## 留言板

 引用本文: 尚新春, 张锐, 任会兰. 受热弹性复合球体空化问题的分析[J]. 应用数学和力学, 2011, 32(5): 556-562.
SHANG Xin-chun, ZHANG Rui, REN Hui-lan. Analysis for Cavitation Problem of Elastic Composite Ball Heated[J]. Applied Mathematics and Mechanics, 2011, 32(5): 556-562. doi: 10.3879/j.issn.1000-0887.2011.05.005
 Citation: SHANG Xin-chun, ZHANG Rui, REN Hui-lan. Analysis for Cavitation Problem of Elastic Composite Ball Heated[J]. Applied Mathematics and Mechanics, 2011, 32(5): 556-562.

## 受热弹性复合球体空化问题的分析

##### doi: 10.3879/j.issn.1000-0887.2011.05.005

###### 作者简介:尚新春(1958- ),男,山西人,教授,博士,博士生导师(联系人.E-mail:shangxc@ustb.edu.cn).
• 中图分类号: O343；O175；TB301；TG113

## Analysis for Cavitation Problem of Elastic Composite Ball Heated

• 摘要: 研究了由两种弹性固体材料组成的复合球体，在均匀变温场作用下的空化问题．采用了几何大变形的有限对数应变度量和Hooke弹性固体材料的本构关系，建立了问题的非线性数学模型．求出了复合球体大变形热弹性膨胀的参数形式的解析解．给出了空穴萌生时临界温度随几何参数和材料参数的变化曲线,以及空穴增长的分岔曲线．算例的数值结果指出：超过临界温度后空穴半径将迅速增大，并且空穴萌生时环向应力将成为无限大，这意味着如果内部球体是弹塑性材料，则会在空穴表面附近产生塑性变形而造成材料的局部损伤．另外，当内部球体材料的弹性接近于不可压时，复合球体可以在较低的变温下空化．
•  [1] Tvergaard V. Material failure by void growth to coalescence[J].Advances in Applied Mechanics.1990, 27: 83-151. [2] McClinitock F A. A criterion for ductile fracture by growth of holes [J]. J Appl Mech, 1968, 35: 363-371. [3] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. J Mech Phys Solids, 1969, 17(3): 201-217. [4] Ball J M. Discontinuous equilibrium solutions and cavitation in nonlinear elasticity[J]. Phil Trans R Soc London, A, 1982, 306(1496): 557-610. [5] Horgan C O, Abeyaratne R. A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void [J]. J Elasticity, 1986, 16(2): 189-200. [6] Horgan C O, Polignone D A. Cavitation in nonlinearly elastic solid: a review[J]. ASME Appl Mech Rev, 1995, 48(6): 471-485. [7] 尚新春，程昌钧. 超弹性材料中的球形空穴分岔[J]. 力学学报, 1996， 28(6)：751-755.(SHANG Xin-chun, CHENG Chang-jun. The spherical cavitation bifurcation in hyperelstic materials[J]. Acta Mech Sinica, 1996, 28(6)：751-755.(in Chinese)) [8] SHANG Xin-chun, CHENG Chang-jun. Exact solution for cavitated bifurcation for compressible hyperelastic material[J]. Int J Eng Sci , 2001, 39(10):1101-1117. [9] 金明，黄克服，武际可.Hooke材料的微孔形空穴分岔[J]. 固体力学学报, 2001, 22(3): 281-286. (JIN Ming, HUANG Ke-fu, WU Ji-ke. A study of the catastrophe and the cavitation for a spherical cavity in Hooke’s material with 1/2 Poisson’s ratio [J]. Acta Mechnica Solida Sinica, 2001, 22(3):281-286. (in Chinese)) [10] SHANG Xin-chun, CHENG Chang-jun. Cavitation in Hookean elastic membranes[J]. Acta Mech Solida, 2002, 15(1):126-129. [11] 尚新春，程昌钧. 弹性固体材料中的空穴萌生于增长[J]. 北京科技大学学报, 2002, 24(3): 380-382. (SHANG Xin-chun, CHENG Chang-jun. Void nucleation and growth for elastic solid materials[J]. J University of Science and Technology Beijing, 2002, 24(3): 380-382. (in Chinese)) [12] SHANG Xin-chun, CHENG Chang-jun, HU Yin-yan. Cavitated bifurcation in Hookean elastic and elastic-plastic materials[C]CHIEN Wei-zang.Proceeding of 4th International Conference on Nonlinear Mechanical. Shanghai: Shanghai University Press, 2002: 315-319. [13] 宁建国, 李伟, 郝玖锋, 刘海燕, 黄筑平. 平面应变条件下孔洞化不稳定性问题的研究. 固体力学学报, 2003, 24(3): 259-263.(NING Jian-guo, LI Wei, HAO Jiu-feng, LIU Hai-yan, HUANG Zhu-ping. Influence of the temperature on the cavitation instability under plane strain condition[J]. Acta Mech Solida Sinica, 2003, 24(3): 259-263. (in Chinese)) [14] 任九生，程昌钧. 热超弹性材料中的空穴生成问题[J]. 固体力学学报，2004, 25(3)：275-278．(REN Jiu-sheng, CHENG Chang-jun. Cavitation problem for thermohyperelastic materials[J]. Acta Mech Solida Sinica, 2004, 25(3): 275-278 (in Chinese))
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##### 出版历程
• 收稿日期:  2011-01-04
• 修回日期:  2011-03-04
• 刊出日期:  2011-05-15

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