纤维束增强复合材料的横向弹塑性性能研究

利用细观力学模型和有限元法研究纤维束复合材料的横向弹塑性力学性能。假设弹性的纤维束均匀地分布于幂硬化弹塑性基体材料中, 并假设纤维束内的纤维接触是光滑的。通过与单丝纤维复合材料的相应结果比较, 研究了纤维成束对复合材料宏观弹塑性性能的影响。通过对硼/铝复合材料的数值研究表明: 纤维的成束对复合材料的横向弹性刚度影响很小, 而对复合材料的塑性变形和切线刚度有显著的影响。      

单向复合材料弹塑性变形行为的研究

本文利用微观力学方法研究了单向连续纤维增强的金属基复合材料的弹塑性变形行为。纤维是线弹性材料,基体是弹性一粘塑性各向同性材料。在复合材料的纵向拉伸、横向拉伸和纵向剪切变形状态下,预测了复合材料的弹性模量和初始屈服应力值,并考虑了应变率对弹塑性变形行为的影响。以硼/铝复合材料为例,进行了数值分析,预测结果与实验值符合较好。      

基体局部软化对纤维/环氧树脂复合材料力学行为影响的数值分析

聚合物基体的变形局部化在复合材料破坏过程中起着重要作用。采用有限元分析方法, 借助用户材料子程序(UMAT), 描述了具有应变软化特点的高聚物弹塑性的本构关系, 研究了纤维/环氧树脂复合材料在拉伸破坏过程中基体局部变形的演化规律, 分析了基体的局部应变软化对纤维/环氧树脂复合材料应力的影响。结果表明: 纤维的应力分布及基体的塑性变形具有不均匀性; 基体局部变形降低了邻近断点的完好纤维的应力集中程度; 随着纤维间距的增加, 邻近断点的完好纤维的应力集中区域变宽, 而且应力集中程度降低。     

碳纤维和SiO2纳米颗粒增强环氧树脂复合材料的压缩性能

纤维增强聚合物复合材料的压缩性能与聚合物基体力学性质密切相关。本文利用连续碳纤维（CF）和含有均匀分散的SiO₂纳米颗粒改性的环氧树脂基体,制备了CF-nano SiO₂/Epoxy微纳米多相复合材料单向层合板,并对其轴向压缩性能进行了系统的研究。试验表明,将纳米颗粒引入基体能够有效提高纤维增强聚合物基复合材料的压缩强度,占nano SiO₂/Epoxy体积为8.7%的纳米颗粒可将复合材料的压缩强度提升约62.7%。基于单向层合板的弹塑性微屈曲模型对纳米颗粒的增强效应进行了理论分析。根据含纳米颗粒的环氧树脂在压缩过程中的损伤行为,提出了一套基于加卸载试验建立纳米复合材料基体压缩本构关系的方法。将模型获得的基体本构关系与经典复合材料弹塑性微屈曲模型耦合,能够较为准确地预测本研究制备的微纳米多相复合材料的压缩强度。经试验检验,预测结果与实测数值达到很好的一致性。      

形状记忆合金短纤维增强弹塑性基体复合材料的力学行为

基于Eshelby等效夹杂方法和Mori-Tanaka的平均化理论推导了针对SMA短纤维增强弹塑性基体复合材料的细观力学模型。利用此模型,分析了这种复合材料的力学行为,讨论了材料温度、纤维体积分数和纤维特征形状等参数对复合材料残余应力和残余应变的影响。这对复合材料的分析和设计都有重要的意义。      

复合材料非线性本构关系的机算机模拟

本文对单向连续纤维增强复合材料的弹塑性本构关系进行了数值模拟。首先提出了基于统一弹粘塑性本构理论的有限无法,然后利用微观力学模型研究了弹性纤维增强弹粘塑性基体的复合材料应力——应变关系。     

复合材料非线性本构关系的机算机模拟

本文对单向连续纤维增强复合材料的弹塑性本构关系进行了数值模拟。首先提出了基于统一弹粘塑性本构理论的有限无法,然后利用微观力学模型研究了弹性纤维增强弹粘塑性基体的复合材料应力——应变关系。      

