Numerical evaluation of generalized stress-intensity factors in multi-layered composites

The problem of the evaluation of the generalized stress-intensity factors for re-entrant corners in multi-layered structural components is addressed. An approximate analytical model based on the theory of multi-layered beams is presented. This approach provides a simple closed-form solution for the direct computation of the Mode I stress-intensity factor for the general problem of a re-entrant corner symmetrically meeting a bi-material interface. For the self-consistency of the theory, re-entrant corners in homogeneous materials and cracks perpendicular to bi-material interfaces can also be gained as limit cases of this formulation. According to this approach, the effects of the elastic mismatch parameters, the value of the notch angle and the thicknesses of the layers on the stress-intensity factor are carefully quantified and the results are compared with FE solutions. FE results are obtained by applying a combination of analytical and numerical techniques based on the knowledge a priori of the asymptotic stress field for re-entrant corners perpendicular to a bi-material interface and on the use of generalized isoparametric singular finite elements at the notch tip. A good agreement between approximate and analytical/numerical predictions is achieved, showing the effectiveness of this approach.     

Numerical modeling of functionally graded materials using a variational formulation

An approach of numerical modeling of heterogeneous, functionally graded materials, by using the finite element method, is proposed. The variational formulation is derived from the generic case so that the implementation of material coefficients, which are functions in space, is realized without any further assumptions. An analytical solution for a simple case is presented and used for validation of the numerical model.     

Thermally induced wrinkling in orthotropic layered plates with irregular delaminations

Delaminated regions figure prominently among potential threats to the structural integrity of layered plate configurations. Under a certain thermal loading threshold, geometrically nonlinear local instabilities in the form of buckling or wrinkling across the delaminated region crop up, giving rise to markedly amplified distributions of contour peeling stresses. The present paper aims to shed light on and quantify the manifold aspects and implications of the delamination-thermal-wrinkling trio. The paper faces the challenges of handling the nature of the layered configuration, the inherent geometrical irregularity of delaminated regions, the discontinuous interfacial conditions, the 3D stress state along the delamination contour, and the nonlinear evolution of local instabilities across an orthotropic delamination. For that purpose, a specially tailored 2D multi layered plate model and a corresponding triangular finite element are derived. The original contribution of the proposed model is in its ability to capture the thermally-driven, nonlinear small scale phenomena related to geometrically nonlinear response of the layered structure, using a 2D multi-layered plate theory solved with efficient 2D multi-layered triangular finite elements, as opposed to computationally expensive 3D finite element analysis. This is accomplished via the integration and synergy of methodologies that include: multi-layered high order plate theory to account for the layered layout, geometrically nonlinear strain-displacement relations to account for geometrical nonlinearities, orthotropic and thermo-elastic constitutive laws to account for thermal loads, and interlayer interface modelling which, combined with a the shear-locking free triangular FE, allows accounting for arbitrarily shaped delaminations. The model is validated against a 1D closed form solution and a 3D continuum based finite element analysis and is then used for a numerical study. In the study, the onset and the evolution of local instabilities in an adhesively bonded orthotropic layer across an irregular delamination are looked into. Special attention is given to the significant influence of material orthotropy and the relative directionality of the delamination on the threshold thermal load, the nonlinear wrinkling patterns, and the peeling traction distribution.     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.     

A biaxial thermomechanical disk test for glassy polymers

Failure criteria for polymers need to include effects from the stress state. For this reason, biaxial test results are of interest. However, biaxial test methods usually require expensive equipment. In the test method presented here, a disk of epoxy is bonded between a steel ring and a steel disk. The temperature is then lowered until fracture is observed. Experiments were performed on three different glassy epoxy polymers. The biaxial stress state was analyzed by finite element analysis and by an approximate analytical model. Experimental observations support the ability of the method to provide material property data. An approximate analytical model was found sufficiently accurate for stress analysis and determination of the stress state at failure.     

