Elastic Deformation of Dispersely Failing Unidirectionally Reinforced Composites

A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Dependences are presented for determining all unknown constants from simple mechanical experiments. As an example, an actual unidirectionally reinforced GFRP is considered, for which the main two-dimensional sections of corresponding failure surfaces are also constructed.     

有限变形弹性圆杆中的孤波

在同时引入横向惯性和横向剪切应变的情况下,导出了有限变形弹性圆杆的非线性纵向波动方程,方程中包含了二次和三次的非线性项以及由横向剪切与横向惯性导致的两种几何弥散效应．借助Mathematica软件,利用双曲正割函数的有限展开法,对该方程和对应的截断的非线性方程进行求解,得到了非线性波动方程的孤波解,同时给出了这些解存在的必要条件．     

A Deformation Model of Brittle Failing Composites with Couple-Stresses and Disperse Microdamages

A mathematical model for calculating the relation between macroscopic strains and stresses in brittle failing 3D composites upon their arbitrary deformation is suggested. The model is based on the Voigt scheme in a differential form corrected for the effect of couple-stresses arising in the matrix of composites due to relative rotation of reinforcing fibers. The nonlinearity of composites is derived as a consequence of the progressive accumulation of disperse microdamages in the material under deformation, which lead to degradation of the mechanical properties of the composites. As an example, a ±/2 angle-ply structure is considered, and it is shown how the unknown constants for the materials of such a structure can be found from the uniaxial tension or compression curves.     

Description of the elastic deformation and degradation of elastic properties of dispersedly failing isotropic materials

A model is put forward for describing the elastic deformation of a quasi-homogeneous isotropic material capable of accumulating scattered microdamages during loading, which eventually leads to its total failure. The degree of damage of the material at a point is characterized by a centrosymmetric scalar function on the unit sphere, named the damage function, whose values depend on a dimensionless equivalent stress. This function is approximated by a fourth-rank tensor, which is used to construct a constitutive relation between stresses and strains in a differential form. By way of example, the elastic deformation of concrete and the degradation of its linearly elastic properties are described, and the basic three-dimensional sections of the corresponding strength surface are constructed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 193–208, March–April, 2006.     

有限变形弹性杆中的几何非线性波

利用有限变形理论的Lagrange描述,借助非保守系统的Hamilton型变分原理,导出了描述弹性杆中几何非线性波的波动方程．为了使非线性波动方程有稳定的行波解,计及了粘性效应引入的耗散和横向惯性效应导致的几何弥散．运用多重尺度法将非线性波动方程简化为KdV-Bergers方程,这个方程在相平面上对应着异宿鞍-焦轨道,其解为振荡孤波解．如果略去粘性效应或横向惯性,方程将分别退化为KdV方程或Bergers方程,由此得到孤波解或冲击波解,它们在相平面上对应着同宿轨道或异宿轨道．     

Deformation behavior and strength of unidirectional carbon fiber laminates

The elastic deformation behavior and the load-carrying capacity of unidirectional carbon fiber laminates under static loading at room and cryogenic (down to 77 K) temperatures are investigated. The possible ways of predicting their elastic and strength characteristics proceeding from the volume content and mechanical parameters of fibers and matrix are analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 583–598, September–October, 2006.     

A Deformation Model for Dispersely Failing Elastoplastic Unidirectionally Reinforced Composites

A calculation model is proposed for unidirectionally reinforced elastoplastic composites capable of gradually accumulating disperse microdamages under loading. The composite is assumed to be a homogeneous transversely isotropic solid. To describe its elastoplastic behavior, an incremental plasticity theory with a nonlinear combined hardening mechanism is invoked. At each point of the solid, its damage is characterized by a centrally symmetric scalar function on a unit sphere. This function is approximated by a fourth-rank tensor, which is used for describing the degradation of the elastic properties of the solid due to the accumulation of disperse microdamages. It is shown how to determine, using the known experimental data, all material constants appearing in the theoretical relations suggested.     

Experimental verification of some elastic properties of unidirectional composites

The first part of the paper deals with homogenization models of unidirectional composites, in which each phase of the material is bounded by parallel cylindrical surfaces. For a GFRP with epoxy resin and glass fibres, five elastic constants for six models of the composite are calculated. In the second part, the results of strain gauge tests, photoelasticity investigations, and scanning electron inspection are discussed. With these data, some elastic constants of the composite in tension and compression are found. A comparison of experimental and analytical results is presented. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 195–206, March–April, 2008.     

