Response of 3-D and Plain-Weave S-2 Glass Composites in Out-of-Plane Tension and Shear

An extensive suite of experiments was conducted to characterize the mechanical response of an S-2 glass composite. The primary interest was the response of a 3-D composite, consisting of unidirectional (non-woven) layers of glass fibers interlaced by through-thickness Z-yarns. A plain-weave material was also characterized for comparison purposes. Additionally, epoxy-only specimens were fabricated to assist in understanding the contribution of the SC-15 epoxy resin in the response of the composite system. Two new specimen geometries (torsion and hourglass) were developed specifically for this characterization effort. The response of these specimens provides considerable insight into the failure mechanics of the plain weave and 3-D weave composites. It was shown that the matrix material has an elastic-plastic response, but with different strengths in tension and torsion. The response of the composite in tension is controlled by the epoxy until failure at the glass-resin interface. The strength falls to zero for the plain-weave composite, but the Z-yarns can support tensile stress until the yarns begin to fail. The fibers contribute to the elastic stiffness in shear for the plain-weave material, but the failure strength in shear is the same as the matrix. The 3-D weave composite also fails at the failure strength of the matrix, but retains some shear strength because of the Z-yarns.     

Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate

In this paper, an improved theoretical interfacial stress analysis is presented for simply supported concrete beam bonded with a FRP plate. The adherend shear deformations have been included in the present theoretical analyses by assuming a linear shear stress through the thickness of the adherends, while all existing solutions neglect this effect. Remarkable effect of shear deformations of adherends has been noted in the results. Indeed, the resulting interfacial stresses concentrations are considerably smaller than those obtained by other models which neglect adherent shear deformations. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

Slight asymmetry in the winding angles of reinforcing collagen can cause large shear stresses in arteries and even induce buckling

Many models of the mechanical response of arteries assume a reinforcement with two families of helically wound fibres of collagen of opposite pitch. Motivated by experimental observations, the consequences for the internal pressurisation of arteries of a slight asymmetry in the winding angles is investigated here. It is shown that a torsional shear stress is generated as a result of this flaw, with some common models of the mechanical response of arteries exhibiting significant shear stresses. If the shear stress is significant, then the corresponding model would not seem to be robust, given that an infinitesimal change in a model parameter results in a large change in system response, although it is also shown that there is a ‘magic-angle’ for fibre winding that eliminates torsional shear stress for many of the commonly used models. Finite Element simulations are used to further illustrate the main consequences of fibre asymmetry for some of the more common models of arterial response. If the fibre asymmetry is localised in a region, then simulations show that there is the possibility of significant bending of the artery centred in this region at physiological blood pressure.     

平纹编织陶瓷基复合材料面内剪切细观损伤行为研究

采用约西佩斯库(Iosipescu)纯剪切试件,研究了平纹编织SiC/SiC和C/SiC复合材料的面内剪切应力-应变行为和细观损伤特性.通过试验获得了材料不同方向上的单调和迟滞应力-应变行为,对比分析了两种材料的剪切损伤特性,结果表明材料的剪切损伤演化规律受热残余应力水平影响严重.由试件断口电镜扫描结果发现剪切加载状态下桥连纤维承受显著的弯曲载荷和变形,据此提出了纤维弯曲承载机制,并结合裂纹闭合效应分阶段阐释了材料的剪切迟滞环形状.基于材料的剪切细观损伤机制,通过两个损伤变量表征了材料的剪切损伤演化进程,得到了材料的面内剪切细观损伤演化模型.对比发现2D-C/SiC复合材料45°方向基体裂纹的起裂应力明显小于2D-SiC/SiC复合材料,而两者0°/90°方向裂纹的起裂应力基本相同.      

Static analysis of functionally graded doubly-curved shells and panels of revolution

The Generalized Differential Quadrature (GDQ) Method is applied to study four parameter functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The generalized strains and stress resultants are evaluated by applying the Differential Quadrature rule to the generalized displacements. The transverse shear and normal stress profiles through the thickness are reconstructed a posteriori by using local three-dimensional elasticity equilibrium equations. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained with semi-analytical formulations and with 3D finite element method. A parametric study is performed to illustrate the influence of the parameters on the mechanical behavior of functionally graded shell structures made of a mixture of ceramics and metal.     

A BEM solution to transverse shear loading of composite beams

In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of composite beams of arbitrary constant cross-section. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson’s ratio and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross-section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear centre of the cross-section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson’s ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ‘exact’ elastic beam theory is remarkable.     

