constitutive equation 中文意思是什麼

Perhaps constitutive equation has to be fortified by experimental evidence.

本構方程或許還得用試驗數據予以驗證。

Damage constitutive equation and experiment of layered rock

復合巖石損傷本構方程與實驗

Constitutive equation of roll casting in two - phase region of liquid and solid

鑄軋液固兩相區本構方程

Viscoplastic constitutive equation

粘塑性本構方程

Analysis of two - axial tension - compression stochastic damage constitutive equation of concrete

壓隨機本構方程分析

Parameter determination of the dynamic constitutive equation for polycrystal copper

晶體結構多晶銅的動態本構方程參數確定

With the material dynamic constitutive equation including damage and the effect of stain rate the predictable formula about ballistic limit velocity of fiber composite target. secondly based on the damage feature about ceramic / fiber composite target caused by impact load, analysis model about defense performance of ceramic / composite material target is formed and the predictable formula about ballistic limit velocity is also given. lastly using the reflection and projectile theory of stress wave the paper discusses the design of ceramic / composite material target, optimizes the design of double layer ceramic / composite targets, gains optimal coefficient under certain area density and discusses the variety relationship of area density and thickness with optimal coefficient u nder some ballistic limit velocity 3

首先，分析了纖維類正交鋪層復合靶板在沖擊載荷作用下的損傷破壞機理，結合包含損傷和應變率效應的材料動態本構方程，建立了纖維復合材料板彈道極限速度的預測公式；其次，根據陶瓷/纖維材料復合靶板在沖擊載荷下的破壞特點，建立了陶瓷/復合材料靶板抗彈性能分析模型，給出了彈道極限速度預測公式；最後，利用應力波反射和透射理論討論了陶瓷/復合材料靶板的設計問題，對雙層陶瓷復合靶板的優化設計進行了分析，給出了在一定面密度下的最佳優化系數，討論了一定彈道極限速度下的面密度和厚度隨優化系數的變化關系。

Like the active control, acld has a lot to be studied because there are a lot of problems such as : the constitutive equation of smart materials is very complicated ; the feedback control methods should be improved ; it is very difficult to deploy and optimize the sensors and actuators ; it is complicated to collect and feedback correctly the information of the structures without any time delay

和主動控制結構一樣，由於壓電結構本構關系比較復雜，控制策略還有待于進一步完善，如何配置和優化傳感器以及作動器，如何準確的採集和反饋結構的信息以及控制反饋的時間滯后等問題的存在，壓電智能結構的振動控制問題還有待于進一步的研究。

The corresponding control equation is given. the control equation and boundary condition about the addiontional small deformation ' s effect caused by initial stress using virtual principal theory in cylindrical reference frame. generalized stress and strain and equivalent constitutive equation are given

第四章提出了描寫柱形薄殼中初應力的數值特徵，將應力的三維分佈轉化為二維分佈，給出相應的支配方程；在柱坐標系中，利用虛功方程建立了初應力對附加小變形影響的控制方程和邊界條件；給出了廣義應力、廣義應變及等效本構關系。

Accordingly, a new framework, which provides a common scheme for the numerical simulation on the macroscopic behavior of ferroelectrics though multi - scale analysis on the coupled thermo - electrics - mechanical behavior of multiphase in heterogeneous material, is induced to construct the effective constitutive equation of multiphase. in chapter four, based on the law of domain nucleation and domain wall motion of 1800 domain switching, a new scheme of domain switching and numerical simulation approach is put forward on the foundation of thermodynamics. driving traction, nucleation criterion, velocity of domain wall motion, kinetic relation and rate of domain switching in a single grain are given

第四章以鐵電體1800疇變的過程中形核規律和疇界運動規律的實驗觀察結果為基礎，根據熱力學理論建立鐵電體疇變的理論框架和數值模擬方法；給出了單疇內疇變驅動力、新疇形核準則、疇界運動速度公式、疇變動力學的表達式，單晶的疇變速率公式；用細觀力學的觀點給出了對多晶鐵電體多場耦合的有效性質進行包含疇變速率影響的多尺度分析方法。

( 2 ) using craze density dcraze (, ) to illustrate the damage degree of material, considering strain equivalent hypothesis, non - linear visco - elastic constitutive equation of pmma taken into consideration of the operation of craze damage is arrived. the pmma sheet is loaded under different forces to validate the non - linear visco - elastic constitutive equation with damage. the result shows that the theory curves obtained by the nonlinear viscoelasticity constitutive relation agrees with experimental data considerably well