薄壳非线性变形理论

对薄壳的非线性变形,给出了应变与位移之间的精确关系.经过合理的简化,给出了壳的挠度与厚度同级的大变形基本公式.当薄壳为无限长柱形且作柱形变形时,精确地求得了壳的挠度与长度同级的大变形基本公式.     

页岩储层各向异性对水平井坍塌压力的影响

为揭示层理页岩强度各向异性对水平井井壁坍塌压力的影响规律,对取自四川盆地龙马溪组页岩钻井不同层理角度的岩芯,通过岩芯观测、偏光显微镜、扫描电镜试验分别从宏观和微观角度研究了页岩层理特征,并基于单轴抗压强度研究了页岩强度各向异性特征.层理结构发育导致页岩呈现出显著的各向异性特征,粗略地将页岩视为各向同性体及简单采用Mohr-Coulomb准则作为破坏判据,使得预测的维持井壁稳定的坍塌压力不能满足安全钻井的需要.该文在研究层理地层岩石力学特性的基础上,采用横观各向同性地层井周应力分析模型,研究了弹性模量及地应力各向异性比对井周应力的影响;并结合考虑中间主应力的Mogi-Coulomb判据,分析了井壁坍塌压力对弹性模量E和Poisson(泊松)比ν各向异性比值变化的敏感性.实例分析结果表明:弹性模量和水平地应力各向异性比值的变化会对井周应力产生较大影响;Poisson比各向异性对井壁坍塌压力没有明显影响,而弹性模量比值的变化对井壁坍塌压力影响较大;横观各向同性地层中井壁坍塌压力与储层水平和垂直方向的硬脆性强弱关系有关,弹性力学参数各向异性既有可能利于井壁稳定,也可能更易导致井壁的剪切破坏;在实际工程中应根据储层岩石水平和垂直方向的硬脆性强弱关系,确定安全钻井液密度窗口.该结果对现场施工具有很好的指导意义.     

基于S-R分解理论的变形激光频谱测量法

在傅立叶频谱分析器中,当激光正射前焦面的图象时,其后焦面上形成一个个衍射斑,即傅立叶频谱;前焦面上的图象发生变形时后焦面上的频谱亦发生改变,通过分析频谱的这种改变量就可以获得图象变形信息。以现代光学中的Fraunhofer衍射理论和有限变形的S-R分解理论为基础,论述了用激光频谱来分析测量有限应变和转动的数学力学基础、测量原理和方法以及计算机识别与处理技术,作为对这一学术思想提出者陈至达教授逝世一周年的缅怀和纪念。     

向量在微小变形中的应用

本文首先引进了在微小变形情况下弹性体中应变向量的概念,并指出一点处的应变状态可用该点处应变向量的投影形式来描述,然后对各向同性弹性体给出了应变向量和应力向量间的关系,进而推出了应变向量和应力向量重合及材料是不可压缩和条件。     

横向剪变形对具有一小圆孔的浅壳应力集中系数的影响

本文导出了分析计及横向剪变形的浅壳小孔应力集中问题的简化方程.对浅球壳和圆柱壳带一小圆孔的情况,获得了方程的级数形式通解.对均匀内压作用下的圆柱壳,求得了小圆孔边上应力集中系数的近似显式解,并计算了数值结果.     

非线性尺规近似法在圆杆颈缩局部有限变形分析中的应用

形变局部化和不稳定的研究是当前力学问题的一个热点,其中最典型的问题是圆杆拉伸颈缩和滑移带的塑性分析。传统的微小变形弹塑性力学不能彻底解决此问题。本文采用以S(应变)-R(转动)分解定理为基础的非线性尺规数值计算法,并应用计算机模拟优化技术求出圆杆拉伸轴对称塑性有限变形的局部应变分布与发展形态。     

An analysis of contact deformation of auxetic composites

The adaptive mode of frictional interaction has been studied as a self-locking effect upon contact deformation of isotropic and anisotropic auxetic materials with a negative Poisson ratio. This effect manifests itself in the fact that the bearing capacity of the joint rises with increasing shear load. In particular, the parameters of stress state (contact load, tangential stresses, slippage, etc.) were determined for a double-lap joint under conditions of compression with or with out shear. The contact interaction was analyzed by the finite-element method for three profiles of symmetrically located contact elements (plane, cylindrical, and wedge-shaped). The Poisson ratio was varied within the range theoretically admissible for isotropic elastic media. Analogous calculations were also performed for a joint with a deformed element made of an anisotropic auxetic composite, whose reinforcement angle was varied. The maximum loads, tangential stresses, and slippage are obtained as nonlinear functions of Poisson ratio (in the isotropic case) and reinforcement angle of the composite material. The stress concentration and the increased ultimate shear forces are also estimated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 681–692, September–October, 2006.     