Influence of Density Fluctuation on DNS of Turbulent Channel Flow in the Presence of Temperature Stratification

To investigate the effect of density variation on turbulent heat transfer prediction, we perform a direct numerical simulation (DNS) of turbulent flow in a horizontal channel with varying wall temperature using a new method dealing with the effect of density variation. As a result, asymmetric profiles are observed in turbulence statistics. This tendency cannot be reproduced by the Boussinesq approximation, which is based on the constant-density formulation. A quadrant analysis of the turbulent shear stress finds that the density variation affects ejection events in the vicinity of the walls. It is also revealed that the variable viscosity and thermal conductivity change the dynamic and thermodynamic balances of the flow.     

On the compressive strength of open-cell metal foams with Kelvin and random cell structures

Two families of finite element models of anisotropic, aluminum alloy, open-cell foams are developed and their predictions of elastic properties and compressive strength are evaluated by direct comparison to experimental results. In the first family of models, the foams are idealized as anisotropic Kelvin cells loaded in the <100> direction and in the second family more realistic models, based on Surface Evolver simulations of random soap froth with N³ cells are constructed. In both cases the ligaments are straight but have nonuniform cross sectional area distributions that resemble those of the foams tested. The ligaments are modeled as shear deformable beams with elasto-plastic material behavior. The calculated compressive response starts with a linearly elastic regime. At higher stress levels, inelastic action causes a gradual reduction of the stiffness that eventually leads to a stress maximum, which represents the strength of the material. The periodicity of the Kelvin cell enables calculation of the compressive response up to the limit stress with just a single fully periodic characteristic cell. Beyond the limit stress, deformation localizes along the principal diagonals of the microstructure. Consequently beyond the limit stress the response is evaluated using finite size 3-D domains that allow the localization to develop. The random models consist of 3-D domains of 216, 512 or 1000 cells with periodicity conditions on the compressed ends but free on the sides. The compressive response is also characterized by a limit load instability but now the localization is disorganized resembling that observed in experiments. The foam elastic moduli and strengths obtained from both families of models are generally in very good agreement with the corresponding measurements. The random foam models yield 5–10% stiffer elastic moduli and slightly higher strengths than the Kelvin cell models. Necessary requirements for this high performance of the models are accurate representation of the material distribution in the ligaments and correct modeling of the nonlinear stress–strain response of the aluminum base material.     

复合材料层合壳有限元分析的预测-修正法

对于复合材料层合壳的有限元分析，本文根据Reissner-Mindlin型的全局位移场给出了一个预测一修正法。首先按照一般的有限元分析过程(没有引入剪切修正系数)计算出全局响应(如挠度，频率和屈曲载荷等)的预测值；然后利用Lagrange插值构造横向剪应力的一般形式，使得满足层间连续和表面上为零的条件，通过最小二乘法拟合三维应力平衡方程获得横向剪应力；最后在单元上计算和引入剪切修正系数，再经过有限元分析计算出全局响应的修正值。     

3-D numerical study on the bending of symmetric composite laminates

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Optimization of Digital Image Correlation for High-Resolution Strain Mapping of Ceramic Composites

Digital image correlation (DIC) is assessed as a tool for measuring strains with high spatial resolution in woven-fiber ceramic matrix composites. Using results of mechanical tests on aluminum alloy specimens in various geometric configurations, guidelines are provided for selecting DIC test parameters to maximize the extent of correlation and to minimize errors in displacements and strains. The latter error is shown to be exacerbated by the presence of strain gradients. In a case study, the resulting guidelines are applied to the measurement of strain fields in a SiC/SiC composite comprising 2-D woven fiber. Sub-fiber tow resolution of strain and low strain error are achieved. The fiber weave architecture is seen to exert a significant influence over strain heterogeneity within the composite. Moreover, strain concentrations at tow crossovers lead to the formation of macroscopic cracks in adjacent longitudinal tows. Such cracks initially grow stably, subject to increasing app lied stress, but ultimately lead to composite rupture. Once cracking is evident, the composite response is couched in terms of displacements, since the computed strains lack physical meaning in the vicinity of cracks. DIC is used to identify the locations of these cracks (via displacement discontinuities) and to measure the crack opening displacement profiles as a function of applied stress.     

