饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式，导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析，采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．     

Boundary conditions at fluid-permeable interfaces in porous media: A variational approach

A general set of boundary conditions at fluid-permeable interfaces between dissimilar fluid-filled porous matrices is established starting from an extended Hamilton–Rayleigh principle. These conditions do include friction and inertial effects. Once linearized, they encompass boundary conditions relative to volume Darcy–Brinkman and to surface Saffman–Beavers–Joseph dissipation effects.     

A phase-field modeling approach of hydraulic fracture in saturated porous media

Continuum porous media theories, extended by a diffusive phase-field modeling (PFM) approach, introduce a convenient and efficient tool to the simulation of hydraulic fracture in fluid-saturated heterogeneous materials. In this, hydraulic- or tension-induced fracture occurs in the solid phase. This leads to permanent local changes in the permeability, the volume fractions of the constituents as well as the interstitial-fluid flow. In this work, the mechanical behaviors of the multi-field, multi-phase problem of saturated porous media, such as the pore-fluid flow and the solid-skeleton deformation, are described using the macroscopic Theory of Porous Media (TPM). To account for crack nucleation and propagation in the sense of brittle fracture, the energy-minimization-based PFM procedure is applied, which approximates the sharp edges of the crack by a diffusive transition zone using an auxiliary phase-field variable. Furthermore, the PFM can be implemented in usual continuum finite element packages, allowing for a robust solution of initial-boundary-value problems (IBVP). For the purpose of validation and comparison, simulations of a two-dimensional IBVP of hydraulic fracture are introduced at the end of this research paper.     

A general theory of thermoporoelastoplasticity for saturated porous materials

A general theory of thermoporoelastoplasticity for saturated porous materials is presented. The theory is derived from the thermodynamics of open systems and irreversible processes. The thermal effects, due to the saturating fluid, are taken into account through a latent heat associated with the increase of fluid mass content. The theory does not assume incompressibility nor infinitesimal displacements for the saturating fluid. To take into account the plastic compressibility of the skeleton, the notion of plastic porosity is introduced. This plastic porosity is different from the overall plastic dilatation. The usual isothermal phenomenological theories appear to be particular cases of the proposed general theory.     

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。     

A finite element approach to study cavitation instabilities in non-linear elastic solids under general loading conditions

This paper proposes an effective numerical method to study cavitation instabilities in non-linear elastic solids. The basic idea is to examine—by means of a 3D finite element model—the mechanical response under affine boundary conditions of a block of non-linear elastic material that contains a single infinitesimal defect at its center. The occurrence of cavitation is identified as the event when the initially small defect suddenly grows to a much larger size in response to sufficiently large applied loads. While the method is valid more generally, the emphasis here is on solids that are isotropic and defects that are vacuous and initially spherical in shape. As a first application, the proposed approach is utilized to compute the entire onset-of-cavitation surfaces (namely, the set of all critical Cauchy stress states at which cavitation ensues) for a variety of incompressible materials with different convexity properties and growth conditions. For strictly polyconvex materials, it is found that cavitation occurs only for stress states where the three principal Cauchy stresses are tensile and that the required hydrostatic stress component at cavitation increases with increasing shear components. For a class of materials that are not polyconvex, on the other hand and rather counterintuitively, the hydrostatic stress component at cavitation is found to decrease for a range of increasing shear components. The theoretical and practical implications of these results are discussed.     

A stochastic model for the permeability characteristics of saturated cemented porous media undergoing freezing

As the temperature of a saturated porous medium drops, the water in the pores starts to freeze. Since the temperature at which the phase change takes place is dependent on the pore size, the permeability of the medium changes continuously. Simultaneously, due to the expansion of water on freezing, it is forced to migrate through the pore body thus inducing stresses in material matrix. The stresses developed and the consequent frost damage are therefore dependent on the change in the permeability characteristics of the medium on freezing. This paper deals with the numerical prediction of permeability characteristics of porous cemented media saturated with water undergoing progressive freezing.A bond percolation model is used to generate the pore structure according to an assumed poresize distribution. Permeability of the medium at various temperatures is computed by solving the network problem. The computed results are compared with other analytical and experimental results. The proposed model predicts a threshold temperature below which permeability drops to zero. This phenomenon is crucial in developing a deeper understanding of the mechanism of frost damage to cemented porous materials such as bricks, stone, concrete, etc.     

