橡胶类材料的分叉问题研究
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摘要
橡胶类材料是一种性质特异的高分子材料,它的高弹性奠定了它在工业领域中不可取代的位置。目前橡胶制品在日常生活和精密仪器、航空、航天、航海、国防军事、轻纺等方面都有应用。世界上橡胶制品的总数已达到8万-10万种。故研究橡胶类材料的分又问题具有重要的理论意义和广阔的工程背景。本文正是基于以上目的而展开了一系列的研究。本文的主要工作如下:
1、系统地研究了高玉臣给出的一类应变能函数,得到了本构参数的限制条件和意义。结果表明:对不可压缩应变能函数,当本构参数满足α＞0,n＞0,各种限制条件能够得到满足且变形也是稳定的;而对可压缩应变能函数,则要求本构参数满足α＞0,n＞0,6＞nα3~(n-2)/2。本构参数n可看成是橡胶类材料无量纲的强化参数;而本构参数a,b则是与弹性模量同量纲的量。由算例结果表明这两种应变能函数均能较好地描述橡胶类材料的有限变形特性。
2、给出了可压缩薄膜充气管平面应变时的Poisson函数,并利用Poisson函数法首次得到了该问题的显性解,且当γ_0=0.5时能退化成不可压缩时的情形。
3、研究了在更为普遍的扰动位移作用下的可压缩球膜的分叉问题,给出了符合实验现象的分叉判据。若应变能函数为高玉臣给出的一类可压缩应变能函数时,给出了具体的分叉判据。结果表明:可压缩球膜分又解的控制微分方程组与不可压缩时非常相似,都只有3个独立的弹性系数,但弹性系数的定义是不同的:从理论分析的角度证明了可压缩球膜的分叉也是在内压达到极大值之后发生的,且在球膜的膨胀过程中,当内压达到极大值后,球膜的形状不再是标准的球形,此时球膜分叉了,这与实验结果是一致的。
4、研究了不可压缩均匀球体和柱体的空穴生成和分叉问题,得到了该问题的解析解。若产生分叉,还给出了发生何种分叉的判据。结果表明:当0＜n＜1.5时,均匀球体有分叉解;当0＜n＜1时,橡胶圆柱体存在分叉解。本构参数n对问题的分叉解均具有重要的影响。对于均匀柱体还考虑了轴向主伸长对分叉解的影响。若发生右分叉,在卸载阶段当外载荷P_0稍稍大于临界载荷p_(cr)时,应力在空穴壁处均有边界层效应。对均匀球体,分叉判据与临界载荷p_(cr)/α、本构参数n密切相关:对均匀柱体,分叉判据还与轴向主伸长λ_z有关。温度场对均匀柱体的分叉解具有重要的影响。分叉问题可视为描述预先存在的微孔洞生长的一个理想模型。
5、研究了不可压缩组合球体和柱体的空穴生成和分叉问题,得到了该问题的解析解。同样若发生分叉,还给出了发生何种分叉的判据。研究结果显示:与均匀情形时一致,当0＜n＜1.5时,组合球体有分叉解:当0＜n＜1时,组合柱体存在分叉解。临界载荷仅与组合结构的内部材料性质有关。本构参数n、组合系数m对问题的分叉解均具有重要的影响。对于组合柱体还考虑了轴向主伸长对分叉解的影响。若发生右分叉,应力在某些特定的情形下在空穴壁处也有边界层效应。对组合球体,分叉判据与p_(cr)/α~((1)、本构参数n、体积分数f和组合参数m密切相关;对组合柱体,分叉判据还与轴向主伸长λ_z有关。也证实了分叉问题可视为描述预先存在的微孔洞生长的一个理想模型。
6、应用高玉臣给出的一类应变能函数,在有限变形动力学的框架内分析了不可压缩均匀球体和柱体突受拉伸死载荷作用时空穴的动态生成和分叉问题,得到了问题的解析解。结果表明:动态模型可以方便地退化成静态模型;与静态情形一致,当本构参数满足0＜n＜1.5时,橡胶球体才存在动态的分叉解;本构参数满足0＜n＜1时,橡胶柱体才存在动态的分叉解。本构参数n对球体的动态分叉解具有重要的影响,对柱体还考虑了轴向主伸长λ_z的影响。当外加载荷大于临界载荷时,结构中心处存在一个突然生成并能迅速增大的空穴,且空穴半径随着时间的演化是周期性的非线性振动并给出了空穴半径振动的相图以及近似振动周期。
7、基于高玉臣给出的一类应变能函数,运用势能原理分析了含单个微孔橡胶矩形板在受单向压缩作用下的有限变形问题。结果表明:高玉臣给出的应变能函数能较好地描述橡胶类材料的有限变形特性;含有单个圆柱微孔的三维橡胶矩形板受压与受拉时的力学特性相差较大。
本文得出的分析结果可以为橡胶类材料的设计、生产和应用提供一定的理论参考依据。
Rubberlike material is a kind of the unique macromolecular material and plays the indispensable role in the industry because of its high elasticity. At present the rubber products are full of our daily life and manufacture, such as precision instrument, aviation, navigation, national defense, textile industry. In the world, the kinds of the practical rubber products add up to eighty thousand-ten thousand. So there are important theoretical meanings and vast engineering backgrounds to study the bifurcation problems of rubberlike materials. Just based on the above purpose, a series of researches are finished. This paper makes the following jobs.
1. A kind of strain energy function proposed by Gao Y C was systematically studied, and the limit conditions as well as physical meanings of the constitutive parameters included in the strain energy function were also obtained. The results indicated: for the incompressible strain energy function, when the constitutive parameters met a > 0, n > 0, all kinds of limit conditions can be satisfied and the deformation was also stable; while for the compressible strain energy function, the constitutive parameters should meet a > 0, n>0, b> na3~(n-2)/2. The constitutive parameter n can be seen as the dimensionless strengthening parameter, while the constitutive parameters a, b were the quantities which had the same dimension as the elastic modulus. The results of the examples showed that these two kinds of strain energy function can reflect the finite deformation characters of rubberlike materials well.
2. The Poisson function of the compressible membrane inflatable tube under plane strain was given, and with the help of Poisson function method, the explicit solutions to this question were firstly obtained. When the Poisson ratioγ_0 = 0.5, this solutions can degenerate into the incompressible case.
3. The bifurcation problem of the compressible spherical membrane under a more universal disturbance displacement was built, and the bifurcation criterion same as the test was also given. If the compressible strain energy function proposed by Gao Y C was adopted, the detail bifurcation criterion can be gained. The results indicated: the controlling differential equations of the compressible situation were very similar with the incompressible case. They all had three absolute elastic coefficients, but the definitions of these coefficients were different. It was proved that the bifurcation would happen after the internal pressure reached the maximum from the theoretical analytical view. In the expanding process of the spherical membrane, its shape was no longer spherical after the internal pressure reached the maximum. That is to say the spherical membrane bifurcated, which was the same as the conclusion of the experiment.
4. The questions about the cavity formation and bifurcation of the incompressible homogeneous solid sphere and circular cylinder were studied, and the analytical solutions were also acquired. If the bifurcation happened, the criterion on which bifurcation took place was also given. The results indicated: only if 0 < n < 1.5, the homogeneous solid sphere had bifurcation solution; while for the circular cylinder, the constitutive parameter n should meet 0 < n < 1. The constitutive parameter n had important influences on the bifurcation solutions. For the homogeneous circular cylinder, the influences of the axial principal stretch were also considered. If the right bifurcation took place, when the load p_0 was slightly bigger than the critical load p_(cr) in the stage of unload, the stresses had the phenomenon of boundary layer at the cavity wall. For the homogeneous solid sphere, the bifurcation criterion was relative to the critical load p_(cr)/a and the constitutive parameter n, while for the circular cylinder, it still did something with the axial principal stretchλ_z. The temperature field had strong effects on the bifurcation solution for the homogeneous solid circular cylinder. The bifurcation problem can be viewed as providing an idealized model for describing the sudden growth of a pre-existing micro-void.
