一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

From Single-Phase to Compositional Flow: Applicability of Mixed Finite Elements

In this paper we discuss the formulation of the governing equations that describe flow of fluids in porous media. Various types of fluid flow, ranging from single-phase flow to compositional flow, are considered. It is shown that all the differential equations governing these types of flow can be effectively rewritten in a fractional flow formulation; i.e., in terms of a global pressure and saturation (or saturations), and that mixed finite element methods can be accurately exploited to solve the pressure equation. Numerical results are presented to see the performance of the mixed methods for the flow equations in three space dimensions.     

Dimensions of attractors for discretizations for Navier-Stokes equations

In this paper, we discretize the 2-D incompressible Navier-Stokes equations with the periodic boundary condition by the finite difference method. We prove that with a shift for discretization, the global solutions exist. After proving some discrete Sobolev inequalities in the sense of finite differences, we prove the existence of the global attractors of the discretized system, and we estimate the upper bounds for the Hausdorff and the fractal dimensions of the attractors. These bounds are indepent of the mesh sizes and are considerably close to those of the continuous version.     

基于物理界面的双重介质有限裂隙渗流模型

基于连续介质或者离散裂隙假设,含裂隙的多孔介质渗流问题有多种数学力学模型。受物理界面的启发,提出一种新的有限裂隙连续介质力学模型,可以为宏观裂隙-多孔介质内的流体输运问题等提供近似计算方案。该模型属于一类双重介质模型,将曲面上低维度的流场转化为三维空间的流场,并且与连续的多孔介质的流场耦合,在数学上表示为统一的输运控制方程和初始边界条件。这个近似模型为不方便实施高维度-低维度耦合求解的数值计算方法提供新的模拟思路,如光滑粒子流体动力学等无网格粒子类方法。     

Kinematically exact curved and twisted strain-based beam

The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the constant strain field along the element. The relation between the total three-dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed. The analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential. Despite the analytical relationship between rotations and rotational strains, the governing equations of the beam are in general too demanding to be solved analytically. A finite-element strain-based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals. Some interesting connections between quantities and non-linear expressions of the beam are revealed. These relations can also serve as useful guidelines in the development of new finite elements, especially in the choice of suitable shape functions.     

On the Permeability of Fractal Tube Bundles

The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions, and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability?Cporosity relationships represented by the Kozeny?CCarman equations and Archie??s law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The aim of this article is the evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the tube bundles generated by finite iterations of the corresponding geometric fractals can be used to model porous media where the permeability?Cporosity relationships are derived analytically. Several examples of the tube bundles are constructed, and the relevance of the derived permeability?Cporosity relationships is discussed in connection with the permeability measurements of highly porous metal foams reported in the literature.     

基于参数变分原理的Cosserat连续体弹塑性分析

基于参数变分原理,提出了Cosserat模型弹塑性计算的算法,给出了基于Cosserat理论的参数最小势能原理,基于所提出的变分方程,建立了Cosserat理论弹塑性分析的参数二次规划模型,进一步将算法应用于平面应变软化问题计算中,获得的结果具有良好的非网格依赖性.     

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF COSSERAT CONTINUUM

A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy principle of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.     

两种弹性损伤模型的基本方程与色散关系讨论

分析了传统连续介质损伤理论的控制方程在损伤过程中的变化特点,方程类型的改变导致错误预测波不能在损伤区域传播.二阶隐式应变梯度损伤理论是对传统理论的一种改进,严格证明了其控制方程在损伤过程中类型不变,这意味着损伤区域能传播波,同时有助于克服病态的网格相关性.色散分析结果表明:传统连续介质损伤理论不能反映色散现象,隐式梯度模型可以并对波长有上限截断作用.     

非饱和多孔介质中热-渗流-力学耦合的混合元法

提出了一个非饱和多孔介质中热-渗流-力学耦合分析的混合有限元 方法. 固相位移、应变和净应力；孔隙水和气的压力、压力空间梯度和Darcy速度；多相混 合介质的温度、温度空间梯度和热流量在单元内均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多孔介质中热-渗流-力学耦合问题控制方程的单元弱形式，导 出了单元公式. 采用共旋公式进行几何非线性分析. 数值结果证明了所提出的单元模拟以 应变局部化为特征的渐进破坏的能力     

A parallel monolithic algorithm for the numerical simulation of large‐scale fluid structure interaction problems

