Introduction to the theory of poro-elasticity

M. Sazid et al.Stress Measurement with Rheological Stress Recovery Method and Its Application.Mathematical Problems in Engineering, 2016, Article ID: 7059151.https:///10.1155/2016/7059151[46]Jaeger, N.G.W.C.J.C. and Zimmerman, R.W. (2007) Fundamentals of Rock Me-chanics. 4th Edition, Wiley-Blackwell, Hoboken.[47]Gowida, A., Elkatatny, S. and Gamal, H. (2021) Unconfined Compressive Strength(UCS) Prediction in Real-Time While Drilling Using Artificial Intelligence Tools.Neural Computing and Applications, 33, 8043-8054.https:///10.1007/s00521-020-05546-7[48]Al Dhaif, R., Ibrahim, A.F. and Elkatatny, S. (2022) Prediction of Surface Oil Ratesfor Volatile Oil and Gas Condensate Reservoirs Using Artificial Intelligence Tech-niques. Journal of Energy Resources Technology, Transactions of the ASME, 144,Article 033001.https:///10.1115/1.4051298[49]Fang, X., Feng, H., Wang, Y. and Fan, T. 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Scientific Reports,11,Ar-ticle No. 23445.https:///10.1038/s41598-021-02959-9[53]Lawal, A.I. and Kwon, S. (2021) Application of Artificial Intelligence to Rock Me-chanics: A n Overview. Journal of Rock Mechanics and Geotechnical Engineering,13, 248-266.https:///10.1016/j.jrmge.2020.05.010World Journal of Engineering and Technology, 2023, 11, 273-280https:///journal/wjetISSN Online: 2331-4249ISSN Print: 2331-4222Establishment of Unstable Flow Model and Well Testing Analysis for Viscoelastic Polymer FloodingZheng Lv, Meinan WangBohai Oilfield Research Institute of CNOOC Ltd., Tianjin Branch, Tianjin, ChinaAbstractAt present, the polymer solution is usually assumed to be Newtonian fluid orpseudoplastic fluid, and its elasticity is not considered on the study of poly-mer flooding well testing model. A large number of experiments have shownthat polymer solutions have viscoelasticity, and disregarding the elasticity willcause certain errors in the analysis of polymer solution seepage law. Based onthe percolation theory, this paper describes the polymer flooding mechanismfrom the two aspects of viscous effect and elastic effect, the mathematicalmodel of oil water two-phase three components unsteady flow in viscoelasticpolymer flooding was established, and solved by finite difference method, andthe well-test curve was drawn to analyze the rule of well test curve in polymerflooding. The results show that, the degree of upward warping in the radialflow section of the pressure recovery curve when considering polymer elastic-ity is greater than the curve which not considering polymer elasticity. The re-laxation time, power-law index, polymer injection concentration mainly af-fect the radial flow stage of the well testing curve. The relaxation time, pow-er-law index, polymer injection concentration and other polymer floodingparameters mainly affect the radial flow stage of the well testing curve. Thelarger the polymer flooding parameters, the greater the degree of upwarpingof the radial flow derivative curve. This model has important reference signi-ficance for well-testing research in polymer flooding oilfields.KeywordsPolymer Flooding, Viscoelasticity, Well Testing, Mathematical Model,Seepage Law1. IntroductionPolymer flooding is an important way to improve oil recovery in production oil-How to cite this paper: Lv, Z. and Wang,M.N. (2023) Establishment of UnstableFlow Model and Well Testing Analysis forViscoelastic Polymer Flooding. World Jour-nal of Engineering and Technology, 11,273-280.https:///10.4236/wjet.2023.112019Received: April 6, 2023Accepted: May 6, 2023Published: May 9, 2023Copyright © 2023 by author(s) andScientific Research Publishing Inc.This work is licensed under the CreativeCommons Attribution InternationalLicense (CC BY 4.0)./licenses/by/4.0/Open AccessZ. Lv, M. N. Wangfields. It has been widely industrialized in China and has achieved good applica-tion