周期性蜂窝材料微极等效模型及其微观应力的一种快速算法

将周期性蜂窝材料等效为具有非局部本构的微极连续介质,以解释实验中出现的尺度效应和边界层效应.在评论相关的多种不同方法(能量法、体积平均的均匀化法等)之后,提出了一种基于位移连续和单胞力平衡的推导微极等效本构参数的新方法.以正方形单胞制成的结构为例,在不同的结构与单胞尺寸比下,考虑承受集中点载荷、均布轴力和均布剪力三种载荷工况,比较了离散完全计算、经典连续介质等效和不同微极连续体等效本构的计算结果,建议了较好的微极本构参数值.数值模拟表明,集中点载荷和剪切载荷作用时,在加载点附近和边界部分,微极等效可以显著提高计算精度.最后,给出了一种映射算法,可以根据微极等效连续体分析的结果,快速计算出对应微观单胞构件的应力,以开有圆孔的方板应力集中为例,验证并考察了所提快速算法的有效性和计算精度.     

偶应力理论的等效量定义

从应力和偶应力、外加面力和体力、外加面力偶矩和体力偶矩满足的平衡方程及其边界条件出发,讨论应力和偶应力场的静力学性质.由此导出代表性体积上等效应力和等效偶应力的定义,给出它们与相应的体积平均值间的差异.用本文给出的等效应力和等效偶应力的定义,单位体积上虚功的表达式与均匀介质具有同一性.如果用体积平均值作为等效应力和等效偶应力的定义,则虚功的表达式与均匀介质不具有同一形式.     

基于应变梯度理论的微尺度蜂窝等效模量计算方法

本文提出了一种新的能够计及尺度效应的微纳米蜂窝等效模量的计算方法。将一种单参数应变梯度理论引入到本构方程当中,并基于能量等效原理推导了蜂窝面内等效模量地计算公式。算例分析表明,本文方法能够有效地计及尺度效应对蜂窝等效模量的影响。尺度效应与胞壁厚度和长度的值都有关,当胞壁厚度较小时,尺度效应显著,本文方法预测的模量会明显高于传统方法;而当胞壁厚度较大时,尺度效应变得微弱乃至可以忽略不计。但如果胞壁的长度/厚度比很大,则面内等效模量会趋近于0,此时是否考虑尺度效应意义不大。     

类石墨烯二维原子晶体的微态理论模型

基于微态(Micromorphic) 连续介质理论,提出了针对类石墨烯二维原子晶体的新力学模型. 该模型以有限大小的布拉维单胞为基元体,考虑基元粒子的宏观位移和微观变形,依据微态理论基本方程,推导了全局坐标系下模型的主导方程. 然后针对布拉维单胞中含有两个原子的类石墨烯晶体,通过分析单胞中声子振动模式与基元体自由度的关系,获得了微态形式下声子色散关系的久期方程,并根据二维晶体声子色散特性对久期方程进行了简化,进而确定了类石墨烯晶体模型的本构方程. 最后,以石墨烯和单层六方氮化硼为例,利用简化的表达式拟合了它们面内声子色散关系数据,计算了模型材料的常数,石墨烯模型的等效杨氏模量、泊松比分别为1.05 TPa 和0.197,氮化硼分别为0.766 TPa 和0.225,均与已有的实验值相符合.      

一种孔隙介质力学模型及在水泥基材料的应用

基于细观力学和断裂力学的基本理论提出一个新的分析模型, 对孔隙介质的力学性能进行了分析. 依据孔隙介质内部孔隙的几何描述和状态参数,如孔隙率、形状、尺度及分布等,通过等效夹杂理论获得孔隙介质的等效本构方程,其最终变量为应力、应变和孔隙的形态参数. 根据断裂理论中材料承受载荷作用下破坏增长过程中的能量守恒,对孔隙介质变形过程中机械能、弹性应变能和载荷提供的势能进行分析, 根据能量守恒定律建立能量守恒方程,其最终变量也为应力、应变和孔隙的形态参数. 根据等效本构方程和能量守恒方程,获得孔隙介质承受载荷作用下的应力应变关系. 最后将该力学模型应用于水泥基材料,计算水泥基材料的力学性能并与文献中的结果进行对比分析,结果显示模型的计算结果准确有效.      

水饱和花岗岩本构模型及地下爆炸波的数值研究

采用广义自洽方法描述介质的细观几何结构,基于混合物理论建立了水饱和岩石含损伤弹塑性本构模型,提出了一个适用于爆炸波数值计算的饱和水体积分数演化方程,也即给出了本构关系中的闭合方程.使用Biot有效应力描述水压对岩石强度的影响,在有效应力空间里建立了水饱和岩石剪切屈服和破坏的强度准则,并引入了剪胀效应对强度的影响因子.对地下封闭核爆炸的力学效应开展了数值模拟,系统地研究了含水花岗岩中地下爆炸波的传播特征以及含水量对爆炸应力波传播规律的影响.     

