Micromechanics of piezoelectric composites with improved effective piezoelectric constant

This paper is concerned with the derivation of a micromechanics model of a new type of piezoelectric fiber reinforced composite (PFRC) materials. A continuum mechanics approach is employed to determine the effective properties of these composites. The piezoelectric fibers of these composites are considered to be electroded at the fiber–matrix interface such that the electric fields in the fiber and matrix become equal in the direction transverse to the fiber direction. The model has been verified with the existing models. The present model also predicts that the effective piezoelectric coefficient of these PFRC which accounts for the actuating capability in the fiber direction due to the applied field in the direction transverse to the fiber direction improves over the corresponding coefficient of the material of the piezoelectric fibers if the fiber volume fraction exceeds a critical fiber volume fraction.     

Nonlinear electro-mechanical responses of functionally graded piezoelectric beams

This study presents analyses of the nonlinear electro-mechanical responses of functionally graded piezoelectric beams undergoing small deformation gradients. The studied functionally graded beams comprise of electro-active and inactive constituents with gradual compositions varying through the thickness of the beams. Two types nonlinear electro-mechanical responses are considered for the active constituents, which are nonlinear electro-mechanical behaviors for the polarized piezoelectric constituent under electric fields smaller than the coercive limit, and polarization switching responses due to cyclic electric fields with high amplitude. The inactive constituent is modeled with uncoupled linear electro-elastic response. The functionally graded beam is discretized into several graded layers through its thickness. Each layer is comprised of different compositions of the active (piezoelectric) inclusions and conductive matrix. A particle-unit-cell micromechanical model is used to obtain the nonlinear electro-mechanical responses in each layer and is integrated within the laminate theory in order to obtain the overall nonlinear electro-mechanical responses of the functionally graded piezoelectric beams. The numerical predictions are compared with experimental data available in literature. Parametric studies are then performed in order to examine the effects of the thickness of the beam, of the concentration of the constituent, and the frequency of the cyclic electric field on the overall electro-mechanical response of the functionally graded piezoelectric beams.     

炭黑增强橡胶复合材料的大变形细观力学模型

为考察炭黑对橡胶复合材料超弹性力学行为的影响,首先,利用不同填充体积分数的炭黑增强橡胶复合材料的准静态力学试验数据,对现有的基于均质化方法的"变形放大"细观力学模型的大变形表征能力进行了评估。其次,在此基础上提出了新的"第一不变量放大"关系,并获得了较为合理的预测结果。最后,利用随机序列吸附算法建立了较接近材料真实细观结构的球形颗粒填充数值模型,进行了大变形情况下的三维数值模拟;为考察颗粒聚集效应的影响,还设置了颗粒均匀随机分布和团聚随机分布两种形式。计算结果与试验数据的对照表明:提出的三维细观数值模型已经能在一定程度上预测填充橡胶的大变形宏观力学行为,且颗粒团聚随机分布模型的预测能力更好一些。试验结果验证了该模型的合理性,所建模型为进一步的相关研究提供了参考。     

Micromechanics models for the elastic constants and failure strengths of plain weave composites

In this paper, two models are presented for plain weave composites. One is finite element analysis (FEA) model for elastic constants, namely, sinusoidal yarn model. Another is analytical model for failure strengths, namely, sinusoidal beam model. The FEA model is generated by interfacing an in-house computer code with FEA software strand6, and the analytical model is developed using the theory of elasticity. Numerical studies are carried out using the present models to investigate the effects of some major geometrical parameters on the properties of plain weave composites. It is concluded that the failure strengths are closely related to the fiber volume fraction of a yarn, and the mechanical properties are closely related to the overall fiber volume fraction of the composites. An experimental testing program is conducted for T300/934 plain weave composites to validate the developed models. A good agreement exists between the predicted and measured results.     

