, 1991, Georgia Institute of Technology, Atlanta, Georgia, USA.     

Nonlinear transient dynamic response of damped plates using a higher order shear deformation theory

Damped transient dynamic elasto-plastic analysis of plate is investigated. A finite element model based on a C ⁰ higher order shear deformation theory has been developed. Nine noded Lagrangian elements with five degrees of freedom per node are used. Selective Gauss integration is used to evaluate energy terms so as to avoid shear locking and spurious mechanisms. Von Mises and Tresca yield criteria are incorporated along with associated flow rules. Explicit central difference time stepping scheme is employed to integrate temporal equations. The mass matrix is diagonalized by using the efficient proportional mass lumping scheme. A program is developed for damped transient dynamic finite element analysis of elasto-plastic plate. Several numerical examples are studied to unfold different facets of damping of elasto-plastic plates.     

饱和多孔介质大变形分析的一种有限元-有限体积混合方法

建立了饱和多孔介质大变形分析的一种有限元-有限体积混合计算方法.将饱和多孔介质视为由固体骨架和孔隙水组成的两相体,其基本方程包括动力平衡方程和渗流连续方程.基于u-p假定和更新的Lagrange方法,饱和多孔介质的动力平衡方程在空间域内采用有限元方法进行离散,而渗流连续方程在空阃域内则采用有限体积法进行离散.通过两个数值算例,一维有限弹性固结和动力荷载作用下堤坝动力响应的计算,验证了该方法的有效性.     

A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers

The stress response of amorphous polymers exhibits tremendous change during the glass transition region, from soft viscoelastic response to stiff viscoplastic response. In order to describe the temperature-dependent and rate-dependent stress response of amorphous polymers, we extend the one-dimensional small strain fractional Zener model to the three-dimensional finite deformation model. The Eyring model is adopted to represent the stress-activated viscous flow. A phenomenological evolution equation of yield strength is used to describe the strain softening behaviors. We demonstrate that the stress response predicted by the three-dimensional model is consistent with that of one-dimensional model under uniaxial deformation, which confirms the validity of the extension. The model is then applied to describe the stress response of an amorphous thermoset at various temperatures and strain rates, which shows good agreement between experiments and simulation. We further perform a parameter study to investigate the influence of the model parameters on the stress response. The results show that a smaller fractional order results in a larger yield strain while has little effect on the yield stress when the temperature is below the glass transition temperature. For the stress relaxation tests, a smaller fractional order leads to a slower relaxation rate.     

Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good agreement with the results of the proposed theoretical model.Finally, the stress-deformation curve, as predicted by the model, is plotted for the simple shear problem at room and elevated temperatures using the same material properties for AA5754-O aluminium alloy.     

基于显式有限元方法的两相介质弹塑性动力反应计算分析

针对增量形式的流体饱和两相多孔介质弹塑性波动方程组,运用基于显式逐步积分格式的时域显式有限元方法对该波动方程组进行求解,并应用基于SMP破坏准则的弹塑性动力本构模型描述两相介质的动力反应性质,对两相介质在输入地震波作用下的弹塑性动力反应进行计算和分析,将计算结果与相应的弹性动力反应的计算结果进行对比;对本文应用的弹塑性...     

Discrete element-embedded finite element model for simulation of soft particle motion and deformation

The motion and deformation of soft particles are commonly encountered and important in many applications. A discrete element-embedded finite element model (DEFEM) is proposed to solve soft particle motion and deformation, which combines discrete element and finite element methods. The collisional surface of soft particles is covered by several dynamical embedded discrete elements (EDEs) to model the collisional external forces of the particles. The particle deformation, motion, and rotation are independent of each other in the DEFEM. The deformation and internal forces are simulated using the finite element model, whereas the particle rotation and motion calculations are based on the discrete element model. By inheriting the advantages of existing coupling methods, the contact force and contact search between soft particles are improved with the aid of the EDE. Soft particle packing is simulated using the DEFEM for two cases: particle accumulation along a rectangular straight wall and a wall with an inclined angle. The large particle deformation in the lower layers can be simulated using current methods, where the deformed particle shape is either irregular in the marginal region or nearly hexagonal in the tightly packed central region. This method can also be used to simulate the deformation, motion, and heat transfer of non-spherical soft particles.     

