复合固体推进剂黏弹性微裂纹损伤本构模型

为建立复合固体推进剂的损伤本构模型,在介观尺度上视其为微裂纹损伤,选取微裂纹密度为损伤内变量。在Abdel-Tawab本构方程的基础上,基于微裂纹均匀化理论,推导了损伤映射张量的一般形式。该张量通常具有非完全对称性,其物理意义是将真实应力空间中各向异性材料的多轴加载映射为等效应力空间中各向同性材料的更为复杂的多轴加载。其次,基于黏弹性动态裂纹扩展模型和裂纹扩展阻力曲线的概念,建立了损伤内变量的演化方程。该演化方程仅含4个物理意义明确的细观参数,并且参数的取值规律与宏观应力曲线的变化规律相一致。数值结果表明,建立的模型能够有效反映材料损伤的应变率、温度依赖性及各向异性特征,并且具有一定的蠕变损伤预测能力。     

各向异性双重孔隙介质的应力与油水两相渗流耦合理论模型

针对天然裂缝性油藏的特性,建立了描述双重孔隙介质中油水两相流体流动特性的流固耦合理论模型。该模型不仅考虑了渗透率的各向异性,而且考虑了岩石固体骨架变形的各向异性。渗流方程是依据双重孔隙的概念建立起来的,而固体骨架变形控制方程则是根据Biot 的等温、线性孔隙弹性理论建立起来的。同时,给出了横向各向同性及结构各向异性、固体材料各向同性时的双重孔隙介质的应力与油水两相渗流耦合理论模型。对该模型进行了简化,并将其简化后模型与单相流的各项同性和各向异性双重孔隙介质流固耦合理论模型进行了比较。     

岩石类材料裂隙形成和扩展的相场方法模拟

相场方法通过定义一个连续分布函数来近似表示自由不连续裂纹,在此基础上建立最小能量变分框架,从而得到描述裂纹发展的控制方程。不需要提前设定裂纹的形状、尺寸和方向,相场方法就能很好地描述裂纹的形成和扩展,为利用数值方法模拟裂纹扩展提供了一个严谨准确的理论框架。该文首次将相场方法用于模拟岩石裂隙扩展问题,预测包含不同岩桥倾角的预制双裂隙岩石类材料在单轴压缩作用下的损伤和破坏过程,并与室内试验结果进行对比。结果表明相场方法非常适合模拟岩石类材料内部复杂裂隙的萌生、扩展和连接过程,在岩体工程稳定性分析领域具有广阔的应用前景。     

含裂纹夹杂多孔材料的渗透性理论与数值分析

多孔材料的裂纹网络对宏观渗透性的影响显著,正确描述裂纹网络对材料渗透率的影响具有重要的工程意义。该文将开裂多孔材料视作由多孔基体和裂纹夹杂二相组成的复合材料,基于细观力学理论模型中的相互作用直推法(IDD)给出了渗透率张量的IDD理论解。为分析裂纹长度、密度、取向、间距和连通度等裂纹网络细观形貌参数对宏观渗透率的影响,该文使用具有周期结构的重复单元模型建立了二维数值分析模型,采用有限单元法进行数值求解并与IDD理论解进行了对比验证。理论研究表明,IDD理论模型采用单一的开裂密度指标来表征多孔介质的裂纹网络,在开裂密度不大时能够统一地描述裂纹长度、取向、平均横向间距和纵向间距等多个细观形貌指标对材料整体渗透性能的影响,具有良好的适用性和精度;数值分析表明,在裂纹网络的密度不断增大、裂纹相互趋近并最终连通的过程中,IDD理论解逐渐偏离数值解并低估裂纹间相互作用,此时材料渗透率与裂纹密度呈对数关系;网络裂纹一旦连通,整体渗透率则发生突变,此时渗透率的确定需要特别考虑连通裂纹之间的强烈近场相互作用。     

弹性损伤理论的几何-拓扑描述

材料内部微观几何缺陷通常是作为物理非线性问题在本构方程中考虑。针对连续介质弹性损伤理论作几何拓扑,采用非完整标架方法把材料内部微观几何缺陷转化为材料空间的弯曲,并体现在基本几何法则中。首先由连续损伤变量定义拟塑性张量,给出这些基本张量所满足的连续性方程和基本几何法则。由此建立了弹性损伤缺陷与Riemann流形的对应关系,将物理非线性问题转化为物理线性和材料所在空间的弯曲之和。最后讨论了二维情况下,各向同性晶格材料受各向异性损伤的算例。     