5. The questions about the cavity formation and bifurcation of the incompressible composite solid sphere and circular cylinder were also studied, and the analytical solutions were acquired as well. If the bifurcation happened, the criterion on which bifurcation took place was still given. The results indicated: only if 0 < n < 1.5, the solid sphere had the bifurcation solution; while for the circular cylinder, the constitutive parameter n should meet 0 < n < 1, which were the same as the homogeneous cases. The critical loads were only relative to the internal materials of the composite structures. The constitutive parameter n and combined coefficient m had important influences on the bifurcation solutions. For the composite circular cylinder, the influences of the axial principal stretch were also considered. If the right bifurcation took place, the stresses still had the phenomenon of boundary layer at the cavity wall under some special conditions which were similar with the homogeneous cases. For the composite solid sphere, the bifurcation criterion was relative to the critical load p_(cr)//a~((1)), constitutive parameter n, volume fraction f and combined coefficient m . while for the composite circular cylinder, it still did something with the axial principal stretchλ_z. It was also proved that the bifurcation problem can be viewed as providing an idealized model for describing the sudden growth of a pre-existing micro-void.
6. With the help of the strain energy function proposed by Gao Y C and the theory of finite deformation dynamics, the questions about the cavity dynamical formation and bifurcation of the incompressible homogeneous solid sphere and circular cylinder under a suddenly applied uniform tensile dead-load were studied, and the analytical solutions were given too. The results indicated: the dynamical model can degenerate into the static model conveniently. If 0 < n < 1.5, the solid sphere had the dynamical bifurcation solutions; while for circular cylinder, the constitutive parameter n should meet 0 < n < 1, which were the same as the static cases. The constitutive parameter n had important influences on the dynamical bifurcation solutions. For the circular cylinder, the influences of the axial principal stretch were also considered. When the load was larger than the critical load, a cavity suddenly appeared in the centers of the structures and can grow quickly. The cavity displayed a periodic nonlinear oscillation. At the same time, the oscillation phase diagram of the cavity radius and the approximative oscillation period were also given.
7. Based on the strain energy function which was proposed by Gao Y C, a rubber rectangular including a void under uniaxial compression was analyzed with the potential energy principle. The results indicated that this strain energy function can reflect the finite deformation character of the rubber material correctly, and that the rubber rectangular under uniaxial compression had a different mechanical features compared with the case under uniaxial extension.
The analytical results in present paper may be helpful as a theoretical reference in the design, production and application of the rubberlike materials.
1、系统地研究了高玉臣给出的一类应变能函数,得到了本构参数的限制条件和意义。结果表明:对不可压缩应变能函数,当本构参数满足α＞0,n＞0,各种限制条件能够得到满足且变形也是稳定的;而对可压缩应变能函数,则要求本构参数满足α＞0,n＞0,6＞nα3~(n-2)/2。本构参数n可看成是橡胶类材料无量纲的强化参数;而本构参数a,b则是与弹性模量同量纲的量。由算例结果表明这两种应变能函数均能较好地描述橡胶类材料的有限变形特性。
2、给出了可压缩薄膜充气管平面应变时的Poisson函数,并利用Poisson函数法首次得到了该问题的显性解,且当γ_0=0.5时能退化成不可压缩时的情形。
3、研究了在更为普遍的扰动位移作用下的可压缩球膜的分叉问题,给出了符合实验现象的分叉判据。若应变能函数为高玉臣给出的一类可压缩应变能函数时,给出了具体的分叉判据。结果表明:可压缩球膜分又解的控制微分方程组与不可压缩时非常相似,都只有3个独立的弹性系数,但弹性系数的定义是不同的:从理论分析的角度证明了可压缩球膜的分叉也是在内压达到极大值之后发生的,且在球膜的膨胀过程中,当内压达到极大值后,球膜的形状不再是标准的球形,此时球膜分叉了,这与实验结果是一致的。
4、研究了不可压缩均匀球体和柱体的空穴生成和分叉问题,得到了该问题的解析解。若产生分叉,还给出了发生何种分叉的判据。结果表明:当0＜n＜1.5时,均匀球体有分叉解;当0＜n＜1时,橡胶圆柱体存在分叉解。本构参数n对问题的分叉解均具有重要的影响。对于均匀柱体还考虑了轴向主伸长对分叉解的影响。若发生右分叉,在卸载阶段当外载荷P_0稍稍大于临界载荷p_(cr)时,应力在空穴壁处均有边界层效应。对均匀球体,分叉判据与临界载荷p_(cr)/α、本构参数n密切相关:对均匀柱体,分叉判据还与轴向主伸长λ_z有关。温度场对均匀柱体的分叉解具有重要的影响。分叉问题可视为描述预先存在的微孔洞生长的一个理想模型。
5、研究了不可压缩组合球体和柱体的空穴生成和分叉问题,得到了该问题的解析解。同样若发生分叉,还给出了发生何种分叉的判据。研究结果显示:与均匀情形时一致,当0＜n＜1.5时,组合球体有分叉解:当0＜n＜1时,组合柱体存在分叉解。临界载荷仅与组合结构的内部材料性质有关。本构参数n、组合系数m对问题的分叉解均具有重要的影响。对于组合柱体还考虑了轴向主伸长对分叉解的影响。若发生右分叉,应力在某些特定的情形下在空穴壁处也有边界层效应。对组合球体,分叉判据与p_(cr)/α~((1)、本构参数n、体积分数f和组合参数m密切相关;对组合柱体,分叉判据还与轴向主伸长λ_z有关。也证实了分叉问题可视为描述预先存在的微孔洞生长的一个理想模型。
6、应用高玉臣给出的一类应变能函数,在有限变形动力学的框架内分析了不可压缩均匀球体和柱体突受拉伸死载荷作用时空穴的动态生成和分叉问题,得到了问题的解析解。结果表明:动态模型可以方便地退化成静态模型;与静态情形一致,当本构参数满足0＜n＜1.5时,橡胶球体才存在动态的分叉解;本构参数满足0＜n＜1时,橡胶柱体才存在动态的分叉解。本构参数n对球体的动态分叉解具有重要的影响,对柱体还考虑了轴向主伸长λ_z的影响。当外加载荷大于临界载荷时,结构中心处存在一个突然生成并能迅速增大的空穴,且空穴半径随着时间的演化是周期性的非线性振动并给出了空穴半径振动的相图以及近似振动周期。
7、基于高玉臣给出的一类应变能函数,运用势能原理分析了含单个微孔橡胶矩形板在受单向压缩作用下的有限变形问题。结果表明:高玉臣给出的应变能函数能较好地描述橡胶类材料的有限变形特性;含有单个圆柱微孔的三维橡胶矩形板受压与受拉时的力学特性相差较大。
本文得出的分析结果可以为橡胶类材料的设计、生产和应用提供一定的理论参考依据。
Rubberlike material is a kind of the unique macromolecular material and plays the indispensable role in the industry because of its high elasticity. At present the rubber products are full of our daily life and manufacture, such as precision instrument, aviation, navigation, national defense, textile industry. In the world, the kinds of the practical rubber products add up to eighty thousand-ten thousand. So there are important theoretical meanings and vast engineering backgrounds to study the bifurcation problems of rubberlike materials. Just based on the above purpose, a series of researches are finished. This paper makes the following jobs.
1. A kind of strain energy function proposed by Gao Y C was systematically studied, and the limit conditions as well as physical meanings of the constitutive parameters included in the strain energy function were also obtained. The results indicated: for the incompressible strain energy function, when the constitutive parameters met a > 0, n > 0, all kinds of limit conditions can be satisfied and the deformation was also stable; while for the compressible strain energy function, the constitutive parameters should meet a > 0, n>0, b> na3~(n-2)/2. The constitutive parameter n can be seen as the dimensionless strengthening parameter, while the constitutive parameters a, b were the quantities which had the same dimension as the elastic modulus. The results of the examples showed that these two kinds of strain energy function can reflect the finite deformation characters of rubberlike materials well.
2. The Poisson function of the compressible membrane inflatable tube under plane strain was given, and with the help of Poisson function method, the explicit solutions to this question were firstly obtained. When the Poisson ratioγ_0 = 0.5, this solutions can degenerate into the incompressible case.
3. The bifurcation problem of the compressible spherical membrane under a more universal disturbance displacement was built, and the bifurcation criterion same as the test was also given. If the compressible strain energy function proposed by Gao Y C was adopted, the detail bifurcation criterion can be gained. The results indicated: the controlling differential equations of the compressible situation were very similar with the incompressible case. They all had three absolute elastic coefficients, but the definitions of these coefficients were different. It was proved that the bifurcation would happen after the internal pressure reached the maximum from the theoretical analytical view. In the expanding process of the spherical membrane, its shape was no longer spherical after the internal pressure reached the maximum. That is to say the spherical membrane bifurcated, which was the same as the conclusion of the experiment.