非均质饱和多孔介质弹塑性动力分析的广义耦合扩展多尺度有限元法

针对非均质饱和多孔介质弹塑性动力问题分析提出了一种广义耦合扩展多尺度有限元方法。首先,提出了基于细尺度等效刚度阵的粗尺度单元数值基函数构造方法,并给出了构造数值基函数的一般公式,所构造的耦合数值基函数有效考虑了动力相关效应与固液之间的耦合效应。其次,针对弹塑性非线性问题迭代求解,给出了基于摄动方法的位移与孔隙压强降尺度计算修正方案。最后,针对材料的强非均质特征,利用多节点粗单元技术来提高多尺度有限元方法的计算精度。通过与基于精细网格的传统有限元分析结果对比,验证了本文所提出方法的有效性与高效性。     

Thermal-hydraulic core analysis of the VVER-1000 reactor using a porous media approach

In this study, a thermal-hydraulic analysis of the VVER-1000 reactor core is performed using a porous media approach. Based on this approach, each fuel assembly was modeled and was divided into a network of lumped regions, each of which was characterized by a volume average parameter. The conservation equations of mass, linear momentum and energy are derived and discretized using the finite volume method in a hexagonal coordinate system. The pressure, velocity and temperature fields are achieved using a numerical analysis of the above mentioned coupled equations. To validate the applied approach, the numerical analysis and COBRA EN code results were compared and showed good agreement.     

智能结构有限元动力模型的建立及主动振动控制和抑制

采用一种新的压电板单元，建立了含有分布压电传感元件和执行元件结构（智能结构）的有限元动力模型。利用两种反馈控制律，研究了智能结构振动控制与抑制的问题，并提出了智能结构主动振动控制和抑制的一种方法。最后，提供了数值示例，说明本文提出方法的应用。     

Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.     

On complex potentials for finite plane deformation of a transversely isotropic material

We consider the finite deformation of plane equilibrium problem for a transversely isotropic layer, using the complex variable approach. We give the general expression for the pertinent complex potentials and state the corresponding fundamental problems. We discuss in detail the boundary value problem for fundamental problem-one. As an application of the espoused method, an analytical solution of “Lame's problem” for an infinite layer is obtained. The nonlinear effect of this is highlighted in the obtained figure.     

A coupled finite element model for the consolidation of nonisothermal elastoplastic porous media

A coupled finite element model for the analysis of the deformation of elastoplastic porous media due to fluid and heat flow is presented. A displacement-pressure temperature formulation is used for this purpose. This formulation results in an unsymmetric coefficient matrix, even in the case of associated plasticity. A partitioned solution procedure is applied to restore the symmetry of the coefficient matrix. The partitioning procedure is an algebraic one which is carried out after integration in the time domain. For this integration, a two-point recurrence scheme is used. The finite element model is applied to the investigation of nonisothermal consolidation in various situations.     

Study of the effect of capillary pressure on the permeability of porous media embedded with a fractal-like tree network

In this paper, the analytical expressions for permeability of (both saturated and unsaturated) porous media embedded with a fractal-like tree network are presented based on fractal theory and technique when the capillary pressure is taken into account. Both the dimensionless effective permeability and the relative permeability of the composites, which are defined as porous media embedded with a fractal-like tree network in this work, are derived and found to be a function of saturation, the capillary pressure and microstructural parameters of the networks. The relative permeabilities predicted by the present fractal model are compared with the available experimental data and a fair agreement between them is found.     

Application of the finite volume method in the simulation of saturated flows of binary Mixtures with particular emphasis on Non-Darcy motions through porous media

Non-Darcy flows in saturated porous media with significative boundary and inertia effects are modelled applying the Continuum Theory of Mixtures approach and simulated by discretization of the governing equations by the finite volume method.

---

Sommario Flussi di tipo ‘Non-Darcy’ in mezzi porosi saturi, con significativi effetti di bordo ed inerziali, vengono modellati applicando l'approccio della Teoria delle Miscele per il Continuo e simulati mediante discretizzazione delle equazioni governanti con il metodo del volume finito.

     

The impact of instability appearance on the quadratic law for flow through porous media

In the present paper, we attempt to explain the macroscopic flow law evolution in porous media according to the Reynolds number. A crenellated channel, considered as an element of such a medium, is used to perform numerical simulations in stationary and non-stationary cases. In the case of non-stationary laminar flows, we point out flow instabilities occurring in the channel at high Reynolds numbers and we focus on their influence on the macroscopic law. We qualitatively prove that they generate an additional quadratic contribution to Forchheimer’s law. We use two methods to study this contribution: first, a periodic disturbance, for which the instabilities appearing at the beginning of disturbance become regular oscillations; then a pulse disturbance of the entry velocity field which enables us to link the additional quadratic contribution to the existence of an accumulation of fluid at low velocity in the channel.