基于分数阶导数的岩石非线性蠕变损伤模型
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摘要
利用Riemann-Liouville分数阶理论,给出一种分数阶软体元件及其本构方程,阶数取值不同,可分别模拟蠕变的三个阶段.采用两个分数阶软体元件与虎克体进行组合,引入岩石硬化函数、损伤变量,提出一种新的含分数阶导数的非线性蠕变损伤模型,并推导出该模型的本构方程.利用砂岩的蠕变试验数据进行验证,发现该模型能有效描述砂岩的蠕变特性.
In this paper,using Riemann-Liouville fractional order theory,a kind of software element and its constitutive equation are given. Different values of fractional order can be used to simulate three stages of creep. Two fractional order software components and the hook body are combined. We introduce the rock hardening function,damage variable,put forward a new containing fractional order derivative of the nonlinear creep damage model,and deduce the constitutive equation of the model. The creep test data of sandstone are used to verify,and the results show that the model can effectively describe the creep properties of sandstone.
In this paper,using Riemann-Liouville fractional order theory,a kind of software element and its constitutive equation are given. Different values of fractional order can be used to simulate three stages of creep. Two fractional order software components and the hook body are combined. We introduce the rock hardening function,damage variable,put forward a new containing fractional order derivative of the nonlinear creep damage model,and deduce the constitutive equation of the model. The creep test data of sandstone are used to verify,and the results show that the model can effectively describe the creep properties of sandstone.
引文
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[16]何明明,李宁,陈蕴生,等.基于分数阶微积分岩石的动态变形行为研究[J].岩土工程学报,2015,37(S1):178-184.
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[18]王学彬.拉普拉斯变换方法解分数阶微分方程[J].西南师范大学学报(自然科学版),2016,41(7):7-12.
[19]穆霞英.蠕变力学[M].西安:西安交通大学出版社,1990.
[2]徐卫亚,杨圣奇,杨松林,等.绿片岩三轴流变力学特性的研究(I):试验结果[J].岩土力学,2005,26(4):531-537.
[3]徐卫亚,杨圣奇,谢守益,等.绿片岩三轴流变力学特性的研究(II):模型分析[J].岩土力学,2005,26(5):23-28.
[4]杨广雨,王伟,熊德发,等.岩石非线性黏弹塑性蠕变模型研究[J].河北工程大学学报(自然科学版),2017,34(4):23-26.
[5]蒋昱州,张明鸣,李良权.岩石非线性黏弹塑性蠕变模型研究及其参数识别[J].岩石力学与工程学报,2008,27(4):832-839.
[6]赵延林,曹平,文有道,等.岩石弹黏塑性流变试验和非线性流变模型研究[J].岩石力学与工程学报,2008,27(3):477-486.
[7]张英.岩石流变的一种非线性黏弹塑性流变模型研究[J].湖南工业大学学报,2015,29(3):10-14.
[8]蒋海飞,胡斌,刘强,等.一种新的岩石黏弹塑性流变模型[J].长江科学院院报,2014,31(7):44-48.
[9]马明军,钟时猷.一个软弱岩石的粘弹塑性流变力学模型[J].中南矿冶学院学报,1990,21(3):236-241.
[10]LIU L,WANG G,CHEN J,et al.Creep experiment and rheological model of deep saturated rock[J].Transactions of Nonferrous Metals Society of China,2013,23(2):478-483.
[11]MARANINI E,YAMAGUCHI T.A non-associated viscoplastic model for the behaviour of granite in triaxial compression[J].Mechanics of Materials,2001,33(5):283-293.
[12]殷德顺,任俊娟,和成亮,等.一种新的岩土流变模型元件[J].岩石力学与工程学报,2007,26(9):1899-1903.
[13]何志磊,朱珍德,朱明礼,等.基于分数阶导数的非定常蠕变本构模型研究[J].岩土力学,2016,37(3):737-744.
[14]吴斐,刘建锋,武志德,等.盐岩的分数阶非线性蠕变本构模型[J].岩土力学,2014,35(S2):162-167.
[15]郭佳奇,乔春生,徐冲,等.基于分数阶微积分的Kelvin-Voigt流变模型[J].中国铁道科学,2009,30(4):1-6.
[16]何明明,李宁,陈蕴生,等.基于分数阶微积分岩石的动态变形行为研究[J].岩土工程学报,2015,37(S1):178-184.
[17]宋勇军,雷胜友.基于分数阶微积分的岩石非线性蠕变损伤力学模型[J].地下空间与工程学报,2013,9(1):91-95.
[18]王学彬.拉普拉斯变换方法解分数阶微分方程[J].西南师范大学学报(自然科学版),2016,41(7):7-12.
[19]穆霞英.蠕变力学[M].西安:西安交通大学出版社,1990.