金属橡胶材料基于微弹簧组合变形的细观本构模型

研究了金属橡胶材料细观本构模型。依据金属橡胶材料变形的主要特征,分析了微弹簧沿轴向和径向变形的规律,分别推导了应力应变关系的解析表达式,由两种微弹簧的组和变形构造了代表性体积单元-微元体。为了反映因铺层引起的工艺各向异性,本构方程中引入了一个新的材料参数铺层比例系数iβ,该参数可以较好地表征细观结构中微弹簧取向的分布状况。在大量试验的基础上,提出了确定铺层系数的实验方法,进而建立了包含金属橡胶材料细观结构信息的本构方程。理论与实验结果比较表明,本文建立的本构模型能较好的反映材料的力学行为。     

水饱和岩石中爆炸应力波传播的数值模拟

基于连续介质力学和不相融混合物理论,假定组分间无相对运动,采用B-W-N-B有效应力准则,在屈服面中引入孔隙影响因子,提出了一种多孔含水介质流固耦合的本构模型,并给出了孔隙的演化方程,对水饱和凝灰岩介质中的爆炸应力波传播作了数值模拟。数值计算给出的应力波形与实测结果有良好的一致性。采用本文中所述流固耦合本构模型,可很好地预测水饱和岩石中爆炸波的演化规律。     

率相关本构方程积分新算法

提出一种积分率相关本构方程的隐式积分新算法,引入0～1范围内的缩放因子λ对本构方程进行间接求解,可以避免直接求解等效塑性应变或等效塑性应变率时,由于其数值过大或过小而造成的收敛困难或收敛失败,实现对率相关本构方程的快速准确求解.以B-P统一本构方程及双曲正弦本构方程为例,验证了算法的可行性.结果表明,新算法对于准静态变形条件下的无硬化本构方程也可以得出准确的解.     

两相混合流体的非线性本构理论

本文从连续介质力学的基本原理出发,建立了微极流体与经典流体两相流动的非线性扩散理论。给出了混合流体本构方程的一般形式。对单相流体、单相微极流体及稀悬浮体三种特殊情形,得到了具体形式的二阶非线性本构方程,并同已有的理论进行了比较。     

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

In this paper, the periodic structure material is modeled as the continuum homogeneous micro-polar media subjecting to thermo-mechanical interaction. Meanwhile, a series of equivalent quantities such as the equivalent stress, couple stress, displacement gradient and torsion tensor were defined by the integral forms of the boundary values of the external surface force, moment, displacement and the angular displacement, and were proved to satisfy the equivalence conditions of virtual work. Based on above works, the displacement boundary value problem was established to deduce the equivalent constitutive equation. Assume the representative volume element is composed of the spatial cross-framework, and applying the boundary value problem of displacement on frame structures, the equivalent elastic coefficients, temperature coefficients of equivalent stress and the temperature gradient coefficients of equivalent couple stress are deduced. In addition, themethod can also be extended to the stress boundary value problem to deduce the equivalent constitutive equation. The calculations indicate that the equivalent result can be obtained from the two kinds of boundary value problems.     

A nonlinear finite element model for the stress analysis of soft solids with a growing mass

The paper presents a new finite element (FE) model for the stress analysis of soft solids with a growing mass based on the work of Lubarda and Hoger (2002). Contrary to the traditional numerical methods emphasizing on the influence of growth on constitutive equations, an equivalent body force is firstly detected, which is resulted from the linearization of the nonlinear equation and acts as the driver for material growth in the numerical aspect. In the algorithm, only minor correction on the traditional tangent modulus is needed to take the growth effects into consideration and its objectivity could be guaranteed comparing with the traditional method. To solve the resulted equation in time domain, both explicit and implicit integration algorithms are developed, where the growth tensor is updated as an internal variable of Gauss point. The explicit updating scheme shows higher efficiency, while the implicit one seems to be more robust and accurate. The algorithm validation and its good performance are demonstrated by several two-dimensional examples, including free growth, constrained growth and stress dependent growth.     