results and economic benefits [1] [2] [3] [4] [5]. Most experts have con-ducted a lot of research on the percolation characteristics of polymer in porous media and its impact on oil displacement effect. However, in most analysis of polymer flooding percolation laws, people usually assume that polymer solution is Newtonian fluid or pseudoplastic fluid, without considering its elasticity. A large number of experiments have shown that polymer solutions have viscoelas-ticity, and disregarding their elasticity will cause certain errors in the analysis of polymer solution seepage law [6] [7] [8] [9] [10]. This article studies the rheo-logical and viscoelastic properties of polymer solution, provides a characteriza-tion method for the elastic viscosity of polymer solutions, and proposes a new polymer flooding well testing model which takes into account the viscoelastic properties of polymer, which guiding the study of percolation law in polymer flooding Oilfields.2. Mathematical Description for the Main Oil Displacement Mechanism of PolymerUnder certain temperature condition, the viscosity of polymer solution increases significantly with increasing concentration. Under static condition, the viscosity of the polymer solution can be expressed as the following equation.()023p w 1p 2p 3p 1A c A c A c µµ=++++ (1)In which, 0p µ is zero shear viscosity of polymer solution, Pa·s; μw is water viscosity, Pa·s; c p is Polymer solution concentration, mg/L; A 1, A 2, A 3 is coeffi-cient.Due to the generally low concentration of polymer solutions, 33pA c and its subsequent terms are often overlooked.()02p w 1p 2p 1A c A c µµ=++ (2)Using the Kerry model to describe the viscoelasticity of polymer solution.()()()1220eff pppf 1n µµµµθγ−∞∞ =+−+⋅(3)In which, μeff is viscoelastic polymer viscosity, Pa·s; pµ∞is ultimate shear rate viscosity, Pa·s; θf is relaxation time, s; n is power-law index.3. Establishment and Solution of a Mathematical Model for Oil-Water Two-Phase Flow in Polymer FloodingAssuming that polymer flooding is an isothermal displacement process and mul-tiphase flow satisfies the generalized Darcy’s law, the fluid consists of oil-water two-phase flow, with only oil components in the oil phase and water and polymer components in the water phase. Ignoring the influence of capillary pressure and gravity, the continuity equation of oil-water two-phase flow can be expressed as the following equations.()o ro o o o o o K K p q S t ρρφµ ⋅∂∇⋅∇+= ∂(4)Z. Lv, M. N. Wang()w rw w w w w eff KK p q S t ρρφµ ∂∇⋅∇+= ∂(5)()rw p w w p w p eff KK c p q c S c t φµ ∂∇⋅∇+= ∂(6)In which, ρo is oil phase density, kg/m 3; ρw is water phase density, kg/m 3; K is absolute permeability, m 2; K ro is oil relative permeability; K rw is water relative permeability; µo is oil phase viscosity, Pa·s; p o is oil phase pressure, Pa; p w is water phase pressure, Pa; ϕ is porosity; q o is oil recovery intensity, m 3/(s·m 3); q w is water injection intensity, m 3/(s·m 3); S o is oil saturation; S w is water saturation.From Equations (4) and (5), the pressure differential equations for the oil and water phases can be obtained as the following equations.o o o o o o ox oy wx wy w w o o o to w wp p p p x x y y x x y y p C q q t ρρλλλλρρρφρρ∂∂∂∂∂∂∂∂⋅+⋅+⋅+⋅ ∂∂∂∂∂∂∂∂∂−−∂ (7)o o wx wy ww o o w w w f w w w p p q x x y y S p p S C S C t t tλλφρρφφρ∂∂ ∂∂⋅+⋅+ ∂∂∂∂∂∂∂=++∂∂∂ (8) Under the condition of uniform grid, the oil phase pressure Equation (7), the water phase saturation seepage Equation (8), and the polymer component con-centration Equation (6) are respectively processed by finite difference, and the fi-nite difference model corresponding to the oil-water two-phase seepage mathe-matical model can be established.11111,o ,1,o 1,,o ,,o 1,,o ,1,n n n n n i j i j i j i j i j i j i j i j i j i j i j c p a p e p b p d p f +++++−−++++++=(9) ()()()111111w ,1,o ,11,o 1,1,o ,1,o 1,1,o ,1w ,w