含金属芯压电压磁纤维/聚合物基复合材料时变、非线性和多物理场响应的细观力学模型

为有效模拟新型多功能智能材料——金属芯压电压磁纤维/聚合物基复合材料(MPPF/PMCs)的有效时变、非线性和多物理场响应,基于变分渐近法建立增量形式的细观力学模型。首先分别导出聚合物、压电压磁材料和金属芯的增量本构关系,建立统一的本构方程;以此为基础,推导出能量变化泛函的变分表达式。考虑材料的时变和非线性特征,建立与求解瞬时切线电-磁-力耦合矩阵有关的增量过程;通过最小化近似泛函求解场变量的波动函数,并通过有限元数值实现,从而建立逼近物理和工程真实性的细观力学模型。通过含铝芯压电(BaTiO_3)压磁(CoFe_2O_4)聚合物基复合材料算例表明:构建的模型可用于模拟不同多物理场下MPPF/PMCs的有效响应,可准确捕捉纤维与基体间的应力突变现象。     

金属芯压电纤维/聚合物复合材料压电-黏弹-塑性行为的细观力学模型

为了表征金属芯压电纤维增强聚合物基（MPF/PM）复合材料非线性、时变的压电-黏弹-塑性行为,基于变分渐近理论建立MPF/PM增量形式的细观力学模型。首先分别导出聚合物和MPF增量型本构方程,基于汉密尔顿扩展原理推导出MPF/PM压电-黏弹-塑性变分原理的能量泛函。考虑材料的时变和非线性特征,建立与求解瞬时有效机-电耦合矩阵有关的增量过程,并通过有限元技术实现模型的数值模拟。利用构建模型研究了不同铝芯体积分数、电场变化率和加载条件对MPF/PM有效全局应力-应变和单轴纵向拉伸性能的影响。结果表明,构建的模型能准确模拟MPF/PM多场耦合作用下的非线性、时变行为,为该新型智能材料的实际工程应用奠定理论基础。     

机电耦合载荷下的压电层合板瞬态响应分析

针对压电层合板在机电耦合激振下的瞬态响应问题, 提出一种高效混合数值计算方法。经过位移场、 电势场在厚度方向的离散, 利用机电耦合理论和哈密顿原理, 推导出结构的运动方程。引入傅里叶变换, 得到波数域内运动控制方程。应用模态分析方法求解波数域内的位移场和电势场, 对结果进行傅里叶逆变换, 得到空间域内的瞬态响应。以PZT-5A/0° PVDF铺层两相材料复合压电层合板为算例, 分析了力、 电耦合线载荷激励下, 位移场和电势场的瞬态响应历程与分布规律, 计算结果给出了该结构的动力学基本特征。该方法结合了有限元法、 傅里叶变换和模态分析法, 计算高频载荷激振下的压电层合板瞬态响应较一般有限元法大幅减少了单元的划分。该方法可推广至分析任意机电载荷下的各类铺层材料压电层合板瞬态响应问题。      

Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities

Summary A micromechanical framework is proposed to investigate effective mechanical properties of elastic multiphase composites containing many randomly dispersed ellipsoidal inhomogeneities. Within the context of the representative volume element (RVE), four governing micromechanical ensemble-volume averaged field equations are presented to relate ensemble-volume averaged stresses, strains, volume fractions, eigenstrains, particle shapes and orientations, and elastic properties of constituent phases of a linear elastic particulate composite. A renormalization procedure is employed to render absolutely convergent integrals. Therefore, the micromechanical equations and effective elastic properties of a statistically homogeneous composite are independent of the shape of the RVE. Various micromechanical models can be developed based on the proposed ensemble-volume averaged constitutive equations. As a special class of models, inter-particle interactions are completely ignored. It is shown that the classical Hashin-Shtrikman bounds, Walpole's bounds, and Willi's bounds for isotropic or anisotropic elastic multiphase composites are related to the noninteracting solutions. Further, it is demonstrated that the Mori-Tanaka methodcoincides with the Hashin-Shtrikman bounds and the noninteracting micromechanical model in some cases. Specialization to unidirectionally aligned penny-shaped microcracks is also presented. An accurate, higher order (in particle concentration), probabilistic pairwise particle interaction formulation coupled with the proposed ensemble-volume averaged equations will be presented in a companion paper.     

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.     