Limit analysis of multi-layered plates. Part II: Shear effects

In the first part of this work [Dallot, J., Sab, K., 2007. Limit analysis of multi-layered plates. Part I: the homogenized Love-Kirchhoff model. J. Mech. Phys. Solids, in press, doi:10.1016/j.jmps.2007.05.005], the limit analysis of a multi-layered plastic plate submitted to out-of-plane loads was studied. The authors have shown that a homogeneous equivalent Love-Kirchhoff plate can be substituted for the heterogeneous multi-layered plate, as the slenderness (length-to-thickness) ratio goes to infinity. In fact, the out-of-plane shear stresses are shown to become asymptotically negligible when compared to in-plane stresses, as the slenderness ratio goes to infinity. Actually, failure of thick multi-layered structures often occurs by shearing in the core layers and sliding at the interfaces between the layers. Both shearing and sliding are caused by the out-of-plane shear stresses. The purpose of the present paper is to build an enhanced Multi-particular Model for Multi-layered Material (M4) taking into account shear stress effects. In this model, each layer is seen as a Reissner-Mindlin plate interacting with its neighboring layers through interfaces. The proposed model is asymptotically consistent with the homogenized Love-Kirchhoff model described in the first part of the work, as the slenderness ratio goes to infinity. Kinematic and static methods for the determination of the limit load of a thick multi-layered plate which is submitted to out-of-plane distributed forces are described. The special case of multi-layered plates under cylindrical bending conditions is studied. These conditions lead to simplifications which often allow for the analytical resolution of the Love-Kirchhoff and the M4 limit analysis problems. The benefit of the proposed M4 model is demonstrated on an example. A comparison between the heterogeneous 3D model, the Love-Kirchhoff model and the M4 model is performed on a three-layer sandwich plate under cylindrical bending conditions. Finite element calculations are used to solve the 3D problem, while both the Love-Kirchhoff and the M4 problems are analytically solved. It is shown that, when the contrast between the core and the skins strengths is high, the Love-Kirchhoff model fails to capture the plastic collapse modes that cause the ruin of the sandwich plate. These modes are well captured by the M4 model which predicts limit loads that are very consistent with the limit loads predicted by the heterogeneous 3D model (the relative error is found to be smaller than 1%).     

Squeezing flow of continuous fibre-reinforced composites

An experiment is presented in which a model fibre-reinforced composite undergoes squeeze-flow. Results are presented for two different fibre lay-ups over a range of fibre volume fractions. The response of the material is an initial rapid compression followed by a limiting deformation and a key feature of the experimental tests is their reproducibility. The experimental results show poor agreement with existing analytical treatments of the problem in which the material is modelled as an anisotropic continuum. Consequently, a two-dimensional finite element approach is developed in which the composite is treated as a Newtonian fluid containing cylindrical voids that represent the fibres and convect with the fluid.     

多层薄膜热应力模拟

针对MEMS器件和光电器件的薄膜结构在高温下产生的应力与应变会严重影响器件结构与功能的问题,本文采用Suhir异质生长薄膜热应力计算理论分析了三层薄膜结构的热应力大小分布情况,得到了不同镀膜温度、膜厚、基底厚度等条件下的热应力变化趋势,解决了困扰有限元分析的奇异点问题。通过分析模型与有限元分析结果的比对,得到该计算模型的应力分布较为符合有限元分析的结果,最大剪切应力差距约为6.1%。列举了一个通过分析关系对材料进行优化的实例。这些研究结果对恶劣工作环境下的MEMS器件以及光电子器件的薄膜设计具有一定的借鉴意义。     

Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element.     

计及剪切影响的RC梁的非线性分析

为提高钢筋混凝土RC梁的计算效率和精度,提出了一种基于梁截面弯矩-曲率关系的宏观有限元方法,可用于各种跨高比RC梁的材料非线性分析。首先假定了混凝土和钢筋的非线性应力-应变关系,然后引入经过修正的Rodriguez截面模型,根据边界顶点把截面划分成若干梯形单元,利用quasi-Newton法求解由两个变量耦合而成的截面非线性平衡方程,由此建立RC截面的弯矩-曲率关系。在此基础上利用Timoshenko梁弯曲理论建立考虑横向剪切变形影响的RC梁的有限元分析模型。通过对试验梁的分析对比验证了所提出的分析方法的适用性。     

