Analysis of progressive fiber debonding in elastic laminates

The evolution of fiber debonding, and sliding, in fibrous laminates is modeled by a coupled micro/macro-mechanical analysis scheme. The laminates under consideration have a symmetric layup, and are subjected to mechanical loads. The individual plies are elastic, have a unidirectional reinforcement, and can suffer local damage at the fiber/matrix interface when the resolved normal and shear stresses exceed their ultimate magnitudes. The local fields in the plies are assumed to be periodic, and are approximated by the finite element method for overall loads and local resolved stresses that are in excess of the interface strength. Local effects in the individual plies are scaled up to the laminate analysis through stress transformation factors, which are a function of the elastic properties of the plies and their stacking configuration.The proposed analysis was implemented for a periodic array model of the laminas, and for in-plane loading of the laminate. The model predictions for a unidirectional steel/epoxy system subjected to transverse loading compare remarkably well with experimental measurements. This result, and several other examples given for axial and off-axis loading of SiC/CAS laminates, illustrate the model capabilities in predicting the overall strains in the presence of simultaneous, progressive debonding in the individual plies.     

Analysis of transient response of saturated porous elastic soil under cyclic loading using element-free Galerkin method

A two-dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading. The procedure is based on the element-free Galerkin method and incorporated into the periodic conditions (temporal and spatial periodicity). Its shape function is constructed by moving least-square approximants, essential boundary conditions are implemented through Lagrange multipliers and the periodic conditions are implemented through a revised variational formulation. Time domain is discretized through the Crank–Nicolson scheme. Analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions. For only temporal periodic problems, a one-dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading. For both temporal and spatial periodic problems, a typical two-dimensional wave-induced transient problem with the seabed of finite thickness is analysed. Finally, a moving boundary problem is analysed. It is found that the current procedure is simple, efficient and accurate in predicting the response of soil layer under cyclic loading.     

Micromechanical analysis of yielding of metal matrix composites

A recently proposed micromechanics model is employed to generate initial yield surfaces of unidirectional and cross-ply metal matrix composites under a variety of loading conditions. The yield surfaces are calculated using two different methodologies: on the basis of local matrix stresses and average stresses in the entire matrix phase. It is shown that the results obtained on the basis of local matrix stresses correlate very well with finite-element predictions for most loading directions considered in the present investigation. A critical direction or cone of directions is found that should be avoided with the outlined micromechanics model. This direction corresponds to a particular combination of longitudinal tension (compression) and equal biaxial transverse tension (compression) whose ratio is a function of the constituent properties.It is also illustrated that the results generated on the basis of average matrix stresses generally underestimate initial yielding (i.e., predict higher yield stresses), the extent of which may be significant depending on the direction of loading. Thus, the use of average matrix stresses in analyzing elastoplastic response of composites should be approached with caution.     

Elastic–plastic behavior of non-woven fibrous mats

Electrospinning is a novel method for creating non-woven polymer mats that have high surface area and high porosity. These attributes make them ideal candidates for multifunctional composites. Understanding the mechanical properties as a function of fiber properties and mat microstructure can aid in designing these composites. Further, a constitutive model which captures the membrane stress–strain behavior as a function of fiber properties and the geometry of the fibrous network would be a powerful design tool. Here, mats electrospun from amorphous polyamide are used as a model system. The elastic–plastic behavior of single fibers are obtained in tensile tests. Uniaxial monotonic and cyclic tensile tests are conducted on non-woven mats. The mat exhibits elastic–plastic stress–strain behavior. The transverse strain behavior provides important complementary data, showing a negligible initial Poisson's ratio followed by a transverse:axial strain ratio greater than ?1:1 after an axial strain of 0.02. A triangulated framework has been developed to emulate the fibrous network structure of the mat. The micromechanically based model incorporates the elastic–plastic behavior of single fibers into a macroscopic membrane model of the mat. This representative volume element based model is shown to capture the uniaxial elastic–plastic response of the mat under monotonic and cyclic loading. The initial modulus and yield stress of the mat are governed by the fiber properties, the network geometry, and the network density. The transverse strain behavior is linked to discrete deformation mechanisms of the fibrous mat structure including fiber alignment, fiber bending, and network consolidation. The model is further validated in comparison to experiments under different constrained axial loading conditions and found to capture the constraint effect on stiffness, yield, post-yield hardening, and post-yield transverse strain behavior. Due to the direct connection between microstructure and macroscopic behavior, this model should be extendable to other electrospun systems and other two dimensional random fibrous networks.     

Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach

This paper presents an analytical investigation on the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory (FSDT) and subjected to mechanical, thermal and thermo-mechanical loads. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. An analytical approach is used to reduce the governing equations of stability and then solved using an analytical solution which is named as power series Frobenius method for symmetric sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of the plate aspect ratio, side-to-thickness ratio, loading type, sandwich plate type, volume fraction index, elastic foundation coefficients and boundary conditions on the buckling response of FGM sandwich plates. This has not been done before and serves to fill the gap of knowledge in this area.     

Parametric finite-volume micromechanics of periodic materials with elastoplastic phases

The recently incorporated parametric mapping capability into the finite-volume direct averaging micromechanics (FVDAM) theory has produced a paradigm shift in the theory’s development. The use of quadrilateral subvolumes made possible by the mapping facilitates efficient modeling of microstructures with arbitrarily shaped heterogeneities, and eliminates artificial stress concentrations produced by the rectangular subvolumes employed in the standard version. Herein, the parametric FVDAM theory is extended to the inelastic domain by implementing additional formulation required to accommodate plastic and thermal loading. Two different approaches of implementing plasticity have been investigated. The first approach is based on the treatment employed in previous versions of the theory wherein plastic strain fields are represented by a series expansion in Legendre polynomials. The second approach is based on direct surface-averaging of plastic strains calculated at a number of collocation points along the quadrilateral subvolumes’ surfaces, and offers substantial simplification in the parametric finite-volume theory’s elastic–plastic framework. Moreover, substantial reductions in execution times without loss of accuracy are realized due to the elimination of redundant plastic strain calculations in the subvolumes’ interiors employed in the evaluation of the Legendre polynomial coefficients. Numerical studies demonstrate the advantages of the parametric FVDAM theory relative to the standard version, together with new results that highlight its modeling capabilities vis-a-vis an emerging class of periodic lamellar materials with wavy microstructures and the thus-far undocumented architectural effects amplified by plasticity.     

APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR DYNAMIC CALCULATION OF VISCOELASTIC LAYERED PERIODIC PLATE

由于周期性隔振结构动力计算中较少考虑轨道交通载荷及材料黏弹性,因此,本文以黏弹性层状周期板为研究对象,提出了垂向移动简谐载荷下,可以考虑材料黏弹性及板内横向剪切变形的黏弹性层状周期板动力计算近似理论并给出解析解答.设板中性面的横向剪切变形为横截面的整体剪切变形,利用Reissner-Mindlin假设及提出的剪切变形补充计算条件,得到了中性面法线转角与中性面剪应力的关系.基于平衡方程和应力连续条件,建立了黏弹性层状周期板振动控制方程,推导了对边简支对边自由条件下,板垂向位移的简化Fourier级数形式解.与经典层合板模型和有限元计算结果进行了比较,验证了本文解答的有效性.结果表明：（1）黏弹性层状周期板可以显著降低单一材料板在自振频率处的振动响应,但会引起局部低频频段的振动放大;（2）板的垂向位移随着载荷速度的增大而增大,当载荷速度超过300 km/h后,其对板振动响应的影响减弱;（3）黏弹性层剪切模量存在最佳设计值,可使结构的隔振性能最佳;（4）黏弹性层的阻尼特性在低频范围内对结构振动影响较小;（5）可在满足工程实际的情况下适当增加板长,以提高结构的隔振性能.     

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.     

沿厚度非均匀复合材料的动态断裂力学研究

对于非均匀复合材料中多个裂纹的动态断裂力学问题，提出了一种分析方法，假设复合材料为正交各向异性并含有多个垂直于厚度方向的裂纹，材料参数沿厚度方向为变化的，沿该方向将复合划分为许多单层，假设单层材料参数为常数，Ｆｏｕｒｉｅｒ变换法，在Ｌａｐｌａｃｅ域内推导出了控制问题的奇异积分方程组并用虚位移原理求解，然后利用Ｌａｐｌａｃｅ数值反得刺裂纹尖端的动态应力强度因子和能量释放率，作为算例，研究了带有两个裂     

Optimizing a fin ray for stiffness

We optimize the elastic constants of the supporting structure in flexible fish fins—the fin ray—to obtain the least deflection under loading. We first solve the problem numerically for rays with shear layers of uniform thickness. The optimal distributions of bending and shear moduli are nonzero on disjoint regions. The numerical solution suggests the form of the analytical solution, which we obtain using calculus of variations on two intervals with continuity conditions at the interface. The deflection of the optimal ray is less than half that of the uniform ray. When the shear layer thickness is allowed to vary, we find a tapered thickness distribution which gives zero deflection for a given positive loading.     