A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory

This paper presents a hybrid stress approach for the analysis of laminated composite plates. The plate mechanical model is based on the so called First-order Shear Deformation Theory, rationally deduced from the parent three-dimensional theory. Within this framework, a new quadrilateral four-node finite element is developed from a hybrid stress formulation involving, as primary variables, compatible displacements and elementwise equilibrated stress resultants. The element is designed to be simple, stable and locking-free. The displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and a suitable approximation for stress resultants is selected, ruled by the minimum number of parameters. The transverse stresses through the laminate thickness are reconstructed a posteriori by simply using three-dimensional equilibrium. To improve the results, the stress resultants entering the reconstruction process are first recovered using a superconvergent patch-based procedure called Recovery by Compatibility in Patches, that is properly extended here for laminated plates. This preliminary recovery is very efficient from the computational point of view and generally useful either to accurately evaluate the stress resultants or to estimate the discretization error. Indeed, in the present context, it plays also a key role in effectively predicting the shear stress profiles, since it guarantees the global convergence of the whole reconstruction strategy, that does not need any correction to accommodate equilibrium defects. Actually, this strategy can be adopted together with any plate finite element. Numerical testing demonstrates the excellent performance of both the finite element and the reconstruction strategy.     

单箱双室组合箱形梁桥静力学特性的研究

为了准确分析单箱双室波纹钢腹板组合箱梁的竖向弯曲力学性能,考虑了组合箱梁的剪力滞、剪切变形、腹板褶皱效应以及剪滞翘曲应力自平衡等因素,设置了3个剪滞纵向翘曲位移差函数,进而基于能量变分法建立了组合箱梁的弹性控制微分方程和自然边界条件。研究表明,褶皱效应对组合箱梁力学性能具有一定影响,且集中荷载下组合箱梁的褶皱效应更为突出;简支边界条件下,组合箱梁剪力滞效应明显,特别是集中荷载组合箱梁的剪力滞效应趋强;本文方法具有一定的理论和工程实用价值,且对该类结构设计具有重要的指导作用。     

Dislocation-based micropolar single crystal plasticity: Comparison of multi- and single criterion theories

Two new formulations of micropolar single crystal plasticity are presented within a geometrically linear setting. The construction of yield criteria and flow rules for generalized continuum theories with higher-order stresses can be done in one of two ways: (i) a single criterion can be introduced in terms of a combined equivalent stress and inelastic rate or (ii) or individual criteria can be specified for each conjugate stress/inelastic kinematic rate pair, a so-called multi-criterion theory. Both single and multi-criterion theories are developed and discussed within the context of dislocation-based constitutive models. Parallels and distinctions are made between the proposed theories and some of the alternative generalized crystal plasticity models that can be found in the literature. Parametric numerical simulations of a constrained thin film subjected to simple shear are conducted via finite element analysis using a simplified 2-D version of the fully 3-D theory to highlight the influence of specific model components on the resulting deformation under both loading and unloading conditions. The deformation behavior is quantified in terms of the average stress-strain response and the local shear strain and geometrically necessary dislocation density distributions. It is demonstrated that micropolar single crystal plasticity can qualitatively capture the same range of behaviors as slip gradient-based models, while offering a simpler numerical implementation and without introducing plastic slip rates as generalized traction-conjugate velocities subject to an additional microforce balance.     

Nonlinear transient response of strain rate dependent composite laminated plates using multiscale simulation

The effects of strain rate dependency and inelasticity on the transient responses of composite laminated plates are investigated. A micromechanics model which accounts for the transverse shear stress effect, the effect of strain rate dependency and the effect of inelasticity is used for analyzing the mechanical responses of the fiber and matrix constituents. The accuracy of the micromechanics model under transverse shear loading is verified by comparing the results with those obtained using a general purpose finite element code. A higher order laminated plate theory is extended to capture the inelastic deformations of the composite plate and is implemented using the finite element technique. A complete micro–macro numerical procedure is developed to model the strain rate dependent behavior of inelastic composite laminates by implementing the micromechanics model into the finite element model. Parametric studies of the transient responses of composite plates are conduced. The effects of geometry, ply stacking sequence, material models, boundary conditions and loadings are investigated. The results show that the strain rate dependency and inelasticity influence the transient responses of composite plates via two significantly different mechanisms.     