三维五向编织复合材料渐进损伤分析的数值方法

基于连续损伤理论, 推导了含损伤裂纹的正交各向异性材料的应力-应变关系。建立了考虑界面脱粘破坏的三维五向编织复合材料细观体胞模型, 并将有限元网格尺寸和单元裂纹尺寸引入损伤演化方程。采用Hashin准则和von-Mises准则分别判断纱线与基体的初始损伤, 结合Eshelby-Mori-Tanaka方法确定材料的刚度退化系数。利用ANSYS有限元软件对材料进行渐进损伤分析, 得到了材料在单向拉伸作用下的应力-应变曲线和极限强度。计算结果表明, 轴纱为材料的主要承力部分, 小编织角材料的破坏模式主要为纱线的拉伸断裂, 界面破坏情况较为严重。模拟计算结果与实验结果吻合较好。     

双曲超材料及其传感器研究进展

超材料为具有超常电磁性质的人工结构,因拥有自然界材料没有的介电常数、磁导率和折射率等电磁性质而引起人们的关注。双曲超材料是具有强各向异性介电张量或磁导率张量的介质,其介电常数张量或磁导率张量的分量在一个或两个空间方向上为负,与其他类型的超材料相比,双曲超材料具有在光学频率下相对容易制造、宽带非共振和三维体响应以及灵活的波长可调谐性等优点。本文综述了双曲超材料的特性、实现方法、可调谐及活性以及其作为超灵敏传感器的发展,重点讨论了基于金属/介质多层结构及金属纳米线阵列的双曲超材料作为生物传感器的原理及研究进展,并指出双曲超材料传感器发展的长期目标是结构简单、便于制备、宽频带和多元分析。     

基于非共轴理论的各向异性砂土应变局部化分析

针对各向异性砂土应变局部化分析中本构模型存在的不足,采用非共轴理论进行改进。传统塑性位势理论采用各向同性假设,导致其模型不能描述非共轴特性和不能较好描述各向异性的不足,为克服传统塑性势理论的局限性,引入非共轴塑性理论建立了砂土的三维非共轴临界状态各向异性本构模型。考虑细观组构张量和应力张量的几何关系,改进模型即可描述主应力轴旋转条件下砂土材料状态的改变,材料状态变化直接导致模型的硬化规律和剪胀性发生变化,从而描述了原生各向异性的影响。非共轴修正后模型可以描述应力诱发各向异性和非共轴特性,结合分叉理论模型可以对不同沉积角度随围压变化的应变局部化特性进行分析。Toyoura砂的单剪试验和平面应变试验验证表明模型改进效果较好。     

基于二阶组构张量的各向异性屈服准则

将四个屈服准则:Tresca准则、Mises准则、Mohr-Coulomb准则以及Drucker-Prager准则归类为剪切屈服准则。Tresca准则和Mohr-Coulomb准则是关于最不利截面的剪切屈服准则,而Mises准则和Drucker-Prager准则是关于各方向截面的剪应力和正应力的某种综合度量的八面体剪应力和八面体正应力的剪切屈服准则。从方向函数(ODF)的概念入手,将各方向截面的剪应力和正应力综合度量直接取为所有方向截面上的剪应力和正应力的平均。对各向同性材料,提出了平均剪切屈服度准则:当平均剪应力和平均正应力的组合达到某一极限值时,材料开始屈服。研究表明,平均剪切屈服准则与Drucker-Prager准则具有相同的形式,当不考虑平均正应力对屈服的影响时,它与Mises准则具有相同的形式。针对由各向异性损伤导致的材料各向异性强度问题,定义截面上的有效正应力和有效剪应力则分别为截面上的法向力和切向力与有效承载面积之比,基于截面上的有效应力提出了各向异性材料的平均剪切屈服准则。各向异性损伤引起的截面上有效应力放大系数为方向函数,可以采用二阶组构张量来近似表示,在任意坐标系中,各向异性屈服准则为应力分量的二次齐次式,导出了其中的系数与二阶组构张量之间的显式关系式。在二阶组构张量的主轴坐标系内,各向异性屈服准则与殷有泉的拓展Hill准则形式完全相同,当不考虑正应力对屈服的影响时,它与Hill准则具有相同的形式。     

裂隙岩体非稳态渗流场与损伤场耦合分析模型

从流体扩散能量叠加原理出发，建立了裂隙岩体介质的尖流张量解析表达式。综合应用断裂力学与损伤理论，探讨了复杂应力状态一湍体在压前、拉剪应力状态下损伤的演化方程，提出了渗透胀量随裂隙损伤发展的关系以及裂隙岩体非稳态渗流场与损伤场事模型。     