4. The questions about the cavity formation and bifurcation of the incompressible homogeneous solid sphere and circular cylinder were studied, and the analytical solutions were also acquired. If the bifurcation happened, the criterion on which bifurcation took place was also given. The results indicated: only if 0 < n < 1.5, the homogeneous solid sphere had bifurcation solution; while for the circular cylinder, the constitutive parameter n should meet 0 < n < 1. The constitutive parameter n had important influences on the bifurcation solutions. For the homogeneous circular cylinder, the influences of the axial principal stretch were also considered. If the right bifurcation took place, when the load p_0 was slightly bigger than the critical load p_(cr) in the stage of unload, the stresses had the phenomenon of boundary layer at the cavity wall. For the homogeneous solid sphere, the bifurcation criterion was relative to the critical load p_(cr)/a and the constitutive parameter n, while for the circular cylinder, it still did something with the axial principal stretchλ_z. The temperature field had strong effects on the bifurcation solution for the homogeneous solid circular cylinder. The bifurcation problem can be viewed as providing an idealized model for describing the sudden growth of a pre-existing micro-void.
5. The questions about the cavity formation and bifurcation of the incompressible composite solid sphere and circular cylinder were also studied, and the analytical solutions were acquired as well. If the bifurcation happened, the criterion on which bifurcation took place was still given. The results indicated: only if 0 < n < 1.5, the solid sphere had the bifurcation solution; while for the circular cylinder, the constitutive parameter n should meet 0 < n < 1, which were the same as the homogeneous cases. The critical loads were only relative to the internal materials of the composite structures. The constitutive parameter n and combined coefficient m had important influences on the bifurcation solutions. For the composite circular cylinder, the influences of the axial principal stretch were also considered. If the right bifurcation took place, the stresses still had the phenomenon of boundary layer at the cavity wall under some special conditions which were similar with the homogeneous cases. For the composite solid sphere, the bifurcation criterion was relative to the critical load p_(cr)//a~((1)), constitutive parameter n, volume fraction f and combined coefficient m . while for the composite circular cylinder, it still did something with the axial principal stretchλ_z. It was also proved that the bifurcation problem can be viewed as providing an idealized model for describing the sudden growth of a pre-existing micro-void.
6. With the help of the strain energy function proposed by Gao Y C and the theory of finite deformation dynamics, the questions about the cavity dynamical formation and bifurcation of the incompressible homogeneous solid sphere and circular cylinder under a suddenly applied uniform tensile dead-load were studied, and the analytical solutions were given too. The results indicated: the dynamical model can degenerate into the static model conveniently. If 0 < n < 1.5, the solid sphere had the dynamical bifurcation solutions; while for circular cylinder, the constitutive parameter n should meet 0 < n < 1, which were the same as the static cases. The constitutive parameter n had important influences on the dynamical bifurcation solutions. For the circular cylinder, the influences of the axial principal stretch were also considered. When the load was larger than the critical load, a cavity suddenly appeared in the centers of the structures and can grow quickly. The cavity displayed a periodic nonlinear oscillation. At the same time, the oscillation phase diagram of the cavity radius and the approximative oscillation period were also given.
7. Based on the strain energy function which was proposed by Gao Y C, a rubber rectangular including a void under uniaxial compression was analyzed with the potential energy principle. The results indicated that this strain energy function can reflect the finite deformation character of the rubber material correctly, and that the rubber rectangular under uniaxial compression had a different mechanical features compared with the case under uniaxial extension.
The analytical results in present paper may be helpful as a theoretical reference in the design, production and application of the rubberlike materials.
引文
[1]Beatty M F.Topics in finite elasticity:hyperelasticity of rubber,elastomer,and biological tissues- with example.Appl Mech Rev,1987,40(3):1699-1734P
[2]詹特A N.张立群等译.橡胶工业.化学工业出版社,2002:1-5页
[3]王作龄.橡胶材料科学的发展.世界橡胶工业,1998,25(2):41-47页
[4]熊祝华,傅衣铭,熊慧而.连续介质力学基础.长沙:湖南大学出版社,1997:116页,46-48页
[5]Fu Y B,Ogden R W.Nonlinear Elasticity.Cambridge:Cambridge University Press,2001:1-50P
[6]Ogden R W.Non-smooth/Nonconvex Mechanics,2001.Holand:Kluwer Academic Publishers,2001:277-299P
[7]Ogden R W.Stress softening and residual strain in the azimuthal shear of a pseudo-elastic circular cylindrical tube.Int J of Nonlinear Mechanics,2001,36(3):477-487P
[8]郭仲衡.非线性弹性理论.北京:科学出版社,1980:1-100页
[9]高玉臣.固体力学基础.北京:中国铁道出版社,1999:1-196页,118,页,119页
[10]王自强.理性力学基础.北京:科学出版社,2000:1-5页,119页
[11]Ericksen J L.Finite Elasticity,ASME,1976.America:ASME-AMD,1976:11-21P
[12]Erbay H A.Finite axisymmetric deformation of elastic tubes,An approximate method.J of Engineering mathematics,1995,29(3):451-472P
[13]史守峡.平面应变不可压缩橡胶圆柱的大变形.固体力学学报,1999,20(4):290-296P
[14]陈少华.橡胶材料的尖点及角点的大变形接触问题.北方交通大学博士 学位论文.1999:53-92页
[15]黄克智,薛明德,陆明万.张量分析.第二版.北京:清华大学出版社,2002:1-117页
[16]Alexander H.Tensile instability of initially spherical balloons.Int J Engng Sci,1971,9(1):151-162P
[17]白以龙.材料的不稳定性.黄克智,徐秉业编.固体力学发展趋势,北京,1995.北京:北京理工大学出版社,1995,95-107页
[18]程昌钧,任九生.非线性材料中空穴生成和增长问题的一些进展.自然杂志,26(1):1-6页
[19]Green A E,Zerna W.Theoretical elasticity.England:Oxford,1954:60-89P
[20]Green A E,Adkins J E.Large elastic deformation and non-linear continuum mechanics.England:Oxford,1960:78-96P
[21]Abeyaratne R,Horgan C O.The pressurized hollow sphere problem in:finite elastostatics for a class of compressible materials.Int J Solids Structures,1984,20(8):715-723P
[22]Chung D T,Horgan C O,Abeyaratne R.The finite deformation of internally pressurized hollow cyiinders and spheres for a class of compressible elastic materials.Int J Solids Structures,1986,22(t2):1557-1570P
[23]Willson A J,Myers P J.On the finite elastostatic deformation of thin-walled sphere and cylinders.Int J Solids Structures,1991,26(3):369-373P
[24]Guo Z H.Problems of spherical membrane in the theory of large defermation.Mech Stos,1962,14(6):921-936P
[25]Shield R T.On the stability of finitely deformed elastic membranes.Part Ⅰ:Stability of a uniformly deformed plane membrane.ZAMP,1971,22(6):1016-1028P
[26]Shield R T.On the stability of finitely deformed elastic membranes. Part II: Stability of inflated cylindrical and spherical membranes. ZAMP, 1972, 23(1): 16-34P
[27] Hill J M. Closed form solutions for small deformations superimposed upon the symmetrical expansion of a spherical shell.Journal of Elasticity, 1976, 6(2):125-136P
[28] Needleman A. Inflation of spherical rubber balloons. Int J Solids Structures, 1977, 13(5):409-421P