（ 2 ）用銀紋密度d _ （ craze ） （ ， t ）來描述材料的損傷度d ，在考慮應變等效性假設的基礎上，得到了pmma材料考慮損傷的非線性粘彈性材料的本構關系，運用此方程對材料在不同載荷水平下進行蠕變實驗，從而對蠕變條件下的應變響應進行模擬和預報。

Based on the damage evolution formation depicted by kachanov of brittle materials in unitary stress state, in this dissertation, the constitutive equation of nonlinear damage material is given, macroscopically, on the assumption that damage variable is exponential relation to strain, d = ( gy i k ) ", where g is the shear module, k is the damage module and the y is the effective strain, d is damage variable and n is hardening exponent

在kachanov描述的一維應力狀態下的脆性材料的損傷演化模型的基礎上，文中給出非線性損傷材料的本構方程，唯象地假設損傷變量與應變成冪次關系， d ~ * = （ g / k ） ~ n ，其中g為剪切模量， k為損傷模量，為有效應變因子， d為損傷變量， n為硬化指數。

In the positive - issue research of bird impact, the thesis carefully explores the basic theories, finite element numerical method and key techniques of the solution process in ls - dyna3d software system for contact - impact issue of viscoelastic bodies at large deformation. the well - chosen cases examine the accuracy of solutions in ls - dyna3d for large deformation impact issues. under the proof work, the incremental constitutive equation of bilinear and nonlinear viscoelastic materials are derived, coded and verified in ls - dyna3d

在鳥撞正問題的研究中，本文詳細推導了大變形粘彈性接觸-碰撞有限元分析的基本理論、數值計算方法、求解過程、關鍵技術以及上述內容在ls - dyna3d中的具體應用，算例考察了ls - dyna3d在求解碰撞以及大變形問題上的計算精度，同時推導了線彈性材料、雙線性彈塑性材料以及非線性粘彈性材料增量法迭代方程，編制了相應的用戶自定義材料子程序，並進行了子程序驗證。

The study of mechanical properties and constitutive equation for bismaleimide modified by o, o - dially phen a

中高溫和動態力學性能試驗研究及本構方程的建立

At the meantime, the rock mass may alternate between loading and unloading and it exists in certain kind of liquid, such as surface water, unconfined water, confined water etc for its intrinsic crannies. the practical rock mass concerned project must solve the key stability pr oblem after the understanding of the complicated mechanical characteristic and the deformation trends to guide the following project design and construction for the demand of security, economy, feasibility and validity. however, the intrinsic nonlinearness and complexity of the engineering rock mass become the main difficulty to predict the stability and deformation, the corresponding structure design must ensure enough safety with all the determinate or random force combination, so a model without the geometry distortion and constitutive equation warp is necessary to be built for the quantificational analysis of practical structure ' s stress, for the simulation of the real process and for the determinate evaluation system and optimization

由於實際工程巖體其固有的非線性和復雜性，使得求解對應的諸如其穩定性、變形等問題面臨較大的困難，而有關的工程結構的設計必須保證該結構在外來因素的作用下具有足夠的安全度、經濟性和合理性，這必然要求對巖體及其工程結構的受力與變形有一套量化評判體系和優化技術，抓住實際工程問題的本質特徵並建立可行的符合幾何模擬、本構模擬、受力模擬、過程模擬四原則的求解模型，通過該模型的數值模擬成果來指導巖體工程的設計、施工及運營、管理；而巖體結構面的存在使得基於傳統連續介質力學理論的理論分析和數值模擬面臨巨大的挑戰，物理模擬的試驗周期和成本也大大增加，而巖土體工程問題則成為典型的數據有限、了解程度有限類問題，這類問題的解決需要綜合應用理論分析、經驗判斷、物理模擬和數值模擬等方法，數值模擬可以完成目前許多技術手段無法完成的實驗，如參數控制，復雜條件下的邊界條件的處理，同時數值模擬具有高可重復性，且數值模擬的成本和人力開銷等遠低於物理模擬，因此研究巖土體工程問題的流形元數值模擬方法是一項具有理論和實際工程應用價值的重要課題。