Mixture theory-based poroelasticity as a model of interstitial tissue growth

This contribution presents an alternative approach to mixture theory-based poroelasticity by transferring some poroelastic concepts developed by Maurice Biot to mixture theory. These concepts are a larger RVE and the subRVE-RVE velocity average tensor, which Biot called the micro–macro velocity average tensor. This velocity average tensor is assumed here to depend upon the pore structure fabric. The formulation of mixture theory presented is directed toward the modeling of interstitial growth, that is to say changing mass and changing density of an organism. Traditional mixture theory considers constituents to be open systems, but the entire mixture is a closed system. In this development the mixture is also considered to be an open system as an alternative method of modeling growth. Growth is slow and accelerations are neglected in the applications. The velocity of a solid constituent is employed as the main reference velocity in preference to the mean velocity concept from the original formulation of mixture theory. The standard development of statements of the conservation principles and entropy inequality employed in mixture theory are modified to account for these kinematic changes and to allow for supplies of mass, momentum and energy to each constituent and to the mixture as a whole. The objective is to establish a basis for the development of constitutive equations for growth of tissues.     

The stresses in the neighborhood of a crack tip under effects of electromagnetic forces

In recent work, some basic problems of the stresses in the neighborhood of a crack tip under the effects of electromagnetic forces are studied, and the basic concept of Maxwell electromagnetic stress tensor is illustrated and used to express the effects of the electromagnetic field to the solid body. The basic governing equations of elastic stress of both potential electromagnetic force and Maxwell stress tensor and the approaches for solving these equations are provided. Two kinds of affects of the electromagnetic field on stress singularity of a crack tip are presented and analyzed. Lastly, several examples about the stress analysis on the effects of the electromagnetic field are provided     

Edge stabilization and consistent tying of constituents at Neumann boundaries in multi‐constituent mixture models

A mixture‐theory‐based model for multi‐constituent solids is presented where each constituent is governed by its own balance laws and constitutive equations. Interactive forces between constituents that emanate from maximization of entropy production inequality provide the coupling between constituent‐specific balance laws and constitutive models. The deformation of multi‐constituent mixtures at the Neumann boundaries requires imposing inter‐constituent coupling constraints such that the constituents deform in a self‐consistent fashion. A set of boundary conditions is presented that accounts for the non‐zero applied tractions, and a variationally consistent method is developed to enforce inter‐constituent constraints at Neumann boundaries in the finite deformation context. The new method finds roots in a local multiscale decomposition of the deformation map at the Neumann boundary. Locally satisfying the Lagrange multiplier field and subsequent modeling of the fine scales via edge bubble functions result in closed‐form expressions for a generalized penalty tensor and a weighted numerical flux that are free from tunable parameters. The key novelty is that the consistently derived constituent coupling parameters evolve with material and geometric nonlinearity, thereby resulting in optimal enforcement of inter‐constituent constraints. Various benchmark problems are presented to validate the method and show its range of application. Copyright © 2016 John Wiley & Sons, Ltd.     

Mixture theory for a thermoelasto-plastic porous solid considering fluid flow and internal mass exchange

A thermoelastic–plastic body consisting of two phases, a solid and a fluid, each comprising two constituents is considered where one constituent in one phase is allowed to exchange mass with another constituent (of the same substance) in the other phase. A large strain setting is adopted and the formulation applies to general anisotropy and the existence of residual stresses. Generalized forms of Fourier’s, Fick’s and Darcy’s laws are derived and also the stresses on the constituent, phase and mixture level are established; in addition, the evolution law for general plasticity is given. Finally, and in particular, a general evolution law for the rate of deformation tensor related to mass exchange is proposed and this leads to general absorption and desorption evolution laws for mass exchange between two constituents (of the same substance), one belonging to the solid phase and the other to the fluid phase. Equilibrium curves for absorption and desorption also emerge from the theory.     