A novel parallel monolithic algorithm has been developed for the numerical simulation of large‐scale fluid structure interaction problems. The governing incompressible Navier–Stokes equations for the fluid domain are discretized using the arbitrary Lagrangian–Eulerian formulation‐based side‐centered unstructured finite volume method. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant–Kirchhoff material, and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. A special attention is given to construct an algorithm with exact total fluid volume conservation while obeying both the global and the local discrete geometric conservation law. The resulting large‐scale algebraic nonlinear equations are multiplied with an upper triangular right preconditioner that results in a scaled discrete Laplacian instead of a zero block in the original system. Then, a one‐level restricted additive Schwarz preconditioner with a block‐incomplete factorization within each partitioned sub‐domains is utilized for the modified system. The accuracy and performance of the proposed algorithm are verified for the several benchmark problems including a pressure pulse in a flexible circular tube, a flag interacting with an incompressible viscous flow, and so on. John Wiley & Sons, Ltd.     

On the mechanics of solids with a growing mass

A general constitutive theory of the stress-modulated growth of biomaterials is presented with a particular accent given to pseudo-elastic soft living tissues. The governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics. The multiplicative decomposition of the deformation gradient into its elastic and growth parts is employed to study the growth of isotropic, transversely isotropic, and orthotropic biomaterials. An explicit representation of the growth part of the deformation gradient is given in each case, which leads to an effective incremental formulation in the analysis of the stress-modulated growth process. The rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function. Physically appealing structures of the stress-dependent evolution equations for the growth induced stretch ratios are proposed.     

A class of elastic-plastic stress distributions

Similarity methods are used to find solutions to the equations governing elastic-plastic torsion of a solid of revolution. The solutions are expressed in terms of integrals of two ordinary differential equations.     

Simulation of elastic wave propagation using cellular automata and peridynamics,and comparison with experiments

Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’s Problem. The results are compared with theoretical solution from classical elasticity and experimental results. This paper is used to validate our implementation of these methods.     

Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids

Based on the Theory of Porous Media (TPM), a formulation of a fluid-saturated porous solid is presented where both constituents, the solid and the fluid, are assumed to be materially incompressible. Therefore, the so-called point of compaction exists. This deformation state is reached when all pores are closed and any further volume compression is impossible due to the incompressibility constraint of the solid skeleton material. To describe this effect, a new finite elasticity law is developed on the basis of a hyperelastic strain energy function, thus governing the constraint of material incompressibility for the solid material. Furthermore, a power function to describe deformation dependent permeability effects is introduced.After the spatial discretization of the governing field equations within the finite element method, a differential algebraic system in time arises due to the incompressibility constraint of both constituents. For the efficient numerical treatment of the strongly coupled nonlinear solid-fluid problem, a consistent linearization of the weak forms of the governing equations with respect to the unknowns must be used.     

A deformational and configurational framework for geometrically non-linear continuum thermomechanics coupled to diffusion

A general framework encompassing both the (conventional) deformational and configurational settings of continuum mechanics is presented. A systematic application of balance principles over a migrating control volume in the undeformed configuration of the continuum body yields the system of governing equations in the bulk, on the surface and on a coherent interface within the continuum. The equations governing the response of the bulk agree with those of the conventional deformational approach. The localised balance equations are expressed in the configurational setting using a pull-back operator and reformulated in terms of the Eshelby stress. The configurational expression of the dissipation elucidates the energy loss associated with configurational changes. The general framework is introduced by considering the problem of coupled deformation, heat conduction and species diffusion within a geometrically non-linear continuum body intersected by a coherent interface. The nature of the coupling is emphasised throughout the presentation and via an example.     

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．     

多孔介质输运性质的分形分析研究进展

首先对多孔介质输运性质的传统实验测量、解析分析和数值模拟计算研究进展作了扼要的评述.然后,着重综述采用分形理论和方法研究多孔介质输运性质分析解的理论、方法和所取得的进展.最后,指出采用分形理论和方法有可能解决其它尚未解决的有关多孔介质输运性质的若干课题和方向.      

欧拉描述的大变形固结理论

以往大变形固结理论主要基于一般的固体力学模型,其控制方程忽视了固结过程中排水引起 的质量变化. 提出饱和土的连续介质模型,并基于连续介质力学的公理体系推导了反映质量 变化的欧拉描述的大变形固结控制方程. 发现传统固结理论中：(1)忽视了渗流速度对土体平衡条件的影响;(2)决定土体平衡的总应力张量只有在土体变形速度和渗流速度方向相同时才具有对称性等. 在忽略变质量效应等条件下,传统理论成为本文理论的特例. 通过算例 的有限元分析,比较了欧拉描述与两种物质描述方法的差别,得到初步结论：(1)欧拉描述 方法计算的地基沉降量要小于物质描述方法的结果;(2)欧拉描述方法计算的侧向位移偏大 于两种物质描述结果.