w w w f o w ,,w n n n n n n n i ji ji j i j i j i j i j i j i j i j i j i jnnni ji j t Scpa p e pb pd p V q tS C C p S φρφρρφ++++++−−++∆=++++∆ ++++ (10) ()()()111111p ,2,o ,12,o 1,2,o ,2,o 1,2,o ,1w ,1w p ,w ,w ,p ,p ,f o p ,,w w ,,nn n n n n n i j i ji j i j i j i j i j i j i j i j i j i jn n n nn i j i j i jn n ni ji j i jni ji ji jt c cp a p e p b p d p S V q c tS S c c C p c S V Sφφ++++++−−+++∆=++++∆− +−++(11)The coefficients in the above equation can be expressed as the following equa-tions.o,11o w w 22i j xi xi a TT ρρ−−=+; o ,11o w w 22i j xi xi b T T ρρ++=+; o ,11o w w 22i j yi yi c T T ρρ−−=+; o,11o w w 22i j yi yi d TT ρρ++=+; ()o t ,,,,,,i j i j i j i j i j i j n C V e a b c d t φρ =−++++ ∆;Z. Lv, M. N. Wang()o t ,o,w ,o ,,w i j n i ji j i j i j n C V f q V q V p t φρρρ=−−−∆; 1,1w 2i j xi a T −=; 1,1w 2i j xi b T+=; 1,1w 2i j yi c T−=; 1,1w 2i j yi d T+=;()w w w f ,1,1,1,1,1,i ji ji j i j i j i j nS C C V e a b c d tφρ + =−−−−−∆; 2,1w 2i jxi a T −=; 2,1w 2i j xi b T +=; 2,1w 2i j yi c T −=; 2,1w 2i j yi d T +=;w p f ,1,1,1,1,1,n i j i j i j i j i j i j n S c C V e a b c d t φ =−−−−−∆; 1o 21o 122j xi xi i i y h T x x λ±±±∆=∆+∆; 1o 21oy 122i yj j j j x h Ty y λ±±±∆=∆+∆; 1w 21w 122j xi xi i i y h Tx x λ±±±∆=∆+∆; 1w 21wy 122i yj j j j x h Ty y λ±±±∆=∆+∆;,i j i j V x y h =∆∆; o ro o o KK ρλµ=; w rww effKK ρλµ=; rw p p eff KK c λµ=The finite difference method is used to solve the problem, and the IMPES me-thod is used to solve the pressure implicitly, the saturation explicitly, and the po-lymer concentration explicitly. The solution process is as follows: Firstly, startingfrom the initial conditions, the pressure value at time n can be obtained from the pressure equation. A fter obtaining the pressure at each time step, the obtained node pressure is substituted into the saturation equation to obtain the water sa-turation value of each node at time n. Then, the water saturation value is substi-tuted into the polymer seepage equation to obtain the polymer concentration value of each node at time n. In this way, the reservoir pressure, oil saturation, water saturation, and polymer concentration values at different time steps can be obtained. Record the bottom hole pressure values at different times and the pres-sure values at any point in the formation, draw a well testing curve, and analyze the curve.4. Analysis of Polymer Flooding Well Testing CurveAfter the text edit has been completed, the paper is ready for the template. Dup-licate the template file by using the Save As command, and use the naming con-vention prescribed by your journal for the name of your paper. In this newly created file, highlight all of the contents and import your prepared text file. You are now ready to style your paper. The viscoelastic polymer flooding mathemat-ical model of the inverse five point method well pattern has been established, the basic parameter variables being are as follow, C t = 5.2 × 10−4 MPa −1, ϕ = 0.3, n = 0.4, K = 0.375 μm 2, c p = 2.0 × 103 mg/L, p e = 20 MPa, h = 10 m, S wi = 0.4. The shut-in pressure recovery test curve of the central polymer injection well was drawn.The comparison of pressure dynamic curves between water flooding and po-lymer flooding is shown in Figure 1.Before polymer injection, the radial flow section of the water drive derivative curve is basically horizontal, and the recovery speed is stable. After polymer in-Z. Lv, M. N. Wangjection, a hump appears in the radial flow stage of the curve, and the pressure and pressure conductivity values are higher than those of water drive. The de-gree of warping in the radial flow section of the well testing curve when consi-dering polymer elasticity is greater than the curve which not considering poly-mer elasticity. A fter polymer injection, the viscosity of the displacement fluid increases, and the flow resistance within the formation increases, resulting in an