[29] Haughton D M, Ogden R W. On the incremental equations in non-linear elasticity—I. Membrane theory. J Mech Phys Solids, 1978, 26(2):93-110P
[30] Haughton D M, Ogden R W. On the incremental equations in non-linear elasticity—II. Bifurcation of pressurized spherical shells. J Mech Phys Solids, 1978, 26(2):111-138P
[31] Haughton D M. Post bifurcation of perfect and imperfect spherical elastic membranes. Int J Solids Structures, 1980, 16(12):1123-1133P
[32] Haughton D M. Inflation and bifurcation of compressible spherical membranes. J Elasticity, 1982, 12(2):239-245P
[33] Haughton D M. Inflation and bifurcation of thick-walled compressible elastic spherical shells. IMA Journal of Applied Mathematics, 1987, 39(2):259-272P
[34] Chen Y C, Healey T J. Bifurcation to pear-shaped equilibria of pressurized spherical membranes. Int J Non-linear Mechanics, 1991,26(3/4):279-291P
[35] Hill J M, Arrigo D J. Small deformations superimposed upon the symmetrical expansion of a spherical shell. Quart J Mech Appl Math,1996,49(3):337-351P
[36] Warne D P, Warne P G. On non-symmetric deformations of an incompressible nonlinearly elastic isotropic sphere. Journal of Elasticity,1997,47(2):85-100P
[37]Verron E,Marckmann G.Numerical analysis of rubber balloons.Thin-walled Structures,2003,41(8):731-746P
[38]Easlach H W,Humphrey J D.Dynamics of biological soft tissue and rubber:internally pressurized spherical membranes surrounded by a fluid.Int J Non-linear Mechanics,2004,39(3):399-420P
[39]范志强.均布内压作用下球膜膨胀和分叉问题的研究.哈尔滨工程大学硕士学位论文.2005:26-63,39页
[40]Green A E,Rivlin R S,Shield R T.General theory of small elastic deformations superposed on finite elastic deformations.Proceedings of Royal Society,1952,A211(1):128-154P
[41]Hill J M,Arrigo D J.On the general structure of small on large problems for elastic deformations of Varga materials Ⅱ:axially symmetric deformations.Journal of Elasticity,1999,54(3):212-227P
[42]Pan F X,Beatty M F.Remarks on the instability of an incompressible and isotropic hyperelastic thick-walled cylindrical tube.Journal of Elasticity,1997,48(3):217-239P
[43]Beatty M F,Pan F X.Stability of an internally constrained,hyperelsatic slab.International Journal of Non-linear Mechanics,1993,33(5):867-906P
[44]Chen Y C.Stabity and bifurcation of finite deformations of elastic cylindrical membranes-Part Ⅰ.Stability analysis.Int J Solids Structures,1997,34(14):1735-1749P
[45]Haughton D M.On non-linear stability in unconstrained non-linear elasticity.Int J Non-linear Mechanics,2004,39(7):1181-1192P
[46]Sawyer K N,Rivlin R S.Instability of an elastic material.Int J Sclids Structures,1973,9(5):607-613P
[47]Fu Y B.Some asymptotic results concerning the bucking of a spherical shell of arbitrary thickness. International Journal of Non-linear Mechanics, 1998, 33(6): 1111-1122P
[48] Ogden R W. Large and global bifurcation phenomena in plane-strain finite elasticity. Int J Solids Structures, 1985, 21(2):121-132P
[49] Ogden R W. On the stability of asymmetric deformation of a symmetrically tensioned elastic sheet. Int J Engng Sci, 1987,25(10): 1305-1314P
[50] Haughton D M, Chao Y C. On the eversion of incompressible elastic shells. ZAMP, 1999, 50(2): 312-326P
[51] Haughton D M, Ogden R W. Bifurcation of inflated circular cylinders of elastic material under axial loading. — I. Membrane theory for thin-walled tubes. J Mech Phys Solids, 1979, 27(3):179-212P
[52] Haughton D M, Ogden R W. Bifurcation of inflated circular cylinders of elastic material under axial loading. —II. Exact theory for thick-walled tubes. J Mech Phys Solids, 1979, 27(5-6):489-512P
[53] Haughton D M, Orr A. On the eversion of incompressible elastic cylinders. Int J Non-linear Mechanics, 1995, 30(2):81-95P
[54] Haughton D M, Orr A. On the eversion of compressible elastic cylinders. Int J Solids Structures, 1997, 34(15):1893-1914P
[55] Ratner A M. Tensile stability of cylindrical membranes. Int J Non-linear Mechanics, 1983, 18(2): 133-147P.
[56] Ogden R W, Steigman D J, Haughton DM. The effect of elastic surface coating on the finite deformation and bifurcation of a pressurized circular annulus. J Elasticity, 1997, 47(2):121-145P
[57] Hill J M, Arrigo D J. On the general structure of small on large problems for elastic deformations of Varga materials I : plane strain deformations. Journal of Elasticity, 1999, 54(3): 193- 211P
[58]Gent A X,Lindley P B.Internal ruptuer of bonded rubber cylinders Intension.Proc R Soc London,1959,A249(2):195-205P
[59]Williams M I,Schapery R A.Spherical flaw instability in hydrostatic tension.Int J Fracture,1965,1(1):64-71P
[60]Lindsey G H.Cavitation in bonded rubber cylinders in tension.J Applied Physics,1967,38(12):4843-4856P
[61]Gent A,Park B.Failure processes in elastomers at or near a rigid spherical inclusion.J Material Science,1984,19(7):1947-1956P
[62]Cho K,Gent A.Cavitation in model elastomeric composites.J Material Science,1988,23(1):141-144P
[63]Ball J M.Discontinuous equilibrium solutions and cavitation in nonlinear elasticity.Phil Trans R Soc London,1982,A306(3):557-611P
[64]Horgan C O,Abeyaratne R.A bifurcation problem for a compressible nonlinearly elastic medium:growth of a micro-void.Journal of Elasticity,1986,16(2):189-200P
[65]Sivaloganothan J.Uniqueness of regular and singular equlibrium fcr spherically symmetric problems of nonlinear elasticity.Arch Rat Mech Anal,1986,96(2):97-136P
[66]Horgan C O,Polignone D A.Cavitation in nonlinearly elastic solids:A review.Applied Mechanics Review,1995,48(8):471-485P
[67]Gent A N.Cavitation in rubber:A cautionary.tale.Rubber Chemistry and Technology,1990,63(6):49-53P
[68]Horgan C O.Nonlinear elasticity,Cambridge University,2001.England:Cambridge University Press,2001:135-159P
[69]Antman S S,Negron-Marrero P V.The remarkable nature of radially symmetric equilibrium states of anisotropic nonlinearly elastic bodies.Journal of Elasticity,1987,18(2):131-164P
[70] Horgan C 0, Pence T J. Void nucleation in tensile dead-loading of a composite incompressible nonlinearly elastic sphere.Journal of Elasticity, 1989, 21(1):61-82P
[71] Horgan C 0, Pence T J. Cavity formation at the center of a composite incompressible non-1inearly elastic sphere. Journal of Applied Mechanics, 1989, 56(2):302-308P
[72] Stringfellow R, Abeyaratne R. Cavitation in an elastomer:comparison of theory with experiment. Material Science Engineering A, 1989, 112: 127-131P
[73] Chou-Wang M S, Horgan C O. Void nucleation and growth for a class of incompressible nonlinearly elastic materials: An example. Int J of solids and structures, 1989, 25(11):1239-1254P
[74] Horgan C O. Void nucleation and growth for compressible nonlinearly elastic materials: An example. Int J of solids and structures, 1992, 29(3):279-291P
[75] Meynard F. Existence and nonexistence results on the radially symmetric cavitation problem. Q Appl Math, 1992, 50(2):201-226P
[76] Polignone D A , Horgan C O. Cavitation for incompressible anisotropic Nonlinearly elastic spheres. J of Elasticity, 1993,33(1):27-65P
[77] Polignone D A, Horgan C O. Effects of material anisotropy and inhomogeneity on cavitation for composite incompressible nonlinearly-elastic spheres. Int J Solids and Structuers, 1993,30(24):3381-3416P
[78] Biwa S. Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. J Nonlinear Mech, 1995,30(4):899-906P
[79] Biwa S. Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. Int J Nonlinear Mechanics, 1995,30(6):899-914P