Computational modelling of the stress-softening phenomenon of rubber-like materials under cyclic loading

When a rubber specimen is subjected to cyclic loading, not only non-linear behaviour but also damage-induced stress-softening phenomena (the Mullins effect) have been observed. Applications of a continuum damage mechanics model and Ogden and Roxburgh's pseudo-elastic model to describe the Mullins effect in elastomers have been considered. Both models together with Gao's elastic law were implemented to describe the mechanical behaviour of rubber-like materials including the stress-softening phenomenon. Two sets of experimental data (a simple tension test and a simple tension and pure shear test) are used to validate the constitutive models. Model parameters are estimated via an inverse technique. Computational results show that both constitutive models together with Gao's elastic law can describe the typical Mullins effect. From engineering point of view, the pseudo-elastic model has the advantages that (i) the model is simple and practical, since it considers that the stress-softening function is only activated on unloading or reloading paths, (ii) the model with a slight modification of the damage variable is very stable in finite element calculations, and (iii) the numerical results agree very well with experimental data in both simple tension and pure shear deformation. Two applications illustrate the capability of combining the pseudo-elastic model with Gao's elastic law in describing the Mullins effect. It is emphasized that both models are applicable to multiaxial states of stress and strain because both models are energy-based and not strain-based.     

Asymptotic construction of Reissner-like composite plate theory with accurate strain recovery

The focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry. The development starts with formulation of the three-dimensional (3-D), anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two-dimensional (2-D) variables. The variational asymptotic method is then used to rigorously split this 3-D problem into a linear one-dimensional normal-line analysis and a nonlinear 2-D plate analysis accounting for classical as well as transverse shear deformation. The normal-line analysis provides a constitutive law between the generalized, 2-D strains and stress resultants as well as recovering relations to approximately but accurately express the 3-D displacement, strain and stress fields in terms of plate variables calculated in the plate analysis. It is known that more than one theory may exist that is asymptotically correct to a given order. This nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple “Reissner-like” plate theory. Although it is not possible in general to construct an asymptotically correct Reissner-like composite plate theory, an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of the Reissner-like formulation. Numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory. The present theory has excellent agreement with the previous theory and exact results.     

形状记忆合金纤维复合材料的等效力学行为

在Aboudi提出的胞元模型以及Liu等建立的形状记忆合金的本构模型的基础上，由Legendre多项式，假设每个子胞元的位移场、应变场和应力场，再由子胞元间交界面的应力连续条件和外荷载边界条件推导出基体为弹塑性材料的形状记忆合金纤维复合材料的胞元模型；模拟了呈周期对称的形状记忆合金纤维复合材料受轴向单向拉伸、横向拉伸和横向剪切荷载作用下的等效力学行为，与有限元解进行了比较，结果基本一致。与有限元法比较起来，本文推导出的形状记忆合金纤维复合材料的胞元模型更具高效性。     

矩形箱梁力学性能分析的修正计算方法

本文对矩形箱梁翼板设置了不同的剪滞翘曲位移差函数,继而综合考虑剪力滞效应、剪切变形以及剪滞翘曲应力和弯矩自平衡条件等因素,且以能量变分原理为基础建立了矩形箱梁的弹性控制微分方程和自然边界条件,基于此修正了现行薄壁结构分析方法。与传统剪滞理论相比,本文方法深刻反映了矩形箱梁的力学特性。研究表明,(1)由于剪滞翘曲应力和弯矩自平衡条件的引入,矩形箱梁力学性能分解为独立的初等梁理论和剪滞理论体系,且箱梁力学性能为两者的叠加效应;(2)矩形箱梁断面尺寸确定,剪滞效应对其正应力的影响值不变,即剪滞效应的竖向力学行为与箱梁跨径无关;(3)尽管矩形箱梁的梁高对箱形梁剪滞翘曲应力和初等梁理论的应力值皆有一定影响,但其剪力滞系数不变,因此剪力滞效应与梁高无关;(4)剪力滞效应不仅影响箱梁翼板力学性能,而且对其腹板力学行为的影响不可忽视。因而,与传统剪滞理论相比,本文修正法不仅计算精度明显提高,而且更能真实反映矩形箱梁的力学性能。     

短纤维金属基复合材料应力传递的有限元分析

基于短纤维增强金属基复合材料的单纤维轴对称和三维细观力学模型,利用弹塑性有限元分析方法对该复合材料中基体与纤维间的应力传递进行研究,研究中主要讨论了基体、纤维和界面的力学性能以及纤维位向的变化对应力传递和应力分布的影响。研究表明,复合材料微结构参数的变化将显著影响基体与纤维间的应力传递和复合材料中的应力分布,复合材料设计过程中必须考虑合理的微结构特征。