upward trend in the radial flow section of the curve compared to water flooding. Compared with water flooding, polymer flooding has a higher viscosity of the displacement fluid, greater resistance to fluid flow in the formation, and higher injection pressure required. Therefore, the pressure and pressure derivative val-ues of polymer flooding well testing curves are higher than those of water flood-ing. Considering the elasticity of the polymer, in addition to shear viscosity, elas-tic viscosity is also taken into account. As the viscosity of the polymer increases, the flow resistance increases, resulting in a greater degree of upward warping in the radial flow section.The polymer flooding oil-water two-phase well test curves corresponding to different relaxation times are shown in Figure 2.Z. Lv, M. N. WangRelaxation time is a physical quantity that measures the elasticity of a polymersolution. From the graph, it can be seen that the relaxation time mainly affectsthe transition section and radial flow section of the well testing curve. The largerthe relaxation time, the greater the pressure and pressure derivative values. Thehigher the “hump” of the transition section and radial flow section, and thegreater the degree of upward warping of the radial flow section. Due to the con-sideration of the elastic viscosity of the polymer solution, the relaxation time af-fects the elastic viscosity of the polymer. As the relaxation time increases, the in-fluence of elasticity on the well testing curve gradually increases; The larger therelaxation time, the greater the elastic viscosity at the same shear rate, the greaterthe apparent viscosity, and the greater the seepage resistance of the fluid duringthe seepage process, resulting in a greater degree of upward warping of the radialflow section.The analysis curve of the influence factors of power law index on polymerflooding oil-water two-phase well testing is shown in Figure 3.The power-law index is a parameter to characterize the non-newtonian prop-erty of polymer solution, and the power-law index of Newtonian fluid is 1. Thepower-law index mainly affects the degree of upwarping in the radial flow sec-tion. The closer the power-law index is to 1, the higher the pressure and pressurederivative curve, and the greater the degree of upwarping in the radial flow sec-tion of the pressure derivative curve. Near the injection well, the closer the pow-er law index is to 1, the weaker the non-newtonian property of the polymer solu-tion is, the lower the shear thinning degree is at the same shear rate, the higherthe viscosity of the polymer solution is, the greater the seepage resistance is, andsistance, and the greater the degree of upward warping in the radial flow section; The higher the viscosity of the polymer, the smaller the range of influence dur-ing the same production time, and the shorter the radial flow section.5. Conclusions1) Compared with water flooding, the radial flow section of the pressure re-covery curve of polymer flooding will appear upward in the early stage, resulting in greater flow resistance in the formation and higher injection pressure re-quired; The degree of upward warping in the radial flow section of the pressure recovery curve when considering polymer elasticity is greater than the curve which not considering polymer elasticity.2) Through the analysis of the influencing factors on the pressure recovery curve of polymer flooding, it can be concluded that each factor mainly affects the radial flow stage. The larger the relaxation time, power law exponent, and poly-mer injection concentration, the greater the degree of upward warping of the radial flow derivative curve.3) The existence of viscoelasticity in polymer solutions is one of the reasons for the increasing in injection pressure. It is necessary to consider the viscoelas-ticity of polymer solutions in the flow theory and flow pattern analysis of poly-mer flooding.Conflicts of InterestThe authors declare no conflicts of interest regarding the publication of this pa-per.References[1]Wang, D.-M., Cheng, J.-C., Xia, H.-F., Li, Q. and Shi, J.-P. (2001) Visco-Elastic Flu-。