( 2 ) because of t he variability of rock subjected to outside action, three new conceptions : postive damage basic damage and negative damage, are suggested, which can deal with the condition that rock density became large. ( 3 ) the present damage variables based on ct number mostly include ct average number of the rock without damage, which is difficult to measure, so a new damage variable, which includes the average ct number is proposed, on the other hand, strain equal theory is generalized because the one put foreword by lemaitre is not good enough to use. ( 4 ) a axial damage constitutive equation is proposed and testified. ( 5 ) with the circle times, the damage propagation laws of two different rocks, subjected to circle of freezing and thawing, are studied, and in the analysis process, traditional analysis method including average ct number and is used, some important conclusions are reached : inner damage of soft rock containing a large mount of apertures is largely propagating with the time increasement of circle, however, at the preliminary time, the hard rock containing a small mount of aperture is a little propagating, at late time, the influence become large ; ( 6 ) zone separation and statistics frequency put forward is used to analysized the three different damage propagation in the open circumstance, when they are subjected to the different circle times of freezing and thawing, in which the temperature variability is linear, different freezing rate, and different freezing temperature, and no water is supplied during the test

在研究過程中本文主要做了以下工作： （ 1 ）針對巖石損傷變化較小時，運用ct均值和方差分析不方便的缺陷，本文提出運用對ct數范圍劃分區段的方法，根據各區段統計頻率的變化規律來分析損傷擴展狀況； （ 2 ）針對巖石受到外部作用的多變性，本文提出了基準損傷，正損傷，負損傷的概念，在某種程度上考慮了巖石受到外部作用時的壓密情況； （ 3 ）現有的基於ct數的損傷變量大多需要用到巖石基體的ct均值，這實際上是很難觀測到的，因此本文建議了一個可運用巖石初始狀態ct均值的損傷變量，由於現有的勒邁特教授應變等價原理使用上的不便，本文在其基礎上進行了推廣； （ 4 ）建議了一個可用巖石初始狀態ct數和彈性模量的單軸損傷本構方程，並用算例進行了驗證； （ 5 ）對兩種不同巖石在開放環境下受到凍融循環作用且融化過程中補水時，內部損傷隨凍融循環次數增加的擴展規律進行了探討，主要運用了常規的ct均值和ct方差的分析方法進行分析，試驗發現：對于孔隙率和含水率較高，密度和強度較低的軟弱巖石，凍融循環次數對損傷結構的擴展有明顯的影響，而對于孔隙率和含水率較低，密度和強度較高的硬巖，凍融循環次數對其損傷結構擴展初期由於含水率低的原因，影響不是太大，而後期由於水補給后，含水率較高的原因，凍融影響逐漸增大； （ 6 ）運用了本文提出的區段劃分和統計頻率的方法，深入地分析了開放環境下的線性溫度變化的凍融循環次數，凍結溫度，凍結速度不同巖石作用時，其內部損傷隨凍融循環次數，凍結速度和凍結溫度變化的擴展規律，需要指出的是除了在試驗前飽水外，凍融過程中沒有補水。

Introducing strain function y /, applying geometry equation, compatibility equation and constitutive equation to deduct the basis equation satisfied by i / / in mode iii crack problem, for different n, small area damage solution of i / is obtained by means of calculation

引入應變函數，應用幾何方程、協調方程和本構方程推導出型裂紋問題中滿足的基本方程，對不同的n值，通過計算可以得出的小范圍屈服解。

Results from experiments with a constant - viscosity, elastic fluids ( boger fluids ) and computations using the corresponding oldroyd _ b constitutive equation are presented

實驗採用作者配置的等粘度彈性流體，並用流變測量的結果確定oldroyd _ b本構方程的參數。

Based on the review of coupling theory of porous media, a nonlinear mathematics mechanical model and the governing differential equation of the coupled problem of thermal - gas fluid - mechanical are derived from the theory of continuum mechanics and mixture theory. a constitutive equation of the porous media is obtained in the coupling processes

在全面系統的回顧與總結多孔介質多物理場耦合分析與模擬的研究成果的基礎上，以混合物理論以及流體、應力、溫度相互作用的機理為基礎，建立溫度場、滲流場、應力場三場耦合分析的非線性數學模型。

Study of reinforcement effect of anchored rock masses and analytic constitutive equation for rock bolt

巖體錨固效應及錨桿的解析本構模型研究