基于弹塑性剪滞理论的单丝复合材料段裂过程的蒙特卡罗模拟

单丝复合材料段裂试验(SFCFT)中,随着外载荷的增加,纤维出现了随机脆断的现象,并在一定的载荷下纤维的段裂数达到"饱和"状态(即纤维段裂数目不再增加),该试验常用于表征纤维与基体间界面性能。针对该试验,本文中充分考虑了组分材料的真实性能(即基体材料的弹塑性性能),利用弹塑性剪滞理论进行纤维与基体间的应力传递分析,初步获得较真实的纤维轴向应力及界面剪应力分布形式;在此基础上,考虑纤维强度分布的非均匀性,利用蒙特卡罗(Monte Carlo)方法对试验中纤维的随机段裂过程进行了模拟预报,获得载荷与纤维的段裂数的关系。模拟预报与试验结果比较吻合,表明该应力分析及模拟方法的有效性。     

短纤维增强金属基复合材料基体中的应力分布及其变形特征

基体行为是影响随机分布短纤维增强金属基复合材料力学性能的一个重要因素。本文作者将在短纤维复合材料单纤维三维模型的基础上, 借助于弹塑性有限元分析方法, 研究在加载过程中, 不同纤维位向和界面结合状态下基体中的应力分布情况及基体的变形特征。研究表明, 该类复合材料中基体的应力分布情况和变形特征将受到纤维位向改变和界面结合强弱的显著影响。      

连续石墨纤维增强铝基复合材料准静态拉伸损伤演化与断裂力学行为

针对连续石墨纤维增强铝基(CF/Al)复合材料,采用三种纤维排布方式的代表体积单元(RVE)建立了其细观力学有限元模型,采用准静态拉伸试验与数值模拟结合的方法,研究了其在轴向拉伸载荷下的渐进损伤与断裂力学行为。结果表明,采用基体合金和纤维原位力学性能建立的细观力学有限元模型,对轴向拉伸弹性模量和极限强度的计算结果与实验结果吻合良好,而断裂应变计算值较实验结果偏低。轴向拉伸变形中首先出现界面和基体合金损伤现象,随应变增加界面发生失效并诱发基体合金的局部失效,最后复合材料因纤维发生失效而破坏,从而出现界面脱粘后纤维拔出与基体合金撕裂共存的微观形貌。细观力学有限元分析结果表明,在复合材料制备后纤维性能衰减而强度较低条件下,改变界面强度和刚度对复合材料轴向拉伸弹塑性力学行为的影响较小,复合材料中纤维强度水平是决定该复合材料轴向拉伸力学性能的主要因素。     

A modification of the Mori-Tanaka estimate of average elastoplastic behavior of composites and polycrystals with interfacial debonding

A modification of the Mori-Tanaka method is proposed to evaluate the average elastoplastic behavior of composites and polycrystals in a virtual matrix. The virtual matrix is an elastic material in which real matrix material and inhomogeneities are embedded, and its volume vanishes as a limit after homogenization. With regard to elasticity, depending on the choice of material properties of this virtual matrix, many kinds of average moduli between the classical bounds can be predicted. In this paper, we extend the application of this method to elastoplastic materials. Furthermore, Weng’s approximate model of interfacial debonding between the inclusions and the matrix is installed, because of its very simple criterion for the initiation of debonding to simulate progressive debonding phenomena. Several numerical examples without interfacial debonding show the applicability of the virtual matrix concept to elastoplastic materials. The characteristics of the model and its overall behaviors are described through the use of typical numerical simulations with debondings. Finally, comparisons with experimental results including debondings demonstrate the eligibility of the proposed method and models, and the application of the present method to designing a hybrid FRP is overviewed.     

弹塑性杆非线性断裂问题的新型增强有限元法

针对一维弹塑性材料杆件的非线性断裂,该文提出了一种新型弹塑性增强有限元。该单元采用von Mises屈服准则和线性等向硬化模型描述开裂前的材料弹塑性变形,而结合利用内聚力关系来描述随后的裂纹萌生和非线性断裂过程。引入内部节点来描述单元内由于裂纹引起的位移不连续,通过单元凝聚获得含裂纹单元的刚度矩阵,并对数值稳定性问题进行了分析。通过与基于材料力学方法推导得到的解析解的对比验证了该新型弹塑性增强有限单元法在列式上的正确性和在数值上的高效性与精确性。     

A four‐node corotational quadrilateral elastoplastic shell element using vectorial rotational variables

A four‐node corotational quadrilateral elastoplastic shell element is presented. The local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product. This local coordinate system rotates rigidly with the element but does not deform with the element. As a result, the element rigid‐body rotations are excluded in calculating the local nodal variables from the global nodal variables. The two smallest components of each nodal orientation vector are defined as rotational variables, leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure. Different from other existing corotational finite‐element formulations, the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables. For elastoplastic analyses, the Maxwell–Huber–Hencky–von Mises yield criterion is employed, together with the backward‐Euler return‐mapping method, for the evaluation of the elastoplastic stress state; the consistent tangent modulus matrix is derived. To eliminate locking problems, we use the assumed strain method. Several elastic patch tests and elastoplastic plate/shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation. Copyright © 2013 John Wiley & Sons, Ltd.     