英文材料期刊简介Journal of Alloys and Compounds《合金与化合物杂志》瑞士ISSN:0925-8388，1959年创刊，全年36期，Elsevier Science出版社出版，SCI收录期刊，SCI2003年影响因子1.080。

国际性材料科学和固体化学与固体物理学杂志。

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文章多用英文发表。

Journal of Composites for Construction《建筑复合材料杂志》美国ISSN:1090-0268，1997年创刊，每年4期，American Society of Civil Engineers,USA出版。

刊载有关建筑用合成纤维增强复合材料的研究论文。

SCI、EI收录期刊，SCI2003年影响因子1.234，被引频次249、即年指标0.125、年载文量40。

2003年EI收录91篇。

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Journal of Materials in Civil Engineering《土木工程材料杂志》美国ISSN:0899-1561，1989年创刊，每年6期，American Society of Civil Engineers,USA出版。

刊载土建材料的开发、加工与现场生产、特性评价、应用和性能等方面的研究论文。

SCI、EI收录期刊，2002年SCI影响因子0.346、被引频次193、即年指标0.015、年载文量66、被引半衰期4.9。

EI2002年收录66篇。

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主要发表研究陶瓷材料结构、特性和加工的原始论文。

elasticity 弹性力学弹性理论theory of elasticity均匀应力状态homogeneous state of stress应力不变量stress invariant应变不变量strain invariant应变椭球strain ellipsoid均匀应变状态homogeneous state ofstrain应变协调方程equation of straincompatibility拉梅常量Lame constants各向同性弹性isotropic elasticity旋转圆盘rotating circular disk楔wedge开尔文问题Kelvin problem布西内斯克问题Boussinesq problem艾里应力函数Airy stress function克罗索夫--穆斯赫利什维Kolosoff-利法Muskhelishvili method基尔霍夫假设Kirchhoff hypothesis板Plate矩形板Rectangular plate圆板Circular plate环板Annular plate波纹板Corrugated plate加劲板Stiffened plate,reinforcedPlate 中厚板Plate of moderate thickness 弯[曲]应力函数Stress function of bending 壳Shell扁壳Shallow shell旋转壳Revolutionary shell球壳Spherical shell [圆]柱壳Cylindrical shell 锥壳Conical shell环壳Toroidal shell封闭壳Closed shell波纹壳Corrugated shell扭[转]应力函数Stress function of torsion 翘曲函数Warping function半逆解法semi-inverse method瑞利--里茨法Rayleigh-Ritz method 松弛法Relaxation method莱维法Levy method松弛Relaxation 量纲分析Dimensional analysis 自相似[性] self-similarity影响面Influence surface接触应力Contact stress赫兹理论Hertz theory协调接触Conforming contact滑动接触Sliding contact滚动接触Rolling contact压入Indentation各向异性弹性Anisotropic elasticity颗粒材料Granular material散体力学Mechanics of granular media 热弹性Thermoelasticity超弹性Hyperelasticity粘弹性Viscoelasticity对应原理Correspondence principle 褶皱Wrinkle塑性全量理论Total theory of plasticity 滑动Sliding微滑Microslip粗糙度Roughness非线性弹性Nonlinear elasticity大挠度Large deflection突弹跳变snap-through有限变形Finite deformation格林应变Green strain阿尔曼西应变Almansi strain弹性动力学Dynamic elasticity运动方程Equation of motion准静态的Quasi-static气动弹性Aeroelasticity水弹性Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波Cylindrical wave水平剪切波Horizontal shear wave竖直剪切波Vertical shear wave 体波body wave无旋波Irrotational wave畸变波Distortion wave膨胀波Dilatation wave瑞利波Rayleigh wave等容波Equivoluminal wave勒夫波Love wave界面波Interfacial wave边缘效应edge effect塑性力学Plasticity可成形性Formability金属成形Metal forming耐撞性Crashworthiness结构抗撞毁性Structural crashworthiness 拉拔Drawing破坏机构Collapse mechanism 回弹Springback挤压Extrusion冲压Stamping穿透Perforation层裂Spalling塑性理论Theory of plasticity安定[性]理论Shake-down theory运动安定定理kinematic shake-down theorem静力安定定理Static shake-down theorem 率相关理论rate dependent theorem 载荷因子load factor加载准则Loading criterion加载函数Loading function加载面Loading surface塑性加载Plastic loading塑性加载波Plastic loading wave简单加载Simple loading比例加载Proportional loading 卸载Unloading卸载波Unloading wave冲击载荷Impulsive load阶跃载荷step load脉冲载荷pulse load极限载荷limit load中性变载nentral loading拉抻失稳instability in tension 加速度波acceleration wave本构方程constitutive equation 完全解complete solution名义应力nominal stress过应力over-stress真应力true stress等效应力equivalent stress流动应力flow stress应力间断stress discontinuity应力空间stress space主应力空间principal stress space静水应力状态hydrostatic state of stress 对数应变logarithmic strain工程应变engineering strain等效应变equivalent strain应变局部化strain localization应变率strain rate应变率敏感性strain rate sensitivity 应变空间strain space有限应变finite strain塑性应变增量plastic