Plane infinite analytical element and hamiltonian system

IntroductionManyinfiniteproblemscanbefoundincivilengineering ,suchastunnelconstruction ,structurefoundation ,etc ..Forotherengineeringproblems,whenthephysicaldimensionsofanobjectaresmallandthesurroundingmediaorstructuresaremuchbiggerthantheobject,thenumericalcalculatingmodelcanbetreatedasoneinaninfinitefield .Sofar,onlyafewanalyticalsolutionsforinfinitefieldproblemscanbefound[1- 3].ManyprojectsrelatedtoinfinitefieldproblemsaresolvedbytheFEM ,whereinfiniteelementmethodsareused[4 ,5 ].Sometime…     

预应力混凝土平面杆系结构的有限元方法

建立了基于有限元方法的考虑材料和几何非线性的任意截面预应力混凝土平面杆系结构的数值分析模型,可用于模拟预应力混凝土大跨度梁、单向偏压细长柱等的非线性全过程结构响应。引入修正的Rodriguez截面模型确定截面切线刚度,其中混凝土的贡献通过截面边界顶点定义的梯形单元来实现;在此基础上利用传统的平面非线性杆单元导出了标准有限元公式。通过两个算例验证了该模型的可靠性和适用性。     

Determination of sensor positions for predictive maintenance of revolving machines

The monitoring by measurement and analysis of vibration is largely used to detect the defects in revolving machines. The determination of the best sensor positions is one of the main research goals in the field of predictive maintenance. This paper proposes a numerical methodology based on a finite element model and a spectral analysis in order to find optimum sensor positions. The bearing is a key component for the vibration propagation from the moving parts to static ones. An analytical bearing model and its numerical implementation in a finite element code are presented. The tangent stiffness matrix of the bearing element is obtained by the Newton–Raphson method and then used for the modal and spectral analyses. Several techniques are used to find the most sensitive zones to common defects. The proposed numerical approach correlate well with the experimental results. The numerical modeling of a grinder shows the interests in industrial applications.     

A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals

A coupled temperature and strain rate microstructure physically based yield function is proposed in this work. It is incorporated along with the Clausius–Duhem inequality and an appropriate free energy definition in a general thermodynamic framework for deriving a three-dimensional kinematical model for thermo-viscoplastic deformations of body centered cubic (bcc) metals. The evolution equations are expressed in terms of the material time derivatives of the elastic strain, accumulated plastic strain (isotropic hardening), and the back stress conjugate tensor (kinematic hardening). The viscoplastic multipliers are obtained using both the Consistency and Perzyna viscoplasticity models. The athermal yield function is employed instead of the static yield function in the case of the Perzyna viscoplasticity model. It is found that the static strain rate value, at which the material shows rate-independent behavior, varies with the material deformation temperature. Computational aspects of the proposed model are addressed through the finite element implementation with an implicit stress integration algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS/Explicit [ABAQUS, 2003. User Manual, Version 6.3. Habbitt, Karlsson and Sorensen Inc., Providence, RI] via the user material subroutine coded as VUMAT. Numerical implementation for a simple compression problem meshed with one element is used to validate the proposed model implementation with applications to tantalum, niobium, and vanadium at low and high strain rates and temperatures. The analysis of a tensile shear banding is also investigated to show the effectiveness and the performance of the proposed framework in describing the strain localizations at high velocity impact. Results show mesh independency as a result of the viscoplastic regularization used in the proposed formulation.     

Modeling fracture in large scale shell structures

We consider a problem of modeling fracture and failure preceded by large scale yielding of ductile shells from the point of view of large-scale structural analysis. We place a special emphasis on the computational efficiency of the constitutive formulation. In this context, we seek the formulation embedded in the shell mechanics framework, which is both theoretically sound and easily implementable into a large-scale explicit dynamic finite element code without precluding vectorization or parallelization. This is achieved through the elasto-plastic damage constitutive model for finite-element analysis of plates and shells. The proposed damage model is purely phenomenological with a scalar damage parameter, which has no physical interpretation, except that it represents on a global scale the micromechanical changes the material undergoes during the process of necking and fracture. The localization leading to softening and fracture is represented by the damage calibration function with exponential damage growth after the onset of necking. The proposed phenomenological damage model uses a general plasticity and shell mechanics frameworks which makes it general and easily implementable into existing finite element codes. The proposed formulation has been implemented into the explicit dynamic finite element software code EPSA (Atkatsh et al., 1980, Atkatsh et al., 1983).     