Micromechanics modeling of viscoelastic properties of hybrid composites with shunted and arbitrarily oriented piezoelectric inclusions

A comprehensive micromechanics model is developed to estimate the effective viscoelastic properties of hybrid composites containing polymer matrix, conductive inclusions and shunted piezoelectric inclusions. The model is derived using the viscoelastic correspondence principle in conjunction with the Mori-Tanaka approach and the orientation averaging scheme. Three dimensional complex moduli are explicitly presented for hybrid composites with any orientation distribution. The model is first validated by comparison with available experimental results. Then, the loss factors are examined for hybrid composites with inclusions of various volume fractions and of shapes ranging from thin disks to long fibers. It is seen that hybrid composites with randomly oriented inclusions exhibit shear loss factors which are not possible with monolithic piezoelectric plate. Furthermore, the numerical results indicate that composites with long spheroid inclusions provide the best damping performance. The results recommend that aligned inclusion composites are good for alleviating longitudinal oscillations. If oscillation energy needs to be dissipated in all directions and for all modes, three dimensional random composites should be used. It is also observed that spherical inclusion composites cannot improve shear damping irrespective of the orientation and the volume fraction. In general, to achieve a pronounced damping piezoelectric inclusions that lie in aspect ratio range 0.1?α?2 should be avoided.     

Analysis of nonlinear transient responses of piezoelectric resonators

The electric transient response method is an effective technique to evaluate material constants of piezoelectric ceramics under high-power driving. In this study, we tried to incorporate nonlinear piezoelectric behaviors in the analysis of transient responses. As a base for handling the nonlinear piezoelectric responses, we proposed an assumption that the electric displacement is proportional to the strain without phase lag, which could be described by a real and constant piezoelectric e-coefficient. Piezoelectric constitutive equations including nonlinear responses were proposed to calculate transient responses of a piezoelectric resonator. The envelopes and waveforms of current and vibration velocity in transient responses observed in some piezoelectric ceramics could be fitted with the calculation including nonlinear responses. The procedure for calculation of mechanical quality factor Q(m) for piezoelectric resonators with nonlinear behaviors was also proposed.     

Micromechanics modeling of smart composites

This paper discusses a summary of analytical modeling as applied to selected smart composites which include piezoelectric composites, shape memory alloy (SMA) fiber composites, and piezoresistive composites. First we discuss the definition of `smart materials' which exhibit coupling among mechanical, thermal and electromagnetic behavior, then the Eshelby's formulations based on a simple algebraic method for predictions of two types of smart composite properties are stated; piezoelectric and SMA composites, followed by the percolation model which is applied to obtain the strain–electric conductivity relations of elastomer composites. The predictions based on these models are shown to be in good agreement with limited experimental results.     

Micromechanics models for mechanical and thermomechanical properties of 3D through-the-thickness angle interlock woven composites

In this paper, a laminate block modeling approach for three-dimensional (3D) through-the-thickness angle interlock woven composites is used to develop one finite element analysis (FEA) model and two analytical models, namely the “ZXY model” and the “ZYX model”. These models can be used to determine the mechanical properties and the coefficients of thermal expansion for 3D through-the-thickness angle interlock woven composites. A parametric study shows that there is good agreement between these FEA and analytical models. The parametric study also demonstrates the effects of the fiber volume fraction of the warp weaver (i.e., z yarn) and the space between two adjacent filler yarns on the mechanical properties and the coefficients of thermal expansion. Finally, the present models are found to correlate reasonably well with the predicted and measured results available in the literature.     

Variational bounds for the effective electroelastic moduli of piezoelectric composites with electromechanical coupling spring-type interfaces

The present work focuses on variational bounds for the effective electroelastic moduli of multiphase piezoelectric composites with thin piezoelectric interphase. Both the inhomogeneities and the matrix are assumed to be piezoelectric and transversely isotropic. The piezoelectric interphase is modeled as the spring-type interface with electromechanical coupling. The inhomogeneities are assumed to be spheroidal so that the reinforcement geometry is able to range from thin flake to continuous fiber. The effective properties of the piezoelectric composite with interfacial imperfection are defined and the principles of minimum internal energy and enthalpy are derived. These principles are applied to analytically obtain the upper and lower bounds for the effective electroelastic moduli. Unlike the Voigt–Reuss-type bounds for perfect interface, the present bounds depend not only on the material properties and volume fraction, but also on the interface parameters, inhomogeneity shape and orientation. An example of a two-phase composite is given for detailed discussion, where dependence of the electroelastic moduli and their bounds on the inhomogeneity shapes and orientations as well as the interface properties is provided and discussed. To qualitatively account for the dependence, analysis based on two possible mechanisms, i.e., the simple mixture rule of composite and the weakening effect by imperfect interface, are also provided.     