strain increment 累积塑性应变accumulated plastic strain 永久变形permanent deformation内变量internal variable应变软化strain-softening理想刚塑性材料rigid-perfectly plasticMaterial 刚塑性材料rigid-plastic material理想塑性材料perfectl plastic material 材料稳定性stability of material 应变偏张量deviatoric tensor of strain 应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain 应力球张量spherical tensor of stress 路径相关性path-dependency线性强化linear strain-hardening应变强化strain-hardening随动强化kinematic hardening各向同性强化isotropic hardening强化模量strain-hardening modulus幂强化power hardening 塑性极限弯矩plastic limit bendingMoment 塑性极限扭矩plastic limit torque弹塑性弯曲elastic-plastic bending 弹塑性交界面elastic-plastic interface 弹塑性扭转elastic-plastic torsion粘塑性Viscoplasticity非弹性Inelasticity理想弹塑性材料elastic-perfectly plasticMaterial 极限分析limit analysis极限设计limit design极限面limit surface上限定理upper bound theorem上屈服点upper yield point下限定理lower bound theorem下屈服点lower yield point界限定理bound theorem初始屈服面initial yield surface后继屈服面subsequent yield surface屈服面[的]外凸性convexity of yield surface 截面形状因子shape factor of cross-section沙堆比拟sand heap analogy 屈服Yield 屈服条件yield condition屈服准则yield criterion屈服函数yield function屈服面yield surface塑性势plastic potential 能量吸收装置energy absorbing device 能量耗散率energy absorbing device 塑性动力学dynamic plasticity 塑性动力屈曲dynamic plastic buckling 塑性动力响应dynamic plastic response 塑性波plastic wave运动容许场kinematically admissibleField 静力容许场statically admissibleField 流动法则flow rule速度间断velocity discontinuity滑移线slip-lines滑移线场slip-lines field移行塑性铰travelling plastic hinge 塑性增量理论incremental theory ofPlasticity米泽斯屈服准则Mises yield criterion 普朗特--罗伊斯关系prandtl- Reuss relation 特雷斯卡屈服准则Tresca yield criterion洛德应力参数Lode stress parameter莱维--米泽斯关系Levy-Mises relation亨基应力方程Hencky stress equation赫艾--韦斯特加德应力空Haigh-Westergaard 间stress space洛德应变参数Lode strain parameter德鲁克公设Drucker postulate盖林格速度方程Geiringer velocityEquation结构力学structural mechanics结构分析structural analysis结构动力学structural dynamics拱Arch三铰拱three-hinged arch抛物线拱parabolic arch圆拱circular arch穹顶Dome空间结构space structure空间桁架space truss雪载[荷] snow load风载[荷] wind load土压力earth pressure地震载荷earthquake loading弹簧支座spring support支座位移support displacement支座沉降support settlement超静定次数degree of indeterminacy机动分析kinematic analysis结点法method of joints截面法method of sections结点力joint forces共轭位移conjugate displacement影响线influence line三弯矩方程three-moment equation单位虚力unit virtual force刚度系数stiffness coefficient柔度系数flexibility coefficient力矩分配moment distribution力矩分配法moment distribution method 力矩再分配moment redistribution分配系数distribution factor矩阵位移法matri displacement method 单元刚度矩阵element stiffness matrix 单元应变矩阵element strain matrix总体坐标global coordinates贝蒂定理Betti theorem高斯--若尔当消去法Gauss-Jordan eliminationMethod 屈曲模态buckling mode复合材料力学mechanics of composites复合材料composite material 纤维复合材料fibrous composite单向复合材料unidirectional composite泡沫复合材料foamed composite颗粒复合材料particulate composite 层板Laminate夹层板sandwich panel正交层板cross-ply laminate斜交层板angle-ply laminate 层片Ply多胞固体cellular solid 膨胀Expansion压实Debulk劣化Degradation脱层Delamination脱粘Debond纤维应力fiber stress层应力ply stress层应变ply strain层间应力interlaminar stress比强度specific strength强度折减系数strength reduction factor 强度应力比strength -stress ratio 横向剪切模量transverse shear modulus 横观各向同性transverse isotropy正交各向异Orthotropy剪滞分析shear lag analysis短纤维chopped fiber长纤维continuous fiber纤维方向fiber direction纤维断裂fiber break纤维拔脱fiber pull-out纤维增强fiber reinforcement致密化Densification最小重量设计optimum weight design 网格分析法netting analysis混合律rule of mixture失效准则failure criterion蔡--吴失效准则Tsai-W u failure criterion 达格代尔模型Dugdale model断裂力学fracture mechanics概率断裂力学probabilistic fractureMechanics格里菲思理论Griffith theory线弹性断裂力学linear elastic fracturemechanics, LEFM弹塑性断裂力学elastic-plastic fracturemecha-nics, EPFM 断裂Fracture 脆性断裂brittle fracture解理断裂cleavage fracture蠕变断裂creep fracture延性断裂ductile fracture晶间断裂inter-granular fracture 准解理断裂quasi-cleavage fracture 穿晶断裂trans-granular fracture 裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹elliptical crack深埋裂纹embedded crack[钱]币状裂纹penny-shape crack预制裂纹Precrack短裂纹short crack表面裂纹surface crack裂纹钝化crack blunting裂纹分叉crack branching裂纹闭合crack closure裂纹前缘crack front裂纹嘴crack mouth裂纹张开角crack opening angle,COA 裂纹张开位移crack opening displacement,COD裂纹阻力crack resistance裂纹面crack surface裂纹尖端crack tip裂尖张角crack tip opening angle,CTOA裂尖张开位移crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularityField裂纹扩展速率crack growth rate稳定裂纹扩展stable crack growth定常裂纹扩展steady crack growth亚临界裂纹扩展subcritical crack growth 裂纹[扩展]减速crack retardation 止裂crack arrest 止裂韧度arrest toughness断裂类型fracture mode滑开型sliding mode张开型opening mode撕开型tearing mode复合型mixed mode撕裂Tearing 撕裂模量tearing modulus断裂准则fracture criterionJ积分J-integralJ阻力曲线J-resistance curve断裂韧度fracture toughness应力强度因子stress intensity factor HRR场Hutchinson-Rice-RosengrenField 守恒积分conservation integral 有效应力张量effective stress tensor 应变能密度strain energy density 能量释放率energy release rate内聚区cohesive zone塑性区plastic zone张拉区stretched zone热影响区heat affected zone, HAZ 延脆转变温度brittle-ductile transitiontempe- rature 剪切带shear band剪切唇shear lip无损检测non-destructive inspection 双边缺口试件double edge notchedspecimen, DEN specimen 单边缺口试件single edge notchedspecimen, SEN specimen 三点弯曲试件three point bendingspecimen, TPB specimen 中心裂纹拉伸试件center cracked tensionspecimen, CCT specimen 中心裂纹板试件center cracked panelspecimen, CCP specimen 紧凑拉伸试件compact tension specimen,CT specimen 大范围屈服large scale yielding 小范围攻屈服small scale yielding 韦布尔分布Weibull distribution 帕里斯公式paris formula空穴化Cavitation应力腐蚀stress corrosion概率风险判定probabilistic riskassessment, PRA 损伤力学damage mechanics 损伤Damage连续介质损伤力学continuum damage mechanics 细观损伤力学microscopic damage mechanics 累积损伤accumulated damage脆性损伤brittle damage延性损伤ductile damage宏观损伤macroscopic damage细观损伤microscopic damage微观损伤microscopic damage损伤准则damage criterion损伤演化方程damage evolution equation 损伤软化damage softening损伤强化damage strengthening损伤张量damage tensor损伤阈值damage threshold损伤变量damage variable损伤矢量damage vector损伤区damage zone疲劳Fatigue 低周疲劳low cycle fatigue应力疲劳stress fatigue随机疲劳random fatigue蠕变疲劳creep fatigue腐蚀疲劳corrosion fatigue疲劳损伤fatigue damage疲劳失效fatigue failure疲劳断裂fatigue fracture 疲劳裂纹fatigue crack疲劳寿命fatigue life疲劳破坏fatigue rupture疲劳强度fatigue strength 疲劳辉纹fatigue striations 疲劳阈值fatigue threshold 交变载荷alternating load 交变应力alternating stress 应力幅值stress amplitude 应变疲劳strain fatigue应力循环stress cycle应力比stress ratio安全寿命safe life过载效应overloading effect 循环硬化cyclic hardening 循环软化cyclic softening 环境效应environmental effect 裂纹片crack gage裂纹扩展crack growth, crackPropagation裂纹萌生crack initiation 循环比cycle ratio实验应力分析experimental stressAnalysis工作[应变]片active[strain] gage基底材料backing material应力计stress gage零[点]飘移zero shift, zero drift 应变测量strain measurement应变计strain gage应变指示器strain indicator应变花strain rosette应变灵敏度strain sensitivity 机械式应变仪mechanical strain gage 直角应变花rectangular rosette引伸仪Extensometer应变遥测telemetering of strain 横向灵敏系数transverse gage factor 横向灵敏度transverse sensitivity 焊接式应变计weldable strain gage 平衡电桥balanced bridge粘贴式应变计bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计bonded wire gage 桥路平衡bridge balancing电容应变计capacitance strain gage 补偿片compensation technique 补偿技术compensation technique 基准电桥reference bridge电阻应变计resistance strain gage 温度自补偿应变计self-temperaturecompensating gage半导体应变计semiconductor strainGage 集流器slip ring应变放大镜strain amplifier疲劳寿命计fatigue life gage电感应变计inductance [strain] gage 光[测]力学Photomechanics光弹性Photoelasticity光塑性Photoplasticity杨氏条纹Young fringe双折射效应birefrigent effect等位移线contour of equalDisplacement 暗条纹dark fringe条纹倍增fringe multiplication 干涉条纹interference fringe 等差线Isochromatic等倾线Isoclinic等和线isopachic应力光学定律stress- optic law主应力迹线Isostatic亮条纹light fringe光程差optical path difference 热光弹性photo-thermo -elasticity 光弹性贴片法photoelastic coatingMethod光弹性夹片法photoelastic sandwichMethod动态光弹性dynamic photo-elasticity 空间滤波spatial filtering空间频率spatial frequency起偏镜Polarizer反射式光弹性仪reflection polariscope残余双折射效应residual birefringentEffect 应变条纹值strain