[80]Lei H C,Chang H W.Void formation and growth in a class of compressible solids.J Eng Math,1996,30(6):693-702P
[81]尚新春,程昌钧.超弹性材料中的球形空穴分叉.力学学报,1996,28(6):751-755页
[82]Murphy J G,Biwa S,Nonmonotonic cavity growth in finite ccmpressible elasticity.Int J of Solids and Structures,1997,34(29):3859-3872P
[83]Shang X C,Cheng C J.Exact solution for cavitated bifurcation for compressible hyperelasitc materials.Int J of Engineering Seience,2001,39(10):1101-1117P
[84]任九生,程昌钧.不可压超弹性材料中的空穴分叉.应用数学和力学,2002,23(8):783-789页
[85]Ren J S,Cheng C J.Cavitation for incompressible anisotropic hyper-elastic materials.J of Shanghai University,2002,6(3):185-190P
[86]宁建国,李伟,郝玖锋等.平面应变条件下孔洞化不稳定性问题研究.固体力学学报,2003,24(3):359-363页
[87]任九生,程昌钧,朱正佑.可压超弹性材料组合球体中心的空穴生成.应用数学和力学,2003,24(9):892-898页
[88]Ren J S,Cheng C J,Zhu Z Y.Cavity formation at the center of a sphere composed of two compressible hyperelastic material.Applied Mathematics and Mechanics,2003,24(9):1009 -1016P
[89]Yuan X G,Zhu Z Y,Cheng C J.Void formation and growth for a class of compressible hyper-elastic sphere.Journal of Shanghai University,2004,8(1):13-18P
[90]任九生,程昌钧.热超弹性材料中的空穴生成问题.固体力学学报,2004,25(3):275-278页
[91]任九生,程昌钧.组合超弹性材料中的空穴生成与增长.力学季刊, 2004,25(2):175-182页
[92]唐立强,范志强,杨勇.不可压缩球体的空穴和分叉.哈尔滨工程大学学报,2005,26(5):624-627页
[93]王勇,唐立强,杨勇.不可压缩橡胶圆柱的空穴和分叉.哈尔滨工程大学学报,2007,28(9):980-984页
[94]Haughton D M.On non-existence of cavitation in incompressible elastic membranes.Q J Mech appl Math,1986,39(2):289-296P
[95]Haughton D M.Cavitation in compressible elastic membranes.J of Engineering Mechanics,1990,28(2):163-168P
[96]Steigmann D J.Cavitation in elastic membranes-an example.J of Elasticity,1992,28(3):277-287P
[97]Knowles J K.Large amplitude oscillations of a tube of incompressible elastic material.Q Appl Math,1960,18(1):71-77P
[98]Knowles J K.On a class of oscillations in the finite deformation theory of elasticity.J Appl Mech,1962,29(2):283-286P
[99]Guo Z H,Solecki R.Free and forced finite amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material.Arch Mech Stos,1963,15(2):427-433P
[100]Calderer C.The dynamical behavior of nonlinear elastic spherical shells.J of Elasitcity,1983,13(1):17-42P
[101]Chou-Wang M S,Horgan C O.Cavitation in nonlinear elastodynamics for neo-Hookean materials.Int J of Engng Sci,1989,27(8):967-973P
[102]任九生,程昌钧.可压缩超弹性球壳的有限振动.振动与冲击,2003,22(4):1-3页
[103]Ren J S,Cheng C J.Dynamical formation of cavity in transversely hyperelastic spheres.Acta Mechanica Sinica,2003,19(4):320-323P
[104]梅波,程昌钧.两个组合热超弹性球体中空穴的动态生成.上海大学 学报,2004,10(4):376-380页
[105]任九生,程昌钧.超弹性材料中空穴的动态生成.固体力学学报,2004,25(1):42-46页
[106]任九生,程昌钧.组合超弹性球体中空穴的动态生成.应用数学和力学,2004,25(11):1117-1123页
[107]Ren J S,Cheng C J.Dynamical formation of cavity in a composed hyper-elastic sphere.Applied Mathematics and Mechanics,2004,25(11):1220-1227P
[108]任九生,程昌钧.横观各向同性超弹性球壳的有限振动.固体力学学报,2004,25(2):221-224页
[109]Yuan X G,Zhu Z Y,Cheng C J.Qualitative analysis of dynamical behavior for an imperfect incompressible Neo-hookean spherical shell.Applied Mathematics and Mechanics,2005,26(8):973-981P
[110]袁学刚,朱正佑,程昌钧.具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析.应用数学和力学,2005,26(8):892-898页
[111]程昌钧,梅波.非均匀温度场中组合热超弹性球体的动态孔穴生成.应用数学和力学,2006,27(4):395-403页
[112]Cheng C J,Mei B.Dynamical formation of cavity for composed thermal hyperelastic spheres in nonuniform temperature fields.Applied Mathematics and Mechanics,2006,27(4):443-452 P
[113]Ren J S,Cheng C J.Static and dynamical cavitation for incompressible hyperelastic-plastic material.Journal of Shanghai University,2006,10(4):283-287P
[114]任九生,程昌钧.超弹性-塑性材料中空穴的动生成.太原理工大学学报,2005,36(6):679-681页
[115]程昌钧,聂波.幂强化材料和超弹性材料组合球体中孔穴的动态生成.固体力学学报,2005,26(3):273-279页
[116]聂波,程昌钧.组合幂强化弹塑性-超弹性球体中的空穴生成.上海大学学报,2004,10(6):612-615页
[117]任九生,程昌钧.可压超弹性-塑性材料中的空穴生成.力学季刊,2003,24(4):440-444页
[118]尚新春,程昌钧.弹性固体材料中的空穴萌生与增长.北京科技大学学报,2002,24(3):380-382页
[119]Shang X C,Cheng C J.Cavitation in hookean elastic membranes.Acta Mechanica Solida Sinica,2002,15(1):1-6P
[120]金明,黄克服,武际可.泊松比为1/2材料中球形空穴突变和球形空穴萌生的分岔问题研究.应用数学和力学,1999,20(8):867-872页
[121]Jin M.A mechanical model on elastic cavitation in solid under hydrostatic tension.Mech Res Comm,2001,28(3):305-315P
[122]Shang X C,Cheng C J.The 4~(th) ICNM,Shanghai university,2002.Shanghai:Shanghai university press,2002:156-162P
[123]Huang Y,Hutchinson J W,Tvergaard V.Cavitation instabilities in elastic-plastic solids.J Mech Phys Solids,1991,39(2):223-241P
[124]Tvergaard V,Huang Y,Hutchinson J W.Cavitation instabilities in a power hardening elastic-plastic solids.Eur J Mech A/Solids,1992,11(2):215-231P
[125]Tvergaard V,Hutchinson J W.Effect of initial void shape on the occurrence of cavitation instabilities in elastic-plastic solids.J of Applied Mech,1993,60(5):807 -812P
[126]Tvergaard V.Effect of void size difference on growth and cavitation instability.J Mech Phys Solids,1996,44(8):1237-1253P
[127]Tvergaard V.Interaction of very small voids with large voids.J Mech Phys Solids,1987,35(12):3989-4000P
[128]Hou H S,Abeyaratne R.Cavitation in an elastic and elastic-plastic solids.J Mech Phys Solids,1992,40(3):571-592P
[129]郭仲衡等译.应用力学的最新进展.北京:科学出版社,1987:1-50页
[130]Rivlin R S.Finite elasticity.New York:The Ameircan Society of Mechanical Engineers,1977.1-200P
[131]Rivlin R S.Stability of plane homogeneous deformation of an elastic cube under dead loading.Q of Applied Mathematics,1974,32(2):265-271P
[132]Kearsley E A.A symmetric stretching of a symmetrically loaded elastic sheet.International J of Solids and Structures,1986,22(2):111-119P
[133]尚新春.类橡胶材料和结构的不稳定性理论及分叉问题.兰州大学博士学位论文,1994:1-60页
[134]任九生,程昌钧.热超弹性圆筒的不稳定性.力学学报,2007,39(2):283-288P
[135]Haughton D M.An exact solution for the stretching of elastic membranes containing a hole or inclusion.Mechanics research Communications,1991,18(1):29-39P
[136]王勇.橡胶圆管与薄膜充气管的有限变形分析.哈尔滨工程大学硕士学位论文,2006:16-21页
[137]Gao Y C.Elastostatic crack tip behavior for a rubber like material.Theoretical and Applied Fracture Mechanics,1990,14(3):219-231P
[138]Gao Y C.Large deformation field near a crack tip in rubber-like material.Theoretical and Applied Fracture Mechanics,1997,25(3):155-162P
[139]Gao Y C,Liu B.Stress singularity near the notch tip of a rubber like specimen under tension.European Journal of Mechanics-A/Solids,1996,15(2):199-211P
[140]Gao Y C,Liu B.A rubber cone under the tension of a concentrated force.International Journal of Solids and Structures,1995,32(11):1485-1493P
[141]Gao Y C,Chen S H.Large strain field near a crack tip in a rubber sheet.Mechanics research Communications,2001,28(1):71-78P
[142]Haughton D M,McKay B A.Wrinkling of Inflated Elastic Cyiindrical Membrane Under Flexure.International Journal of Engineering Science,1996,34(13):1531-1550P
[143]Steigmann D J.Tension field theory.Proceedings of Royal Society London A,1990,429(2):141-173P
[144]Naghdi P M,Tang P Y.Large deformation possible in every isotropic elastic membrane.Phil Trans R Soc Lond A,1977,287(2):145-187P
[145]程昌钧,尚新春.超弹性矩形板单向拉伸时微孔的增长.应用数学和力学,1997,18(6):573-578P
[146]Ren J S,Cheng C J,Shang X C.The growth of a void in a rubber rectangular plate under uniaxial extension.Journal of Shanghai University,2001,5(3):177-182P
[147]任九生,程昌钧.多孔Mooney-Rivlin材料矩形板的单向拉伸.力学季刊,2002,23(3):347-353P
[148]程昌钧,任九生.横观各向同性多孔超弹性矩形板的单向拉伸.应用数学和力学,2003,24(7):675-683P
[149]Cheng C J,Ren J S.Growth of voids in a hyperelastic rectangular plate.Journal of Shanghai University,2005,9(3):194-200P
