形状记忆合金/聚合物有效时变和伪弹性响应的变分渐近细观力学

为有效模拟形状记忆合金增强聚合物基复合材料(SMA/PMCs)有效时变和伪弹性响应,基于变分渐近理论框架构建增量型细观力学模型。首先分别导出聚合物和形状记忆合金增量本构方程,建立统一的本构方程;以此为基础推导出能量泛函的变分表达式。考虑材料的时变和非线性特征,建立与求解切向瞬时有效矩阵有关的增量过程,并通过有限元数值实现。通过数值算例表明:构建的模型可用于模拟SMA/PMCs在不同加载率和温度下的有效时变、伪弹性响应,准确捕捉聚合物基体黏弹性诱发的复合材料率相关、滞回行为等。     

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。     

压电复合材料的电弹耦合特性分析

利用Eshelby 理论及Mori-Tanaka 平均场原理, 推导出压电陶瓷/ 聚合物两相复合材料的有效电弹模量表达式。该表达式能反映两相材料复合的物理本质。并以椭圆柱形压电纤维增强的聚合物基复合材料为例,分析压电复合材料的电弹耦合特性。结果表明: 复合材料的平均电弹模量在很大程度上取决于电弹耦合效应;该效应与组成相的空间连接型、体积占有率及压电夹杂形状有关; 耦合效应的存在是由各组成相材料性能差异引起的。      

聚合物基复合材料有效蠕变响应与单轴拉伸行为的细观力学模拟

基于变分渐近均匀化理论框架建立表征线性黏弹性聚合物基复合材料有效蠕变响应和宏观应力-应变行为的细观力学模型。从线性黏弹性聚合物基复合材料本构方程中构建能量泛函变分表达式出发,采用变分渐近法求解线性黏弹性聚合物基复合材料的有效蠕变柔度系数,并以此为基础计算聚合物基复合材料的时变和单轴拉伸行为。通过算例验证了构建模型的适用性和准确性。由于所有计算均在时间域内完成,不再需要传统线黏弹性复合材料使用的Laplace转换和反演,计算效率大为提高。      

压电复合材料三维壳体简化数值建模研究

为有效分析三维压电复合材料壳体结构非线性、 单向耦合压电弹性问题, 基于变分渐近方法(VAM)建立了壳体结构在机械和电场作用下的简化模型。推导了基于旋转张量分解概念的压电复合材料三维壳体能量表达式; 利用变分渐近法将三维壳体严格拆分为二维壳体线性分析和沿法线方向的一维非线性分析; 进行了降维后近似能量推导及Reissner-Mindlin形式转换; 提供了三维场重构关系以得到沿厚度方向的准确应力分布。通过对由4层压电复合材料构成的壳体柱形弯曲算例分析表明: 基于该理论和重构过程开发的变分渐近程序VAPAS重构生成的三维应力场精确性较一阶剪切变形理论和古典层合理论更好, 与三维有限元精确解相吻合, 表明该压电复合材料壳体模型的有效性。      

压电复合材料层合板的热压电弹性简化模型研究

为有效分析压电复合材料层合板在热、电和载荷下的单向耦合热电弹性问题,基于变分渐近方法(VAM)建立热电弹性简化模型。首先根据虚功原理推导三维压电复合板总势能泛函。然后基于变分渐近法,利用板固有的小参数将三维总势能泛函渐近扩展为系列二维泛函,同时将近似泛函转换为Reissner形式以便实际工程应用。最后建立三维场重构关系以正确预测沿厚度方向的应力分布。计算结果显示:基于该模型重构的沿厚度方向横向剪切应力较古典层合理论和一阶剪切变形理论精确度更好,与三维有限元精确解相一致,表明该模型在压电复合材料层合板应力预测上的有效性。     

多稳态压电振动能量采集器的非线性动力学特性及其实验研究

为了提高非线性双稳态压电振动能量采集器的输出性能,提出了一种基于磁?机?压电耦合的非线性多稳态振动能量采集器,通过在双稳态压电振动能量采集器模型基础上增加一对外部磁铁,构造了具有四个稳态的非线性压电振动能量采集器.利用磁偶极子理论建立了采集器悬臂梁末端磁铁与外部磁铁之间的非线性磁力模型;利用Hamilton原理和Ral...     