fringe value应变光学灵敏度strain-optic sensitivity 应力冻结效应stress freezing effect 应力条纹值stress fringe value应力光图stress-optic pattern暂时双折射效应temporary birefringentEffect 脉冲全息法pulsed holography透射式光弹性仪transmission polariscope 实时全息干涉法real-time holographicinterfero - metry 网格法grid method全息光弹性法holo-photoelasticity 全息图Hologram全息照相Holograph全息干涉法holographic interferometry 全息云纹法holographic moire technique 全息术Holography全场分析法whole-field analysis散斑干涉法speckle interferometry 散斑Speckle错位散斑干涉法speckle-shearinginterferometry, shearography 散斑图Specklegram白光散斑法white-light speckle method 云纹干涉法moire interferometry [叠栅]云纹moire fringe[叠栅]云纹法moire method 云纹图moire pattern离面云纹法off-plane moire method参考栅reference grating试件栅specimen grating分析栅analyzer grating面内云纹法in-plane moire method 脆性涂层法brittle-coating method条带法strip coating method坐标变换transformation ofCoordinates计算结构力学computational structuralmecha-nics 加权残量法weighted residual method 有限差分法finite difference method 有限[单]元法finite element method 配点法point collocation里茨法Ritz method广义变分原理generalized variationalPrinciple 最小二乘法least square method胡[海昌]一鹫津原理Hu-Washizu principle赫林格-赖斯纳原理Hellinger-ReissnerPrinciple 修正变分原理modified variationalPrinciple 约束变分原理constrained variationalPrinciple 混合法mixed method杂交法hybrid method边界解法boundary solution method 有限条法finite strip method半解析法semi-analytical method协调元conforming element非协调元non-conforming element混合元mixed element杂交元hybrid element边界元boundary element 强迫边界条件forced boundary condition 自然边界条件natural boundary condition 离散化Discretization离散系统discrete system连续问题continuous problem广义位移generalized displacement 广义载荷generalized load广义应变generalized strain广义应力generalized stress界面变量interface variable 节点node, nodal point [单]元Element角节点corner node边节点mid-side node内节点internal node无节点变量nodeless variable 杆元bar element桁架杆元truss element 梁元beam element二维元two-dimensional element 一维元one-dimensional element 三维元three-dimensional element 轴对称元axisymmetric element 板元plate element壳元shell element厚板元thick plate element三角形元triangular element四边形元quadrilateral element 四面体元tetrahedral element曲线元curved element二次元quadratic element线性元linear element三次元cubic element四次元quartic element等参[数]元isoparametric element超参数元super-parametric element 亚参数元sub-parametric element节点数可变元variable-number-node element 拉格朗日元Lagrange element拉格朗日族Lagrange family巧凑边点元serendipity element巧凑边点族serendipity family无限元infinite element单元分析element analysis单元特性element characteristics 刚度矩阵stiffness matrix几何矩阵geometric matrix等效节点力equivalent nodal force 节点位移nodal displacement节点载荷nodal load位移矢量displacement vector载荷矢量load vector质量矩阵mass matrix集总质量矩阵lumped mass matrix相容质量矩阵consistent mass matrix 阻尼矩阵damping matrix瑞利阻尼Rayleigh damping刚度矩阵的组集assembly of stiffnessMatrices载荷矢量的组集consistent mass matrix质量矩阵的组集assembly of mass matrices 单元的组集assembly of elements局部坐标系local coordinate system局部坐标local coordinate面积坐标area coordinates体积坐标volume coordinates曲线坐标curvilinear coordinates静凝聚static condensation合同变换contragradient transformation 形状函数shape function试探函数trial function检验函数test function权函数weight function样条函数spline function代用函数substitute function降阶积分reduced integration零能模式zero-energy modeP收敛p-convergenceH收敛h-convergence掺混插值blended interpolation等参数映射isoparametric mapping双线性插值bilinear interpolation小块检验patch test非协调模式incompatible mode节点号node number单元号element number带宽band width带状矩阵banded matrix变带状矩阵profile matrix带宽最小化minimization of band width 波前法frontal method子空间迭代法subspace iteration method 行列式搜索法determinant search method 逐步法step-by-step method纽马克法Newmark威尔逊法Wilson拟牛顿法quasi-Newton method牛顿-拉弗森法Newton-Raphson method 增量法incremental method初应变initial strain初应力initial stress切线刚度矩阵tangent stiffness matrix 割线刚度矩阵secant stiffness matrix 模态叠加法mode superposition method 平衡迭代equilibrium iteration子结构Substructure子结构法substructure technique 超单元super-element网格生成mesh generation结构分析程序structural analysis program 前处理pre-processing后处理post-processing网格细化mesh refinement应力光顺stress smoothing组合结构composite structure。