[150]Hill R,Rice J R.Elastic potentials and the structure of inelastic constitutive laws.SIAM J Appl Math,1973,25(4):448 -461P
[151]Valanis K C.A theory of viscoplasticity without a yield surface.Arch Mech,1971,23(4):517-551P
[152]Valanis K C.On the foundations of the endochronic theory of viscoplasticity.Arch Mech,1975,27(5):857-868P
[153]Pipkin A C,Rivlin R S.Mechanics of rate-independent materials.ZAMP,1965,16(2):313-327P
[154]Lubliner J.A simple theory of plasticity.Int J Solids Struct,1974,10(2):313-319P
[155]Lubliner J.A maximum dissipation principle in generalized plasticity.Acta Mech,1984,52(2):225-237P
[156]Lubliner J.Normality rules in large-deformation plasticity.Mech Mater,1986,5(1):29-34P
[157]黄筑平.连续介质力学基础.北京:高等教育出版社,2003:168-169页
[158]蔡艳红.粘弹性材料动态扩展裂纹尖端场.哈尔滨工程大学博士学位论文,2003:109页
[2]詹特A N.张立群等译.橡胶工业.化学工业出版社,2002:1-5页
[3]王作龄.橡胶材料科学的发展.世界橡胶工业,1998,25(2):41-47页
[4]熊祝华,傅衣铭,熊慧而.连续介质力学基础.长沙:湖南大学出版社,1997:116页,46-48页
[5]Fu Y B,Ogden R W.Nonlinear Elasticity.Cambridge:Cambridge University Press,2001:1-50P
[6]Ogden R W.Non-smooth/Nonconvex Mechanics,2001.Holand:Kluwer Academic Publishers,2001:277-299P
[7]Ogden R W.Stress softening and residual strain in the azimuthal shear of a pseudo-elastic circular cylindrical tube.Int J of Nonlinear Mechanics,2001,36(3):477-487P
[8]郭仲衡.非线性弹性理论.北京:科学出版社,1980:1-100页
[9]高玉臣.固体力学基础.北京:中国铁道出版社,1999:1-196页,118,页,119页
[10]王自强.理性力学基础.北京:科学出版社,2000:1-5页,119页
[11]Ericksen J L.Finite Elasticity,ASME,1976.America:ASME-AMD,1976:11-21P
[12]Erbay H A.Finite axisymmetric deformation of elastic tubes,An approximate method.J of Engineering mathematics,1995,29(3):451-472P
[13]史守峡.平面应变不可压缩橡胶圆柱的大变形.固体力学学报,1999,20(4):290-296P
[14]陈少华.橡胶材料的尖点及角点的大变形接触问题.北方交通大学博士 学位论文.1999:53-92页
[15]黄克智,薛明德,陆明万.张量分析.第二版.北京:清华大学出版社,2002:1-117页
[16]Alexander H.Tensile instability of initially spherical balloons.Int J Engng Sci,1971,9(1):151-162P
[17]白以龙.材料的不稳定性.黄克智,徐秉业编.固体力学发展趋势,北京,1995.北京:北京理工大学出版社,1995,95-107页
[18]程昌钧,任九生.非线性材料中空穴生成和增长问题的一些进展.自然杂志,26(1):1-6页
[19]Green A E,Zerna W.Theoretical elasticity.England:Oxford,1954:60-89P
[20]Green A E,Adkins J E.Large elastic deformation and non-linear continuum mechanics.England:Oxford,1960:78-96P
[21]Abeyaratne R,Horgan C O.The pressurized hollow sphere problem in:finite elastostatics for a class of compressible materials.Int J Solids Structures,1984,20(8):715-723P
[22]Chung D T,Horgan C O,Abeyaratne R.The finite deformation of internally pressurized hollow cyiinders and spheres for a class of compressible elastic materials.Int J Solids Structures,1986,22(t2):1557-1570P
[23]Willson A J,Myers P J.On the finite elastostatic deformation of thin-walled sphere and cylinders.Int J Solids Structures,1991,26(3):369-373P
[24]Guo Z H.Problems of spherical membrane in the theory of large defermation.Mech Stos,1962,14(6):921-936P
[25]Shield R T.On the stability of finitely deformed elastic membranes.Part Ⅰ:Stability of a uniformly deformed plane membrane.ZAMP,1971,22(6):1016-1028P
[26]Shield R T.On the stability of finitely deformed elastic membranes. Part II: Stability of inflated cylindrical and spherical membranes. ZAMP, 1972, 23(1): 16-34P
[27] Hill J M. Closed form solutions for small deformations superimposed upon the symmetrical expansion of a spherical shell.Journal of Elasticity, 1976, 6(2):125-136P
[28] Needleman A. Inflation of spherical rubber balloons. Int J Solids Structures, 1977, 13(5):409-421P
[29] Haughton D M, Ogden R W. On the incremental equations in non-linear elasticity—I. Membrane theory. J Mech Phys Solids, 1978, 26(2):93-110P
[30] Haughton D M, Ogden R W. On the incremental equations in non-linear elasticity—II. Bifurcation of pressurized spherical shells. J Mech Phys Solids, 1978, 26(2):111-138P
[31] Haughton D M. Post bifurcation of perfect and imperfect spherical elastic membranes. Int J Solids Structures, 1980, 16(12):1123-1133P
[32] Haughton D M. Inflation and bifurcation of compressible spherical membranes. J Elasticity, 1982, 12(2):239-245P
[33] Haughton D M. Inflation and bifurcation of thick-walled compressible elastic spherical shells. IMA Journal of Applied Mathematics, 1987, 39(2):259-272P
[34] Chen Y C, Healey T J. Bifurcation to pear-shaped equilibria of pressurized spherical membranes. Int J Non-linear Mechanics, 1991,26(3/4):279-291P
[35] Hill J M, Arrigo D J. Small deformations superimposed upon the symmetrical expansion of a spherical shell. Quart J Mech Appl Math,1996,49(3):337-351P
[36] Warne D P, Warne P G. On non-symmetric deformations of an incompressible nonlinearly elastic isotropic sphere. Journal of Elasticity,1997,47(2):85-100P
[37]Verron E,Marckmann G.Numerical analysis of rubber balloons.Thin-walled Structures,2003,41(8):731-746P
[38]Easlach H W,Humphrey J D.Dynamics of biological soft tissue and rubber:internally pressurized spherical membranes surrounded by a fluid.Int J Non-linear Mechanics,2004,39(3):399-420P
[39]范志强.均布内压作用下球膜膨胀和分叉问题的研究.哈尔滨工程大学硕士学位论文.2005:26-63,39页
[40]Green A E,Rivlin R S,Shield R T.General theory of small elastic deformations superposed on finite elastic deformations.Proceedings of Royal Society,1952,A211(1):128-154P
[41]Hill J M,Arrigo D J.On the general structure of small on large problems for elastic deformations of Varga materials Ⅱ:axially symmetric deformations.Journal of Elasticity,1999,54(3):212-227P
[42]Pan F X,Beatty M F.Remarks on the instability of an incompressible and isotropic hyperelastic thick-walled cylindrical tube.Journal of Elasticity,1997,48(3):217-239P
[43]Beatty M F,Pan F X.Stability of an internally constrained,hyperelsatic slab.International Journal of Non-linear Mechanics,1993,33(5):867-906P
[44]Chen Y C.Stabity and bifurcation of finite deformations of elastic cylindrical membranes-Part Ⅰ.Stability analysis.Int J Solids Structures,1997,34(14):1735-1749P
[45]Haughton D M.On non-linear stability in unconstrained non-linear elasticity.Int J Non-linear Mechanics,2004,39(7):1181-1192P
[46]Sawyer K N,Rivlin R S.Instability of an elastic material.Int J Sclids Structures,1973,9(5):607-613P
[47]Fu Y B.Some asymptotic results concerning the bucking of a spherical shell of arbitrary thickness. International Journal of Non-linear Mechanics, 1998, 33(6): 1111-1122P
[48] Ogden R W. Large and global bifurcation phenomena in plane-strain finite elasticity. Int J Solids Structures, 1985, 21(2):121-132P
[49] Ogden R W. On the stability of asymmetric deformation of a symmetrically tensioned elastic sheet. Int J Engng Sci, 1987,25(10): 1305-1314P
[50] Haughton D M, Chao Y C. On the eversion of incompressible elastic shells. ZAMP, 1999, 50(2): 312-326P
[51] Haughton D M, Ogden R W. Bifurcation of inflated circular cylinders of elastic material under axial loading. — I. Membrane theory for thin-walled tubes. J Mech Phys Solids, 1979, 27(3):179-212P
[52] Haughton D M, Ogden R W. Bifurcation of inflated circular cylinders of elastic material under axial loading. —II. Exact theory for thick-walled tubes. J Mech Phys Solids, 1979, 27(5-6):489-512P
[53] Haughton D M, Orr A. On the eversion of incompressible elastic cylinders. Int J Non-linear Mechanics, 1995, 30(2):81-95P
[54] Haughton D M, Orr A. On the eversion of compressible elastic cylinders. Int J Solids Structures, 1997, 34(15):1893-1914P
[55] Ratner A M. Tensile stability of cylindrical membranes. Int J Non-linear Mechanics, 1983, 18(2): 133-147P.