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.     

考虑耦合质量影响的饱和多孔介质动力响应分析的显式有限元法

根据Biot饱和多孔介质动力方程,采用解耦技术,提出了考虑耦合质量Pd影响的饱和多孔介质中动力响应分析的显式有限元法。文中建立并推导了显式有限元的公式,编制了相应的计算程序并进行了实例计算。计算结果与解析解进行了对比,两者符合很好,表明本文方法是处理饱和多孔介质动力问题的一种有效方法。文中还分析了耦合质量ρa对固相和液相动位移的影响。     

A model for the viscoelastic behavior of polymers at finite strains

Summary A constitutive model is derived for the isothermal nonlinear viscoelastic response in polymers, which do not possess the separability property. The model is based on the concept of transient networks, and treats a polymer as a system of nonlinear elastic springs (adaptive links), which break and emerge due to micro-Brownian motion of chains. The breakage and reformation rates for adaptive links are assumed to depend on some strain energy density. The viscoelastic behavior is described by an integral constitutive equation, where the relaxation functions satisfy partial differential equations with coefficients depending on the strain history. Adjustable parameters of the model are found by fitting experimental data for a number of polymers in tension at strains up to 400 per cent. To validate the constitutive relations, we consider loading with different strain rates, determine adjustable parameters at one rate of strains, and compare prediction of the model with observations at another rate of strains. Fair agreement between experimental data and results of numerical simulation is demonstrated when the rates of strains differ by more than a decade. Received 1 July 1997; accepted for publication 7 October 1997     

A variational framework for the modeling of glassy polymers under finite strains

Continuum Mechanics and Thermodynamics - In this paper, a viscoelastic model able to capture important mechanical features of a wide class of glassy polymers is presented. Among them, the ability...     

A general mathematical modelling for heat and mass transfer in unsaturated porous media: an application to free evaporative cooling

The present paper develops a general mathematical model with some improvements in mass, momentum and energy equations, which introduce more transport mechanisms to simulate simultaneous transfer of heat and mass in the porous media unsaturated with liquid. Numerical calculation results in two-dimension are obtained for the vertical packed bed with its right opening surface exposing to atmospherical environment. The calculating data can demonstrate the cooling effect of the water evaporation for the bed if it is used as a cooling wall of building for room air-conditioning in the hot and dry climate.     

A general analytic solution for plane strain bending under tension for strain-hardening material at large strains

A new analytic solution for plane strain bending under tension of a sheet is proposed for elastic-plastic, isotropic, incompressible, strain-hardening material at large strains. Numerical treatment is only necessary to calculate ordinary integrals and solve transcendental equations. No restriction is imposed on the hardening law. All governing equations and boundary conditions are exactly satisfied. The only exception is that the actual stress distribution over the ends of the sheet is replaced with a concentrated force and a concentrated bending moment. The through-thickness distribution of residual stresses and a measure of springback are also found. The range of validity of the solution is determined. An illustrative example is provided for Swift’s hardening law.     

A micro-mechanical model for the response of filled elastomers at finite strains

Constitutive equations are developed for the isothermal response of particle-reinforced elastomers at finite strains. A rubbery polymer is treated as a network of chains bridged by junctions. A strand between two junctions is thought of as a series of inextensible segments linked by bonds. Two stable conformations are ascribed to a bond: flexed and extended. Deformation of a specimen induces transition of bonds from their flexed conformation to the extended conformation. A concept of trapped entanglements is adopted, according to which not all junctions are active in the stress-free state. Under straining, some entanglements are transformed from their passive (dangling) state to the active state, which results in a decrease in the average length of a strand. Stress–strain relations for an elastomer and kinetic equations for the rate of transition of bonds from their flexed conformation to the extended conformation are derived by using the laws of thermodynamics. Simple phenomenological equations are suggested for the evolution of the number of active entanglements. The model is determined by five adjustable parameters which are found by fitting experimental data in uniaxial tensile tests. Fair agreement is demonstrated between the results of numerical simulation and observations for a polysulfide elastomer reinforced with polystyrene particles and two natural rubber vulcanizates with different cross-linkers.