新工科背景下的材料力学虚拟实验仿真范例库建设

面向新工科创新拔尖人才培养,建设了材料力学课程专属的虚拟实验仿真范例库,尤其融入了火箭筒壳轴压稳定性分析与设计、冬奥滑雪头盔变刚度抗冲击设计等工程案例,构建了问题导引、交互、体验、反思为一体的信息化混合式学习场域,完善了材料力学科教融合工程化教学资源体系。该范例库基于Python语言建立了一系列标准构件及工程实例的建模与有限元分析参数化脚本,可实现典型工程结构的强度、刚度和稳定性有限元分析的自动实施与演示。在此基础上,本文还提出了材料力学课程全学习周期多元形成性评价体系,实现对学生新形势下学习状态与能力的诊断性评价,以促使学生合理制订学习规划并自主开展学习,使得虚拟实验技术的实际教学效果最大化。教学实践表明,该虚拟实验仿真范例库有利于培养学生工程创新能力,激发学生力学报国情怀,成为材料力学课程思政的重要载体。

     

PZT-4紧凑拉伸试样的断裂分析

基于线性压电材料的复势理论,通过解析分析,导出了一种分析有限压电板裂纹问题的解析数值方法. 首先,计算了含中心裂纹有限板的断裂参数,与Woo和Wang的解析数值法(Int J Fract, 1993, 62: 203$\sim$218)相比较,表明该方法具有很高的精度和很好的计算效率. 随后,采用该方法和有限元法计算了PZT-4紧凑拉伸试样在绝缘裂纹面边界条件下断裂时的断裂参数,发现各断裂参数的临界值分散性很大,不能作为压电材料的单参数断裂准则. 进而,针对试样真实的裂隙形状,采用有限元法计算了裂隙尖端的应力、电位移场,比较了裂隙内介质的介电性能对裂隙尖端场的影响,计算了带微裂纹的真实裂隙模型的断裂参数并进行了理论分析.      

一种单元谐波平衡法

基于有限元离散,对于工程中的非线性响应问题,提出一种单元谐波平衡法．与常规的谐波平衡法不同,本文将谐波平衡方程建立在有限元素上,从而兼顾了有限元素法和常规谐波平衡法两大优势．有限元技术的应用能使得求解问题的范围扩大到复杂工程结构,而谐波平衡概念的使用将使得含有复杂变形和复杂本构关系的动力学响应问题得到有效解决．所提方法能适用于工程结构中具有复杂非线性关系的动力学响应问题．由于谐波平衡法的实施依赖于谐波系数方程及其切线刚度矩阵的解析推导,尽管已经局限到有限元素上,但对于较为复杂一些的本构关系,推导仍非易事．为解决这些问题,放弃通常对于变形梯度和应变张量所作的向量假设,而是从连续介质力学中基本的几何关系入手,提出一种矩阵分解形式．通过利用张量的内蕴导数定义以及关于迹函数的有关性质,给出应力增量的一种新的表现形式．当它与变形梯度的矩阵分解相结合时,使得切线刚度矩阵的导出变得十分简单,而且所得计算形式也比通常紧凑和方便许多．     

含材料非线性的复合材料单钉接头累积损伤分析

发展了静拉伸复合材料接头层合板三维逐渐损伤模型,考虑了单层复合材料在材料1-2面及3-1面上具有明显非线性剪切应力-应变关系的叠层非线性效应,结合有限元技术即应力分析、失效判定准则及损伤过程中材料性能退化等,对接头层合板损伤扩展进行了模拟,结果表明考虑材料非线性的影响与实验结果吻合更好.     

A transonic quasi-3D analysis for gas turbine engines including split-flow capability for turbofans

A numerical approximation is taken to the solution of the complex flows existing in gas turbine engines with transonic blading. The quasi-3D approach decouples the problem into through-flow and blade-to-blade solutions. An industrially practical finite element through-flow solution is developed and for blade-to-blade solutions a transonic finite areas method is utilized. The finite element code developed is capable of operating in an analysis or a design mode. In both modes a dynamic relaxation factor is employed and considerable reduction in solution time can be achieved. Comparisons to streamline curvature methods are carried out for simple analytical and complex industrial problems.