A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading

We present and study a nonlinear thermo-elastic constitutive model that under monotonic loading closely reproduces the response seen in plasticity, showing the initial stiff elastic response, kneeing as if yielding, and then showing response resembling post-yield hardening. The proposed large deformation thermo-elastic response model is constructed based on four physically identifiable mechanical parameters, that are closely related to the parameters used to construct plasticity models, thermal expansion parameters and two thermodynamic parameters. The four mechanical parameters are the initial elastic shear and bulk moduli, the yield point in shear, the hardening slope in shear. The thermodynamic parameters are the heat capacity at a reference temperature and its rate of change with changes of temperature. The model can be considered an alternate to deformation plasticity models currently used and, as such, can be used as a lightweight substitute for plasticity modeling in certain analysis. Since the proposed model is thermodynamically based, not only thermal effects are integrated into the model, but also the stress is calculated in terms of the applied deformation, allowing the model to be integrated with other models when conducting numerical analysis. We study the response of the proposed model under simple shear, uniaxial extension, confined compression, partially-confined compression, and biaxial extension. We incorporate the elastic model into ABAQUS using its UMAT subroutine for solid elements and using UHYPER for shell elements. We compare the large deformation response from the proposed elastic model with J2-plasticity, and with plasticity and deformation plasticity models implemented in ABAQUS. The model in most cases compares very favorably to all such models. This comparison is done for both homogeneous and non-homogeneous problems including the case of a cantilever beam under tip loading. We show that for the problems that it applies to, the models run in approximately one tenth the computational time and with one tenth the number of iterations needed to conduct the analysis using the plasticity model in ABAQUS.     

Dynamic fracture mechanics analysis for composite material with material non-homogeneity in thickness direction

The problem considered here is the response of a non-homogeneous composite material containing some cracks subjected to dynamic loading. It is assumed that the composite material is orthotropic and all the material properties depend only on the coordinatey (along the thickness direction). In the analysis, the elastic region is divided into a number of plies of infinite length. The material properties are taken to be constants for each ply. By utilizing the Laplace transform and Fourier transform technique, the general solutions for plies are derived. The singular integral equations of the entire elastic region are obtained and solved by the virtual displacement principle. Attention is focused on the time-dependent full field solutions of stress intensity factor(SIF) and strain energy release rate. As a numerical illustration, the dynamic stress intensity factor of a substrate/functionally graded film structure with two cracks under suddenly applied forces on cracks face are presented for various material non-homogeneity parameters.     

Detachment of a rigid solid from an elastic wavy surface: Experiments

The mechanics of detachment of a rigid solid from an elastic wavy surface has been analyzed in a recent article, in which the axisymmetric case of a sphere and the plane strain case of a cylinder were considered. Due to the qualitative similarities, the discussion was limited to the axisymmetric case only. It was shown that the surface waviness makes the detachment process proceed in alternating stable and unstable segments and each unstable jump dissipates mechanical energy. As a result, the external work and the peak force required to separate a wavy interface are higher than the corresponding values for a flat interface, i.e., waviness causes interface toughening as well as strengthening. In this paper, a systematic experimental investigation is presented which examines the above theoretical analysis, by measuring adhesion between a “rigid” wavy punch and a soft “elastic” material, which is a block of gelatin here. The observed increase in adhesion due to waviness closely agrees with the theoretical predictions within the experimental and material uncertainties. The experiments not only validate the theory, but also demonstrate that adhesion of a soft material can be substantially enhanced by topographic optimization alone, without modifying the surface chemistry.     

