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K. H. Roscoe and his fellows of Cambridge University established the first elastoplastic model of soils which is based on classical plastic theory in 1963. However, due to the complexity of soils, the models that based on the classical metal constitutive theory or its modification accounting on the nature of soils have still much limitation when used to express the soil mechanical behavior. For example, the Duncan-Chang's model based on the generalized Hooke's law can not express the dilatancy of the soils. The uniqueness assumption of the direction of the incremental plastic strain in the classical plastic constitutive theory is not in agreement with some soil experiments.

但由于土的复杂性，目前以传统的本构理论为基础考虑土的一些特性而建立的模型在反映土体的力学特性上还存在很大的局限性，如建立于广义虎克定律基础上的Duncan—Chang模型不能反映土的剪胀性，传统的塑性本构理论中认为塑性应变增量方向具有唯一性的假设与一些土体的试验结果不符合。

Hypoplastic constitutive theory, which was originated from the middle and late stage of the 20th century, is a new type of soil constitutive theory based on rational mechanics. Hypoplastic theory can reflect inelasticity, nonlinearity, dilatancy and other main mechanical properties of granular material.

亚塑性本构理论是20世纪中晚期发展起来的一类基于有理力学的新型的连续介质本构建模理论，主要用于刻画无黏性散粒型上体的非弹性、非线性及剪胀性等主要应力应变特性。

The superstructure has used the model of elastical constitutive relation; the pile-group foundation has quoted the soil-pile equivalent compound model. It has been analyzed the constitutive relation for soil-pile equivalent compound which regarded as the transversely isotropic body this construction relations, and determined the corresponding elastic constant.

上部结构采用线弹性本构模型，下部群桩基础引用了桩土等效复合体模型，分析了将桩土等效复合体视为横观各向同性体的本构关系，确定了相应的弹性常数。

On the other hand, it is exemplified in the present paper that the principle of material frame – indifference with the admissible equivalent dynamic processes of a body by Truesdell and Noll (1965) [14] is more convenient than the form-invariance of constitutive functionals by Svendsen and Bertram (1999) [13] and Liu (2004)[4], especially for the rate-form constitutive equations.

通过例子说明了Truesdell和Noll 用等价动力过程，关于物质标架无关性原理的陈述，比Svendsen 和Bertram及Liu的本构关系在参考标架变换下的形式不变性更合理且方便，尤其是对微分方程形式的本构关系更是如此。

The exploitation is based on the similarity of the constitutive equation of damp-heat and the constitutive equation of piezoelectricity.

应用所开发的功能，进行了压电智能结构振动控制的研究，并用算例验证了其可行性。

At the chapters of theory analysis,constitutive equation of dusty is deduced from the results of the experiment and related theories about oblique shock wave.after that relationship of parameters reflecting flow-field characteristic are deduced from theories of shock wave polar .The paper set up conservation equations depicting gas and solid flow-field by double fluid model,thus equations and constitutive equation of granular phase form closed equations.then the paper uses AUSNT vector splitting method to numerically calculate the equations.

理论部分主要包括：利用实验测试结果以及斜激波理论测试出该堆积粉尘的本构方程，然后利用和激波极曲线理论得到反映流场特征参数的变化曲线；本文还利用双流体模型，建立了描述气—固两相流动的守恒型方程组，与本构方程一起构成封闭方程组。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

Employing the Hopkinson torsion-tension combination bar system, the constitutive relations of soft aluminum under torsion-tension combined high strain—rate was obtained, The constitutive relations of Monel alloy under Dual—direction shearing high strain—rate was also investigated after special modification of above apparatus.

本文还利用分离式扭—拉复台霍布金森杆设备测试软铝在高应变率扭—拉复合载荷作用下的本构关系，并将该设备经特殊改装测试了蒙纳尔合金在高应变率双向剪切下的力学特性，目前也尚未见这方面的公开资料。

The constitutive relations of austenitic and martensitic shape memory alloys associated with mechanics, electricity and calorifics (dissipation energy, sensing and actuation properties) are investigated systematically. And multifunctional constitutive models related with heating rate and loading frequency are established.

系统研究了奥氏体和马氏体形状记忆合金的力－电－热本构关系，建立了包含升温速度和加载频率的SMA多功能本构关系模型。

For considering the effect of stress path,the relations between the constitutive parameters in Gudehus-Bauer model and instantaneous stress path are analyzed and the stress-path factor is integrated into the hypoplastic constitutive model.

为了考虑应力路径的影响，分析了Gudehus-Bauer亚塑性模型参数与瞬时应力路径之间的关系，将应力路径影响引入亚塑性本构模型。

Graf, without question, is the greatest women's player in history.

格拉芙，现在，毫无疑问是女子网坛历史上最伟大的选手。

If not, you will have to look around at all your important data.

如果没有，您将需要检查所有的重要数据。