非定常微分型黏弹性本构模型

康永刚; 张秀娥

doi:10.6052/0459-1879-2012-2-20120231

非定常微分型黏弹性本构模型

防灾科技学院, 河北三河 065201

基金项目: 防灾科技学院防灾减灾青年科技基金资助项目(201008)

详细信息

中图分类号: O631.2+1, O377, O345
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- 文章访问数: 1964
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出版历程
- 收稿日期: 2011-08-14
- 修回日期: 2011-09-09
- 刊出日期: 2012-03-17

THE NON-STATIONARY DIFFERENTIAL CONSTITUTIVE MODELS OF VISCOELASTICITY

Institute of Disaster-Prevention Science and Technology, Sanhe, Hebei 065201, China

Funds: The project was supported by the Foundation of Institute of Disaster-Prevention Science and Technology (201008).

摘要

摘要: 在应力作用下, 材料的力学参数随着微观结构的变化而变化, 需要考虑参数的时间效应. 利用黏滞系数随时间变化的黏性元件, 构造出非定常Maxwell模型、非定常Kelvin模型和非定常Zener模型. 求解非定常模型的微分型本构方程得到它们的松弛模量、蠕变柔量和卸载方程. 结果表明, 可以把常见的经验松弛函数和经验蠕变函数视为非定常微分型本构模型.
- 非定常微分型模型 /
- 经验模型 /
- 应力松弛 /
- 蠕变
Abstract: Based on non-stationary viscous components, the non-stationary Maxwell model, the non-stationary Kelvin model and the non-stationary Zener model were developed. Their relaxation moduli, creep compliances and unloading functions were obtained by resolving the non-stationary constitutive relation. The results show that many empirical functions, such as power law relaxation, stretched exponential relaxation, logarithmic creep, can be seen as non-stationary model. The corresponding relaxation modulus and unloading functions of empirical creep functions, the corresponding creep compliance and unloading functions of empirical relaxation function were obtained by resolving the non-stationary constitutive relation.
- non-stationary differential model /
- empirical model /
- stress relaxation /
- creep

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参考文献(16)

1 Williams G, Watts DC. Non-symmetrical dielectric relaxation behavior arising form a simple empirical decay function. it Trans Faraday Soc, 1970, 66: 80-85

2 郭碧云,李晓阳,曾衍钧等.肋软骨生物力学性能研究.中国生物医学工程学报, 2006, 26(2): 270-275 (Guo Biyun, Li Xiaoyang, Zeng Yanjun, et al. Study on biomechanical characteristics of costal cartilage. it Chinese Journal of Biomedical Engineering, 2006, 26(2): 270-275 (in Chinese))

3 张为民.松弛模量与蠕变柔量的实用表达式.湘潭大学自然科学学报,1999, 21(3): 26-28 (Zhang Weimin. Practical expressions of relaxation modulus and creep compliance. it Natural Science Journal of Xiangtan University, 1999, 21(3): 26-28 (in Chinese))

4 Benioff H. Earthquakes and rock creep. it Bull Seismol Soc Am, 1951, 41: 31-62

5 帅词俊,段吉安,王炯.关于黏弹性材料的广义Maxwell模型.力学学报, 2006, 38(4): 565-569 (Shuai Cijun, Duan Jian, Wang Jiong. A method of establishing generalized maxwell model for viscoelastic material. it Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(4): 565-569 (in Chinese))

6 Surguladze TZ. On certain applications of fractional calculus to viscoelasticity. it J Math Sci, 2002, 112(5): 4517-4557

7 Schiessel H, Metzler R, Blumen A, et al. Generalized viscoelastic models: their fractional equations with solutions. it J Phys A: Math Gen, 1995, 28(23): 6567-6584

8 熊良宵, 杨林德, 张尧. 岩石的非定常Burgers模型.中南大学学报(自然科学版), 2010, 41(2): 679-684 (Xiong Liangxiao, Yang Linde, Zhang Yao. Non-stationary Burgers model for rock. it Journal of Central South University (it Science and Technology), 2010, 41(2): 679-684 (in Chinese))

9蒋昱州, 张明呜, 李良权. 岩石非线性黏弹塑性蠕变模型研究及其参数识别.岩石力学与工程学报, 2008, 27(4): 832-839 (Jiang Yuzhou, Zhang Mingming, Li Liangquan. Study on nonlinear viscoelasto-plastic creep model of rock and its parameter identlficatlon. it Chinese Journal of Rock Mechanics and Engineering, 2008, 27(4): 832-839 (in Chinese))

10施行觉,李成波,Adnan Aydin等. 地球介质的非定常参数黏弹模型. 地球物理学报, 2009, 52(1): 50-56 (Shi Xingjue, Li Chengbo, Adnan Aydin, et al. Viscoelastic model with variable parameters for earth medium. it Chinese Journal of Geophysics, 2009, 52(1): 50-56 (in Chinese))

11 张久鹏,徐丽,王秉纲. 沥青混合料蠕变模型的改进及其参数确定. 武汉理工大学学报(交通科学与工程版), 2010, 34(4): 699-706 (Zhang Jiupeng, Xu Li, Wang Binggang. Modification of creep model of asphalt mixture and parameters determination. it Journal of Wuhan University of Technology(it Transportation Science and Engineering), 2010, 34(4): 699-706 (in Chinese))

12 邵卓平. 木质材料变参数流变模型的研究. 林业科学, 2003, 39(3): 106-110 (Shao Zhuoping. The study on variable coefficients rheological model of woods. it Cientia Silvae Sinicae, 2003, 39(3): 106-110 (in Chinese))

13 陈建康, 黄筑平, 楚海建等. 单向应力条件下松弛时间率相关的非线性黏弹性本构模型. 高分子学报, 2003, 3: 414-419 (Chen Jiankang, Huang Zhuping, Chu Haijian, et al. Nonlinear viscoelastic constitutive relations based on the rate sensitive relaxation time under the condition of uniaxial stress. it Acta Polymerica Sinica, 2003, 3: 414-419 (in Chinese))

14 孙钧.岩石流变力学及其工程应用研究的若干进展.岩石力学与工程学报, 2007, 26(6): 1081-1106 (Sun Jun. Rock rheological mechanics and its advance in engineering applications. it Chinese Journal of Rock Mechanics and Engineering, 2007, 26(6): 1081-1106 (in Chinese))

15张为民, 张淳源.分数指数模型的热力学分析及其应用.工程力学, 2002, 19(2): 95-99 (Zhang Weimin.Zhang Chunyuan. Thermodynamic analysis and application of fractional exponential model. it Engineering Mechanics, 2002, 19(2): 95-99 (in Chinese))

16 金日光, 黄惠金, 周淑梅.关于高分子材料在应力松弛过程中应力-时间关系的研究. 北京化工大学学报,1996, 23(3): 31-38 (Jin Riguang, Huang Huijin, Zhou Shumei. Studies on relationship between stress and time of polymer materials during proeess of stress relaxation. it Journal of Beijing University of Chemical Technology, 1996, 23(3): 31-38 (in Chinese))