压电材料变分原理逆问题的研究——动力学中的逆问题

研究了压电材料耦合动态场中Hamilton 型和Gurtin 型变分原理的逆问题。采用变积方法, 建立了各级变分原理和广义变分原理, 为建立横观各向同性压电材料的动力学有限元分析模型提供了依据。      

压电组件嵌入式风洞模型支撑系统振动主动控制仿真

吹风试验时风洞模型支撑系统往往会产生较大振动,这将影响到风洞试验的准确性和可靠性。因此,研究并实现模型支撑系统的振动控制技术尤其重要。基于压电材料机电耦合行为和振动主动控制原理,设计压电组件嵌入式风洞模型支撑系统;依据刚柔耦合动力学理论,建立模型支撑系统结构振动仿真模型;联合经典PID控制算法,进一步构建模型支撑系统结构控制一体化仿真模型,实现系统主动振动控制仿真;最后,计及接触非线性环节,建立压电组件嵌入式结构有限元模型,校核接触强度,优化嵌入型式。仿真结果表明,压电组件嵌入式模型支撑系统振动控制效果明显,结构安全可靠,具有较强的工程应用性。     

压电圆柱棒基于变分渐近法的广义Timoshenko模型

基于变分渐近方法,对外侧表面无规定电势作用的压电圆柱棒构建了一种新的广义Timoshenko模型,以准确捕捉介质效应、压电材料极化以及机-电耦合性质。利用细长比作为小参数渐近近似计算压电圆柱棒的三维机电焓,得到等效的一维机电焓,并将二阶渐近修正的能量项保存在近似机电焓表达式中。为便于工程应用,将近似机电焓转换为具有6个力自由度和1个附加电自由度的广义Timoshenko模型。通过截面极化下悬臂压电圆柱棒端部挠度算例表明:所构建的模型与ANSYS三维多物理场耦合模拟具有很好的一致性,并能以很小的精度损失极大地简化分析过程。     

Effective nonlinear behavior of electrostrictive multiphase composites: A micromechanical study

The micromechanics modeling of the nonlinear behavior of the electrostrictive multiphase composites is developed using an incremental formulation based on the variational-asymptotic method. The microstructure of composites is assumed to be periodic. Taking advantage of the small size of the microstructure, we formulate a variational statement of energy change of the unit cell through an asymptotic analysis of the functional to predict the effective instantaneous tangential electromechanical matrix of the composites. Several numerical examples are used to demonstrate the capability of the present theory.     

Micromechanical analysis of thermoelastoplastic behavior of metal matrix composites

A micromechanics model based on the variational asymptotic method for periodic composites was developed using an incremental formulation to capture the coupled thermo-elasto-plastic behavior of metal matrix composites. Taking advantage of the small size of the microstructure, a variational statement of the unit cell through an asymptotic expansion of an functional of energy change was formulated to calculate the effective instantaneous tangential elasto-plastic matrix and thermal stress matrix of the composite materials. An iterative homogenization and localization technique was proposed to simulate the nonlinear thermo-elasto-plastic behavior of metal matrix composites. This model was implemented using the finite element method. For validation, a numerical example was examined to demonstrate the application and accuracy of this theory and companion code.     

Micromechanical modeling and experimental characterization on viscoelastic behavior of 1–3 active composites

A study on the temperature-dependent viscoelastic behavior of (1–3 active composites) 1–3 piezocomposites and bulk piezoceramic subjected to electromechanical loading is carried out. The temperature-dependent effective properties are obtained experimentally using resonance based measurement technique. Experiments are also preformed for various fiber volume fractions of 1–3 piezocomposites subjected to constant compressive prestress and cyclic electric field at elevated temperature to understand the time-dependent behavior. Based on the measurements it is observed that the viscoelastic behavior has a significant influence on the electromechanical responses of 1–3 piezocomposites. Hence a viscoelastic based numerical model (unit cell approach) is proposed to predict the time-dependent effective properties of 1–3 piezocomposites. The evaluated effective properties are incorporated in a finite element based 3-D micromechanical model to predict the time-dependent thermo-electro-mechanical behavior of 1–3 piezocomposites and compared with the experimental observations.     