The effect of bonding layer properties on the dynamic behaviour of surface-bonded piezoelectric sensors

The dynamic behaviour of piezoelectric sensors depends on the bonding condition along the interface between the sensors and the host structure. This paper provides a comprehensive theoretical study of the effect of the bonding layer on the coupled electromechanical characteristics of a piezoelectric sensor bonded to an elastic substrate, which is subjected to a high frequency elastic wave. A sensor model with a viscoelastic bonding layer, which undergoes a shear deformation, is proposed to simulate the two dimensional electromechanical behaviour of the integrated system. Analytical solution of the problem is provided by using Fourier transform and solving the resulting integral equations in terms of the interfacial stress. Numerical simulation is conducted to study the effect of the bonding layer upon the dynamic response of the sensor under different loading frequencies. The results indicate that the modulus and the thickness of the bonding layer have significant effects on sensor response, but the viscosity of the bonding layer is relatively less important.     

Thermomechanical vibration analysis of a functionally graded shell with flowing fluid

This paper reports the results of an investigation into the vibration of functionally graded cylindrical shells with flowing fluid, embedded in an elastic medium, under mechanical and thermal loads. By considering rotary inertia, the first-order shear deformation theory (FSDT) and the fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived. Here, heat conduction equation along the thickness of the shell is applied to determine the temperature distribution and material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The equations of eigenvalue problem are obtained by using a modal expansion method. In numerical examples, effects of material composition, thermal loading, static axial loading, flow velocity, medium stiffness and shell geometry parameters on the free vibration characteristics are described. The new features in this paper are helpful for the application and the design of functionally graded cylindrical shells containing fluid flow.     

Mechanics of axisymmetric wavy surface adhesion: JKR–DMT transition solution

Recent work on the mechanics of detachment of a rigid sphere from an elastic axisymmetric wavy surface in the presence of JKR adhesion has shown that the presence of small-amplitude waviness introduces instabilities into the detachment process which dissipate mechanical energy. These instabilities result in interface toughening and strengthening; both the external work and peak force required for separation of a wavy interface are higher than those for a flat interface. In this paper, we summarize the key dimensionless parameters governing axisymmetric wavy surface adhesion in the JKR regime. We then proceed to derive a solution for the JKR–DMT adhesion transition for the axisymmetric wavy surface contact problem using a Maugis–Dugdale cohesive zone formulation. The phenomenon of interface toughening and strengthening due to the presence of surface waviness is seen to be restricted primarily to the JKR adhesion regime.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

Finite-amplitude shear horizontal waves propagating in a pre-stressed layer between two half-spaces

The propagation of finite-amplitude time-harmonic shear horizontal waves, in a pre-stressed compressible elastic layer of finite thickness embedded between two identical compressible elastic half-spaces, is investigated. This is accomplished by combining finite-amplitude linearly polarized inhomogeneous transverse plane wave solutions in the half-spaces and finite-amplitude linearly polarized unattenuated transverse plane wave solutions in the layer. The layer and half-spaces are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. The special case where the interfaces between the layer and the half-spaces are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the shear horizontal wave speed with the pre-stress and the propagation angle.     

Compressive response and failure of braided textile composites: Part 2—computations

In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.     

Assessment of improved zigzag and smeared theories for smart cross-ply composite cylindrical shells including transverse normal extensibility under thermoelectric loading

The improved zigzag theory recently developed by the authors for smart, piezoelectric, and laminated cylindrical shells is assessed for the response of finite-length cross-ply shells and shell panels under mechanical, potential, and thermal loading, in direct comparison with the exact three-dimensional (3D) piezothermoelasticity solution. This theory has the unique features of including the transverse normal strain due to thermoelectric loading without introducing additional deflection variables, capturing the nonlinear potential field and actual temperature profile across laminate thickness, accounting for the layerwise (zigzag) variation of inplane displacements, and satisfying the conditions on transverse shear stresses at the layer interfaces and at the inner and outer surfaces. For the assessment, new results are obtained for the 3D exact solution for smart cylindrical shells having a test laminate with widely different material properties across layers, a piezo-composite laminate and a piezo-sandwich laminate. To ascertain the contribution of the layerwise terms in the inplane displacements, the theory is compared with its smeared counterpart with the same number of primary variables. The effect of inclusion of transverse normal extensibility in these theories is established by comparing with their conventional counterparts that assume constant deflection across the thickness. The effect of span angle (for shell panels), length, and thickness parameters on the error of the 2D theories is illustrated.