[56] Ogden R W, Steigman D J, Haughton DM. The effect of elastic surface coating on the finite deformation and bifurcation of a pressurized circular annulus. J Elasticity, 1997, 47(2):121-145P
[57] Hill J M, Arrigo D J. On the general structure of small on large problems for elastic deformations of Varga materials I : plane strain deformations. Journal of Elasticity, 1999, 54(3): 193- 211P
[58]Gent A X,Lindley P B.Internal ruptuer of bonded rubber cylinders Intension.Proc R Soc London,1959,A249(2):195-205P
[59]Williams M I,Schapery R A.Spherical flaw instability in hydrostatic tension.Int J Fracture,1965,1(1):64-71P
[60]Lindsey G H.Cavitation in bonded rubber cylinders in tension.J Applied Physics,1967,38(12):4843-4856P
[61]Gent A,Park B.Failure processes in elastomers at or near a rigid spherical inclusion.J Material Science,1984,19(7):1947-1956P
[62]Cho K,Gent A.Cavitation in model elastomeric composites.J Material Science,1988,23(1):141-144P
[63]Ball J M.Discontinuous equilibrium solutions and cavitation in nonlinear elasticity.Phil Trans R Soc London,1982,A306(3):557-611P
[64]Horgan C O,Abeyaratne R.A bifurcation problem for a compressible nonlinearly elastic medium:growth of a micro-void.Journal of Elasticity,1986,16(2):189-200P
[65]Sivaloganothan J.Uniqueness of regular and singular equlibrium fcr spherically symmetric problems of nonlinear elasticity.Arch Rat Mech Anal,1986,96(2):97-136P
[66]Horgan C O,Polignone D A.Cavitation in nonlinearly elastic solids:A review.Applied Mechanics Review,1995,48(8):471-485P
[67]Gent A N.Cavitation in rubber:A cautionary.tale.Rubber Chemistry and Technology,1990,63(6):49-53P
[68]Horgan C O.Nonlinear elasticity,Cambridge University,2001.England:Cambridge University Press,2001:135-159P
[69]Antman S S,Negron-Marrero P V.The remarkable nature of radially symmetric equilibrium states of anisotropic nonlinearly elastic bodies.Journal of Elasticity,1987,18(2):131-164P
[70] Horgan C 0, Pence T J. Void nucleation in tensile dead-loading of a composite incompressible nonlinearly elastic sphere.Journal of Elasticity, 1989, 21(1):61-82P
[71] Horgan C 0, Pence T J. Cavity formation at the center of a composite incompressible non-1inearly elastic sphere. Journal of Applied Mechanics, 1989, 56(2):302-308P
[72] Stringfellow R, Abeyaratne R. Cavitation in an elastomer:comparison of theory with experiment. Material Science Engineering A, 1989, 112: 127-131P
[73] Chou-Wang M S, Horgan C O. Void nucleation and growth for a class of incompressible nonlinearly elastic materials: An example. Int J of solids and structures, 1989, 25(11):1239-1254P
[74] Horgan C O. Void nucleation and growth for compressible nonlinearly elastic materials: An example. Int J of solids and structures, 1992, 29(3):279-291P
[75] Meynard F. Existence and nonexistence results on the radially symmetric cavitation problem. Q Appl Math, 1992, 50(2):201-226P
[76] Polignone D A , Horgan C O. Cavitation for incompressible anisotropic Nonlinearly elastic spheres. J of Elasticity, 1993,33(1):27-65P
[77] Polignone D A, Horgan C O. Effects of material anisotropy and inhomogeneity on cavitation for composite incompressible nonlinearly-elastic spheres. Int J Solids and Structuers, 1993,30(24):3381-3416P
[78] Biwa S. Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. J Nonlinear Mech, 1995,30(4):899-906P
[79] Biwa S. Critical stretch for formation of a cylindrical void in a compressible hyperelastic material. Int J Nonlinear Mechanics, 1995,30(6):899-914P
[80]Lei H C,Chang H W.Void formation and growth in a class of compressible solids.J Eng Math,1996,30(6):693-702P
[81]尚新春,程昌钧.超弹性材料中的球形空穴分叉.力学学报,1996,28(6):751-755页
[82]Murphy J G,Biwa S,Nonmonotonic cavity growth in finite ccmpressible elasticity.Int J of Solids and Structures,1997,34(29):3859-3872P
[83]Shang X C,Cheng C J.Exact solution for cavitated bifurcation for compressible hyperelasitc materials.Int J of Engineering Seience,2001,39(10):1101-1117P
[84]任九生,程昌钧.不可压超弹性材料中的空穴分叉.应用数学和力学,2002,23(8):783-789页
[85]Ren J S,Cheng C J.Cavitation for incompressible anisotropic hyper-elastic materials.J of Shanghai University,2002,6(3):185-190P
[86]宁建国,李伟,郝玖锋等.平面应变条件下孔洞化不稳定性问题研究.固体力学学报,2003,24(3):359-363页
[87]任九生,程昌钧,朱正佑.可压超弹性材料组合球体中心的空穴生成.应用数学和力学,2003,24(9):892-898页
[88]Ren J S,Cheng C J,Zhu Z Y.Cavity formation at the center of a sphere composed of two compressible hyperelastic material.Applied Mathematics and Mechanics,2003,24(9):1009 -1016P
[89]Yuan X G,Zhu Z Y,Cheng C J.Void formation and growth for a class of compressible hyper-elastic sphere.Journal of Shanghai University,2004,8(1):13-18P
[90]任九生,程昌钧.热超弹性材料中的空穴生成问题.固体力学学报,2004,25(3):275-278页
[91]任九生,程昌钧.组合超弹性材料中的空穴生成与增长.力学季刊, 2004,25(2):175-182页
[92]唐立强,范志强,杨勇.不可压缩球体的空穴和分叉.哈尔滨工程大学学报,2005,26(5):624-627页
[93]王勇,唐立强,杨勇.不可压缩橡胶圆柱的空穴和分叉.哈尔滨工程大学学报,2007,28(9):980-984页
[94]Haughton D M.On non-existence of cavitation in incompressible elastic membranes.Q J Mech appl Math,1986,39(2):289-296P
[95]Haughton D M.Cavitation in compressible elastic membranes.J of Engineering Mechanics,1990,28(2):163-168P
[96]Steigmann D J.Cavitation in elastic membranes-an example.J of Elasticity,1992,28(3):277-287P
[97]Knowles J K.Large amplitude oscillations of a tube of incompressible elastic material.Q Appl Math,1960,18(1):71-77P
[98]Knowles J K.On a class of oscillations in the finite deformation theory of elasticity.J Appl Mech,1962,29(2):283-286P
[99]Guo Z H,Solecki R.Free and forced finite amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material.Arch Mech Stos,1963,15(2):427-433P
[100]Calderer C.The dynamical behavior of nonlinear elastic spherical shells.J of Elasitcity,1983,13(1):17-42P
[101]Chou-Wang M S,Horgan C O.Cavitation in nonlinear elastodynamics for neo-Hookean materials.Int J of Engng Sci,1989,27(8):967-973P
[102]任九生,程昌钧.可压缩超弹性球壳的有限振动.振动与冲击,2003,22(4):1-3页