Dispersed failure of an anisotropic flywheel

Based on a hereditary damage model of solids, the strength of a cylindrically anisotropic flywheel is calculated. By using a failure criterion, the location and time of initial failure is determined in relation to an anisotropy parameter, for which the ratio of rigidities in the tangential and radial directions is taken. The process of dispersed failure depends on the expansion intensity of the damaged zone. The boundary of the zone is the failure front, whose equations of motion are obtained in the cases of absence and presence of a residual strength for the material behind the failure front. In the second case, the damaged material is modeled by an isotropic elastic medium with considerably reduced values of strength and rigidity characteristics, and variations in the pressure on the failure front are also determined. Graphs of the radial coordinate of failure front as a function of time are constructed and analyzed for different values of the anisotropy parameter, the degree of residual strength and density behind the failure front, and proportions of geometrical sizes of the flywheel. The critical failure times are found. A system of restrictions on the values of mechanical and geometrical parameters is revealed which makes possible the realization of the process of dispersed failure investigated.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 93–108, January–February, 2005.     

考虑高阶横向剪切正交各向异性板非线性弯曲的微分求积分析

采用微分求积方法（DQ方法）讨论了计及高阶横向剪切的正交各向异性弹性板的非线性弯曲问题．导出了非线性控制方程的DQ形式,利用推广的DQWB技巧处理了高阶矩的边界条件．进一步推广并运用新的分析技术简化了非线性方程的计算．为说明该方法的可靠性和有效性,将考虑剪切变形及不计剪切变形的薄板的数值结果与三维弹性解析解及其它数值解进行了比较,同时研究了数值结果的收敛性,并考察了不同的节点分布对收敛速度的影响A·D2还考察了几何、材料参数及横向剪切效应对正交各向异性板非线性弯曲的影响．分析结果表明横向剪切效应对正交各向异性中厚板的影响是显著的．     

非线性弹性大变形问题的率型解法

本文分别采用Ｊａｕｍａｎｎ应力率、Ｔｒｕｅｓｄｅｌｌ应力率和Ｇｒｅｅｎ－Ｎａｇｈｄｉ应力率导出了非线性各向同性弹性体的率型本构表达形式，通过对Ｍｏｏｎｅｙ－Ｒｉｖｌｉｎ材料的简单剪切大变形分析表明，三种率型的本构关系均与全量本构关系相等价。文中还给出了相应的率型变分原理，并采应Ｒｉｔｚ法，数值求解了受单轴拉伸的矩形橡皮薄膜的大变形问题．     

Micromechanical Analysis of Inelastic Deformation of Unidirectional Fibrous Composites under Multiaxial and Shear Loadings

An algorithm is proposed for numerically solving nonlinear 3D problems of micromechanics of a unidirectionally reinforced composite with a regular structure. For the matrix, equations of the deformation theory of plasticity and relations of reduced rigidity in its failure zones are used, whereas the fibers are elastic and indestructible. According to the method of local approximation, fields of microstresses and microstrains are determined in a structural fragment containing nine periodic cells. Boundary conditions of the fragment correspond to an arbitrary combination of longitudinal, transverse, and shear microstresses occurring in the central part of the fragment. The solution to the nonlinear 3D problem is sought by the method of superposition with an iterational refinement based on the successive solution of an antiplane problem and a problem on a generalized plain strain state of the structural segment. Special features of the iteration procedure are considered. The calculated deformation diagrams and ultimate strengths of a unidirectional glass-epoxy composite are presented for several loading trajectories.     

大变形对称弹性理论的广义变分原理

本文以陈至达提出的变形几何非线性理论￣［１］为基础，应用Ｌａｇｒａｎｇｅ乘子法，对大变形对称弹性力学问题进行了研究，给出了相应的位能广义变分原理、余能广义变分原理，以及动力学问题的广义变分原理；同时，文中还证明了位能广义变分原理和余能广义变分原理的等价性。