FEM analysis of electro-mechanical coupling effect of piezoelectric materials

Based on the mechanical and electrical equilibrium equations of piezoelectric materials, the minimum potential theory is presented by using the virtual work principle in this paper. A finite element method (FEM) formulation accounting for the electro-mechanical coupling effect of piezoelectric materials is given. Some problems in the numerical simulation are discussed and the extreme illness of the stiffness matrix is overcome by the dimension changing method. As a simple application, the response of an elliptical cavity in infinite media of piezoelectric materials is analyzed. Such a geometry leads to stress and electric field concentrations.     

Micromechanics of TEMPO-oxidized fibrillated cellulose composites

Composites of poly(lactic) acid (PLA) reinforced with TEMPO-oxidized fibrillated cellulose (TOFC) were prepared to 15, 20, 25, and 30% fiber weight fractions. To aid dispersion and to improve stress transfer, we acetylated the TOFC prior to the fabrication of TOFC-PLA composite films. Raman spectroscopy was employed to study the deformation micromechanics in these systems. Microtensile specimens were prepared from the films and deformed in tension with Raman spectra being collected simultaneously during deformation. A shift in a Raman peak initially located at ~1095 cm(-1), assigned to C-O-C stretching of the cellulose backbone, was observed upon deformation, indicating stress transfer from the matrix to the TOFC reinforcement. The highest band shift rate, with respect to strain, was observed in composites having a 30% weight fraction of TOFC. These composites also displayed a significantly higher strain to failure compared to pure acetylated TOFC film, and to the composites having lower weight fractions of TOFC. The stress-transfer processes that occur in microfibrillated cellulose composites are discussed with reference to the micromechanical data presented. It is shown that these TOFC-based composite materials are progressively dominated by the mechanics of the networks, and a shear-lag type stress transfer between fibers.     

硬化水泥浆体弹性模量细观力学模型

应用复合材料力学理论和有孔介质力学(Poromechanics)理论建立了一个描述硬化硅酸盐水泥浆体弹性模量的细观力学模型, 将硬化水泥浆体从不同尺度上划分为4个层次, 即C-S-H凝胶、 水泥水化产物、 水泥浆体骨架和水泥浆体, 分别应用不同的细观力学模型予以描述: 将C-S-H视为饱和的有孔介质; 应用Mori-Tanaka模型描述水泥水化产物的弹性性质; 应用三相模型(Three-phase model)模拟水泥浆体骨架的有效弹性模量; 最后, 再次应用Mori-Tanaka模型和有孔介质理论, 计算水泥浆体的排水和不排水弹性模量(Drained and undrained elastic moduli)。该模型所需要的参数为水泥浆体各个组成部分的自身弹性性质, 使用方便。通过预测文献中的实测结果, 证明了该模型的有效性。      

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.     

Micromechanics of hemp strands in polypropylene composites

The present paper investigates micromechanics of hemp strands. The main objective of the present work has been the determination of the intrinsic strength of hemp strands. Hemp strands have been used as reinforcement of Polypropylene composites. Different percentages of hemp strands and coupling agents (MAPP) have been tested to obtain a map of the mechanical properties of that kind of composites and the effect of the components on the final properties. Mechanical properties of the different specimens have been tested using standard experimental methods and equipment. Micromechanics of the strands have been obtained using Hirsch model, Bowyer–Bader methodology and Kelly-Tyson model.     

Calculation of effective coefficients for piezoelectric fiber composites based on a general numerical homogenization technique

Numerical unit cell models for 1–3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft non-piezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on the formulation of the boundary conditions that allows the simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method (FEM) and it allows the extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method (AHM) for different fiber volume fractions.