[103]Ren J S,Cheng C J.Dynamical formation of cavity in transversely hyperelastic spheres.Acta Mechanica Sinica,2003,19(4):320-323P
[104]梅波,程昌钧.两个组合热超弹性球体中空穴的动态生成.上海大学 学报,2004,10(4):376-380页
[105]任九生,程昌钧.超弹性材料中空穴的动态生成.固体力学学报,2004,25(1):42-46页
[106]任九生,程昌钧.组合超弹性球体中空穴的动态生成.应用数学和力学,2004,25(11):1117-1123页
[107]Ren J S,Cheng C J.Dynamical formation of cavity in a composed hyper-elastic sphere.Applied Mathematics and Mechanics,2004,25(11):1220-1227P
[108]任九生,程昌钧.横观各向同性超弹性球壳的有限振动.固体力学学报,2004,25(2):221-224页
[109]Yuan X G,Zhu Z Y,Cheng C J.Qualitative analysis of dynamical behavior for an imperfect incompressible Neo-hookean spherical shell.Applied Mathematics and Mechanics,2005,26(8):973-981P
[110]袁学刚,朱正佑,程昌钧.具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析.应用数学和力学,2005,26(8):892-898页
[111]程昌钧,梅波.非均匀温度场中组合热超弹性球体的动态孔穴生成.应用数学和力学,2006,27(4):395-403页
[112]Cheng C J,Mei B.Dynamical formation of cavity for composed thermal hyperelastic spheres in nonuniform temperature fields.Applied Mathematics and Mechanics,2006,27(4):443-452 P
[113]Ren J S,Cheng C J.Static and dynamical cavitation for incompressible hyperelastic-plastic material.Journal of Shanghai University,2006,10(4):283-287P
[114]任九生,程昌钧.超弹性-塑性材料中空穴的动生成.太原理工大学学报,2005,36(6):679-681页
[115]程昌钧,聂波.幂强化材料和超弹性材料组合球体中孔穴的动态生成.固体力学学报,2005,26(3):273-279页
[116]聂波,程昌钧.组合幂强化弹塑性-超弹性球体中的空穴生成.上海大学学报,2004,10(6):612-615页
[117]任九生,程昌钧.可压超弹性-塑性材料中的空穴生成.力学季刊,2003,24(4):440-444页
[118]尚新春,程昌钧.弹性固体材料中的空穴萌生与增长.北京科技大学学报,2002,24(3):380-382页
[119]Shang X C,Cheng C J.Cavitation in hookean elastic membranes.Acta Mechanica Solida Sinica,2002,15(1):1-6P
[120]金明,黄克服,武际可.泊松比为1/2材料中球形空穴突变和球形空穴萌生的分岔问题研究.应用数学和力学,1999,20(8):867-872页
[121]Jin M.A mechanical model on elastic cavitation in solid under hydrostatic tension.Mech Res Comm,2001,28(3):305-315P
[122]Shang X C,Cheng C J.The 4~(th) ICNM,Shanghai university,2002.Shanghai:Shanghai university press,2002:156-162P
[123]Huang Y,Hutchinson J W,Tvergaard V.Cavitation instabilities in elastic-plastic solids.J Mech Phys Solids,1991,39(2):223-241P
[124]Tvergaard V,Huang Y,Hutchinson J W.Cavitation instabilities in a power hardening elastic-plastic solids.Eur J Mech A/Solids,1992,11(2):215-231P
[125]Tvergaard V,Hutchinson J W.Effect of initial void shape on the occurrence of cavitation instabilities in elastic-plastic solids.J of Applied Mech,1993,60(5):807 -812P
[126]Tvergaard V.Effect of void size difference on growth and cavitation instability.J Mech Phys Solids,1996,44(8):1237-1253P
[127]Tvergaard V.Interaction of very small voids with large voids.J Mech Phys Solids,1987,35(12):3989-4000P
[128]Hou H S,Abeyaratne R.Cavitation in an elastic and elastic-plastic solids.J Mech Phys Solids,1992,40(3):571-592P
[129]郭仲衡等译.应用力学的最新进展.北京:科学出版社,1987:1-50页
[130]Rivlin R S.Finite elasticity.New York:The Ameircan Society of Mechanical Engineers,1977.1-200P
[131]Rivlin R S.Stability of plane homogeneous deformation of an elastic cube under dead loading.Q of Applied Mathematics,1974,32(2):265-271P
[132]Kearsley E A.A symmetric stretching of a symmetrically loaded elastic sheet.International J of Solids and Structures,1986,22(2):111-119P
[133]尚新春.类橡胶材料和结构的不稳定性理论及分叉问题.兰州大学博士学位论文,1994:1-60页
[134]任九生,程昌钧.热超弹性圆筒的不稳定性.力学学报,2007,39(2):283-288P
[135]Haughton D M.An exact solution for the stretching of elastic membranes containing a hole or inclusion.Mechanics research Communications,1991,18(1):29-39P
[136]王勇.橡胶圆管与薄膜充气管的有限变形分析.哈尔滨工程大学硕士学位论文,2006:16-21页
[137]Gao Y C.Elastostatic crack tip behavior for a rubber like material.Theoretical and Applied Fracture Mechanics,1990,14(3):219-231P
[138]Gao Y C.Large deformation field near a crack tip in rubber-like material.Theoretical and Applied Fracture Mechanics,1997,25(3):155-162P
[139]Gao Y C,Liu B.Stress singularity near the notch tip of a rubber like specimen under tension.European Journal of Mechanics-A/Solids,1996,15(2):199-211P
[140]Gao Y C,Liu B.A rubber cone under the tension of a concentrated force.International Journal of Solids and Structures,1995,32(11):1485-1493P
[141]Gao Y C,Chen S H.Large strain field near a crack tip in a rubber sheet.Mechanics research Communications,2001,28(1):71-78P
[142]Haughton D M,McKay B A.Wrinkling of Inflated Elastic Cyiindrical Membrane Under Flexure.International Journal of Engineering Science,1996,34(13):1531-1550P
[143]Steigmann D J.Tension field theory.Proceedings of Royal Society London A,1990,429(2):141-173P
[144]Naghdi P M,Tang P Y.Large deformation possible in every isotropic elastic membrane.Phil Trans R Soc Lond A,1977,287(2):145-187P
[145]程昌钧,尚新春.超弹性矩形板单向拉伸时微孔的增长.应用数学和力学,1997,18(6):573-578P
[146]Ren J S,Cheng C J,Shang X C.The growth of a void in a rubber rectangular plate under uniaxial extension.Journal of Shanghai University,2001,5(3):177-182P
[147]任九生,程昌钧.多孔Mooney-Rivlin材料矩形板的单向拉伸.力学季刊,2002,23(3):347-353P
[148]程昌钧,任九生.横观各向同性多孔超弹性矩形板的单向拉伸.应用数学和力学,2003,24(7):675-683P
[149]Cheng C J,Ren J S.Growth of voids in a hyperelastic rectangular plate.Journal of Shanghai University,2005,9(3):194-200P
[150]Hill R,Rice J R.Elastic potentials and the structure of inelastic constitutive laws.SIAM J Appl Math,1973,25(4):448 -461P
[151]Valanis K C.A theory of viscoplasticity without a yield surface.Arch Mech,1971,23(4):517-551P
[152]Valanis K C.On the foundations of the endochronic theory of viscoplasticity.Arch Mech,1975,27(5):857-868P
[153]Pipkin A C,Rivlin R S.Mechanics of rate-independent materials.ZAMP,1965,16(2):313-327P
[154]Lubliner J.A simple theory of plasticity.Int J Solids Struct,1974,10(2):313-319P
[155]Lubliner J.A maximum dissipation principle in generalized plasticity.Acta Mech,1984,52(2):225-237P
[156]Lubliner J.Normality rules in large-deformation plasticity.Mech Mater,1986,5(1):29-34P
[157]黄筑平.连续介质力学基础.北京:高等教育出版社,2003:168-169页
[158]蔡艳红.粘弹性材料动态扩展裂纹尖端场.哈尔滨工程大学博士学位论文,2003:109页