Micromechanical identification of anisotropic damage evolution laws

This paper deals with the establishment of anisotropic conjugate force based damage evolution laws in the framework of Rice's (1971) ‘normality structure’. The damage variable is the second-order crack tensor (Kachanov, 1980), which represents preexisting Griffith microcracks in a solid. The principal results include the deduced damage surfaces, potentials and kinetic equations for the basic internal variables and damage tensor during isothermal processes. The generalized pth order crack tensors and qth order energy release rates are introduced. The deduction in this paper is fully independent of the specific form of the free energy or Gibbs energy functions, so the deduced damage evolution laws have a wide applicable range including plasticity. Using the deviatoric stress as the conjugate force, the two well-established anisotropic yield surfaces, Karafillis and Boyce (1993) and Hill (1950), are recovered from the deduced damage surface. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling arbitrary crack propagation in coupled shell/solid structures with X‐FEM

In this paper, the extended finite element method (X‐FEM) formulation for the modeling of arbitrary crack propagation in coupled shell/solid structures is developed based on the large deformation continuum‐based (CB) shell theory. The main features of the new method are as follows: (1) different kinematic equations are derived for different fibers in CB shell elements, including the fibers enriched by shifted jump function or crack tip functions and the fibers cut into two segments by the crack surface or connecting with solid elements. So the crack tip can locate inside the element, and the crack surface is not necessarily perpendicular to the middle surface. (2) The enhanced CB shell element is developed to realize the seamless transition of crack propagation between shell and solid structures. (3) A revised interaction integral is used to calculate the stress intensity factor (SIF) for shells, which avoids that the auxiliary fields for cracks in Mindlin–Reissner plates cannot satisfy exactly the equilibrium equations. Several numerical examples, including the calculation of SIF for the cracked plate under uniform bending and crack propagation between solid and shell structures are presented to demonstrate the performance of the developed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Acoustic emission theory for moment tensor analysis

Acoustic emission (AE) is extensively applied to nondestructive evaluation of materials and structures. In the conventional AE measurement, several AE parameters are detected and analyzed to elucidate characteristics of microfracturing behaviors in materials.Although theoretical treatment of AE waveforms was proposed more than one decade ago, the quantitative analysis was neither practical nor applicable to general AE waveforms. The crack mechanisms associated with AE generation consist of crack kinetics and crack kinematics. It has already been demonstrated that deconvolution analysis is available for determining crack kinetics. As for crack kinematics, it is known that the moment tensor analysis is promising, but has only been applied to marginal cases. In this respect, a practical procedure for the moment tensor analysis is recently formulated, selecting P wave portion from the full-space Green's function of homogeneous and isotropic material. A multi-channel observation is utilized to locate AE sources, based on arrival time differences of AE waves. Furthermore, a simplified moment tensor analysis is performed by analyzing the amplitudes of the first motions.It is clarified that the eigenvalues of general moment tensor components are available for classifying crack types and for determining crack orientations. To implement these results into an analytical procedure, a unified decomposition of the eigenvalues is proposed.With the emphasis on the development of this practical procedure for the moment tensor analysis, the theory of AE for the source characterization is reviewed. The results of a geological application and a test of reinforced concrete are discussed. A post-analysis is attempted to screen out poor solutions by comparing with theoretical solutions on the synthetic waveforms.     

Modeling of thermal mass transfer in porous media with applications to the organic phase transition in landfills

In order to describe the thermomechanical behavior of landfills, a constitutive model based on the macromechanical Theory of Porous Media (TPM) for a saturated thermoelastic porous body has been developed. The body under investigation consists of an organic and inorganic solid phase and a gas phase. All interaction relations between the constituents such as mass transfers, interaction forces and energy supplies are taken into consideration. Based on a consistent thermomechanical treatment the governing equations are obtained as a set of equations which consists of the balance equations of momentum and mass for each individual constituent, the balance equation of energy for the mixture and the physical constrained conditions. In this set of macroscopic equations, several parameters are contained. They are interrelated by constitutive relationships in order to complete the system of equations. This procedure renders the set of equations solvable. Thus, we obtain a mathematical concept to describe the motion of the solid phase, the pressure of the gas phase, the temperature of the mixture and the biodegradation of organic material into a gas mixture of methane and carbon dioxide produced by bacterial decomposition during stable methane fermentation (biogas).     

A finite element analysis of plane strain dynamic crack growth at a ductile-brittle interface

In this work, steady, dynamic crack growth under plane strain, small-scale yielding conditions along a ductile-brittle interface is analysed using a finite element procedure. The ductile solid is taken to obey the J ₂ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behaviour. The objectives of this work are to establish the validity of an asymptotic solution for this problem which has been derived recently [12], and to examine the effect of changing the remote (elastic) mode-mixity on the near-tip fields. Also, the influence of crack speed on the stress fields and crack opening profiles near the propagating interface crack tip is assessed for various bi-material combinations. Finally, theoretical predictions are made for the variation of the dynamic fracture toughness with crack speed for crack growth under a predominantly tensile mode along ductile-brittle interfaces. Attention is focused on the effect of mismatch in stiffness and density of the constituent phases on the above aspects.