GEOMETRICALLY NON-LINEAR AND ELASTOPLASTIC THREE-DIMENSIONAL SHEAR FLEXIBLE BEAM ELEMENT OF VON-MISES-TYPE HARDENING MATERIAL

A three-dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined. Elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures. The continuum-type equations of plastic model of J₂ mixed hardening are transformed into the beam equations by satisfying beam hypotheses. An effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so-called multistep method which is a method of successive control of residuals on yield surfaces. It avoids severe divergence when the displacement increments become large which is usual for the continuation methods. Material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix. Different from other elements, the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion. A great number of numerical examples are analysed and compared with the literature. The proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre-buckling and large deflection collapse of spatial framed structures.     

幂强化弹塑性材料平面应变反问题

幂强化弹塑性材料在工程领域诸如金属管材制备、岩土工程分析中都具有广泛的应用。幂强化弹塑性材料的本构参数(例如弹性模量)和结构的边界条件(例如位移)往往不容易确定。在这种情况下,反问题为确定这些参数提供了一种新思路。将ABAQUS二次开发的子程序和复变量求导法结合,用于求解基于幂强化弹塑性材料的平面应变力学反问题:以传统的用户单元子程序为框架,将程序中实数变量转换为复数,建立了复数用户单元;采用复变量求导法确定测点位移对反演参数的灵敏度矩阵;结合最小二乘法和高斯消去法对反问题进行迭代求解。给出应用算例讨论了复变量求导法对正问题计算精度影响、算法在反问题求解过程中的精度,以及反演初值、测量误差对反演结果的影响。     

The overall elastopIastic behavior of multiphase materials with isotropic components

Summary A multiphase material is considered, which consists of a homogeneous elastoplastic matrix containing a homogenous statistically uniform random set of ellipsoidal elastic inclusions. An approach based on the multiparticle effective field method is introduced for determining the overall elastoplastic behavior of the material under monotonic loading. A secant modulus concept is employed, and linearized problems are solved at each step of an iterative procedure. Physically consistent assumptions are used for linearizing nonlinear functions which depend on the phase averages of the second invariant of stress and on the stress deviator. Exact expressions for the second moments of the microstresses are employed.     

A scaled boundary finite element formulation for dynamic elastoplastic analysis

This study presents the development of the scaled boundary finite element method (SBFEM) to simulate elastoplastic stress wave propagation problems subjected to transient dynamic loadings. Material nonlinearity is considered by first reformulating the SBFEM to obtain an explicit form of shape functions for polygons with an arbitrary number of sides. The material constitutive matrix and the residual stress fields are then determined as analytical polynomial functions in the scaled boundary coordinates through a local least squares fit to evaluate the elastoplastic stiffness matrix and the residual load vector semianalytically. The treatment of the inertial force within the solution of the nonlinear system of equations is also presented within the SBFEM framework. The nonlinear equation system is solved using the unconditionally stable Newmark time integration algorithm. The proposed formulation is validated using several benchmark numerical examples.     

Inelastic transient dynamic analysis of Reissner–Mindlin plates by the D/BEM

A direct domain/boundary element method (D/BEM) for dynamic analysis of elastoplastic Reissner–Mindlin plates in bending is developed. Thus, effects of shear deformation and rotatory inertia are included in the formulation. The method employs the elastostatic fundamental solution of the problem resulting in both boundary and domain integrals due to inertia and inelasticity. Thus, a boundary as well as a domain space discretization by means of quadratic boundary and interior elements is utilized. By using an explicit time‐integration scheme employed on the incremental form of the matrix equation of motion, the history of the plate dynamic response can be obtained. Numerical results for the forced vibration of elastoplastic Reissner–Mindlin plates with smooth boundaries subjected to impulsive loading are presented for illustrating the proposed method and demonstrating its merits. Copyright © 2000 John Wiley & Sons, Ltd.