金属基复合材料热弹塑性变分渐近细观力学模型

基于变分渐近法建立具有周期性微结构的金属基复合材料（MMCs）细观力学模型及相应的增量方程,以准确预测其典型的热弹塑性行为和初始屈服面。利用细、宏观尺度比很小的特点,对单胞变分能量泛函变化进行渐近扩展,计算得到有效瞬时弹塑性刚度矩阵和热应力矩阵;利用迭代均质化及局域化技术模拟MMCs的非线性热弹塑性性能,并通过有限元技术实现相应的数值模型。算例分析表明:该模型能较好地预测MMCs的初始屈服面,并模拟热弹塑性耦合行为,研究成果为MMCs的进一步研究和实际应用提供了技术支撑。      

Time-dependent response of active composites with thermal, electrical, and mechanical coupling effect

The mechanical and physical properties of materials change with time. This change can be due to the dissipative characteristic of materials like in viscoelastic bodies and/or due to hostile environmental conditions and electromagnetic fields. We study time-dependent response of active fiber reinforced polymer composites, where the polymer constituent undergoes different viscoelastic deformations at different temperatures, and the electro-mechanical and piezoelectric properties of the active fiber vary with temperatures. A micromechanical model is formulated for predicting effective time-dependent response in active fiber composites with thermal, electrical, and mechanical coupling effects. In this micromechanical model limited information on the local field variables in the fiber and matrix constituents can be incorporated in predicting overall performance of active composites. We compare the time-dependent response of active composites determined from the micromechanical model with those obtained by analyzing the composites with microstructural details. Finite element (FE) is used to analyze the composite with microstructural details which allows quantifying variations of field variables in the constituents of the active composites.     

Modeling 1-3 composite piezoelectrics: thickness-mode oscillations

A simple physical model of 1-3 composite piezoelectrics is advanced for the material properties that are relevant to thickness-mode oscillations. This model is valid when the lateral spatial scale of the composite is sufficiently fine that the composite can be treated as an effective homogeneous medium. Expressions for the composite's material parameters in terms of the volume fraction of piezoelectric ceramic and the properties of the constituent piezoelectric ceramic and passive polymer are derived. A number of examples illustrate the implications of using piezocomposites in medical ultrasonic imaging transducers. While most material properties of the composite roughly interpolate between their values for pure polymer and pure ceramic, the composite's thickness-mode electromechanical coupling can exceed that of the component ceramic. This enhanced electromechanical coupling stems from partially freeing the lateral clamping of the ceramic in the composite structure. Their higher coupling and lower acoustic impedance recommend composites for medical ultrasonic imaging transducers. The model also reveals that the composite's material properties cannot be optimized simultaneously; tradeoffs must be made. Of most significance is the tradeoff between the desired lower acoustic impedance and the undesired smaller electromechanical coupling that occurs as the volume fraction of piezoceramic is reduced.     

智能材料电-磁-热-弹耦合性能的细观力学模型

基于变分渐近均匀化方法建立能预测智能材料电-磁-热-弹全耦合性能的细观力学模型。从智能材料电-磁-热-弹耦合本构方程中推导能量泛函变分表达式出发,利用单胞细观尺度与宏观尺度比作为小参数将材料的能量泛函渐近扩展为系列近似泛函,通过最小化近似泛函求解场变量的波动函数,从而建立逼近物理和工程真实性的细观力学模型,并通过有限元数值实现。通过BaTiO₃-CoFe₂O₄纤维/环氧树脂复合材料算例表明:构建的细观力学模型可准确预测电-磁-热-弹耦合性能和重构多物理场局部分布。