压电、压磁材料球对称问题的通解

研究压电、压磁材料在球坐标系下,不计体力、体电荷和体电流的情况下,由平衡方程、梯度方程、压电和压磁的本构方程导出应力、应变、位移、电位移、电场强度、电位势、磁感强度和磁位势各未知量的通解．考虑不同的边界条件,将其通解应用到应力、电学短路以及位移、电学开路和磁场分布的边界条件中,得到不同边界条件下问题的解。     

One-dimensional deformation waves in nonlinear viscoelastic media

This paper is concerned with wave propagation processes in viscoelastic media. The constitutive equation is assumed to be dependent on the strain history, and physical and geometrical nonlinearities are taken into account. Using two equivalent forms of the constitutive equation, the corresponding transport equations are derived along the characteristics of a linear associated process. The high-frequency and low-frequency processes are investigated by making use of the asymptotic transport equations. The similarity of the results obtained by this method and by the singular surface theory is shown and the critical strain gradients derived by both methods are compared. The influence of inhomogeneity of the medium is discussed.     

Elastodynamic analysis of inhomogeneous anisotropic bodies

The integral equation method is presented for elastodynamic problems of inhomogeneous anisotropic bodies. Since fundamental solutions are not available for general inhomogeneous anisotropic media, we employ the fundamental solution for homogeneous elastostatics. The terms induced by material inhomogeneity and inertia force are regarded as body forces in elastostatics, and evaluated in the form of volume integrals. The scattering problems of elastic waves by inhomogeneous anisotropic inclusions are investigated for some test cases. Numerical results show the significant effects of inhomogeneity and anisotropy of materials on wave propagations.     

An analytical homogenization method for heterogeneous porous materials

The objective of this work is to develop an analytical homogenization method to estimate the effective mechanical properties of fluid-filled porous media with periodic microstructure. The method is based on the equivalent inclusion concept of homogenization applied earlier for solid–solid mixture. It is assumed that porous media are described by the poroelastic constitutive law developed by Biot where porosity is a material parameter. By solving the governing equations of poroelasticity in Fourier transformed domain, the relation between periodic strain and eigenstrain in porous media is established. This relation is subsequently used in an average consistency condition involving both solid and fluid phase stresses and strains. The geometry of the porous microstructure is captured in the g-integral. This homogenization method can also be applied to estimate the equivalent properties of solid–fluid mixture where a pure solid and fluid can be modeled by assuming very low and high porosity, respectively. Several examples are considered to establish this new method by comparing with other existing analytical and numerical methods of homogenization. As an application, poroelastic properties of cortical bone fibril are estimated and compared with previously computed values.     

Stress intensity factors of a rectangular crack meeting a bimaterial interface

Using the hypersingular integral equation method based on body force method, a planar crack meeting the interface in a three-dimensional dissimilar materials is analyzed. The singularity of the singular stress field around the crack front terminating at the interface is analyzed by the main-part analytical method of hypersingular integral equations. Then, the numerical method of the hypersingular integral equation for a rectangular crack subjected to normal load is proposed by the body force method, which the crack opening dislocation is approximated by the product of basic density functions and polynomials. Numerical solutions of the stress intensity factors of some examples are given.     

The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials

Residual stress is the stress present in the unloaded equilibrium configuration of a body. Because residual stresses can significantly affect the mechanical behavior of a component, the measurement of these stresses and the prediction of their effect on mechanical behavior are important objectives in many engineering problems. Common methods for the measurement of residual stresses include various destructive experiments in which the body is cut to relieve the residual stress. The resulting strain is measured and used to approximate the original residual stress in the intact body. In order to predict the mechanical behavior of a residually stressed body, a constitutive model is required that includes the influence of the residual stress.In this paper we present a method by which the data obtained from standard destructive experiments can be used to derive constitutive equations that describe the mechanical behavior of elastic residually stressed bodies. The derivation is based on the idea that for each infinitesimal neighborhood in a residually stressed body, there exists a corresponding stress free configuration. We refer to this stress free configuration as the virtual configuration of the infinitesimal neighborhood. The derivation requires that the constitutive equation for the stress free material be known and invertible; it is used to relate the residual stress to the deformation of the virtual configuration into the residually stressed configuration. Although the concept of the virtual configuration is central to the derivation, the geometry of this configuration need not be determined explicitly, and it need not be achievable experimentally, in order to construct the constitutive equation for the residually stressed body.The general mathematical forms of constitutive equations valid for residually stressed elastic materials have been derived previously for a number of cases. These general forms contain numerous unknown material-response functions or material constants that must be determined experimentally. In contrast, the method presented here results in a constitutive equation that is an explicit function of residual stress and includes only the material parameters required to describe the stress free material.After presenting the method for the derivation of constitutive equations, we explore the relationship between destructive experiments and the theory used in the derivation. Specifically, we discuss the use of the theory to improve the design of destructive experiments, and the use of destructive experiments to obtain the data required to construct the constitutive equation for a particular material.