分数阶导数线性流变固体模型及其应用  

LINEAR RHEOLOGICAL SOLID MODEL WITH FRACTIONAL DERIVATIVE AND ITS APPLICATION

作　　者：肖世武[1] 周雄[1] 胡小玲[1] 罗文波[1] 

机构地区：[1]湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处：《工程力学》2012年第10期354-358,共5页Engineering Mechanics

基　　金：教育部新世纪优秀人才支持计划项目(NCET-08-0685);教育部科学技术重点项目(209085);湖南省教育厅重点项目(08A069);湖南省研究生科研创新项目(CX2011B270);湖南省高校科技创新团队支持计划项目(湘财教指[2010]70号)

摘　　要：采用Koeller弹壶元件替代标准线性固体模型中的Newton黏壶,得到分数阶导数线性流变固体模型,给出了表征模型动态黏弹特性的存储模量、损耗模量和损耗因子以及表征模型静态黏弹特性的蠕变柔量和松弛模量。采用分数阶导数线性流变固体模型、标准线性固体模型和五参量固体模型对聚丙烯材料应力松弛特性进行分析。讨论了Mittag-Leffler函数的求和截断误差。结果表明分数阶导数线性流变固体模型能更准确描述聚丙烯材料的应力松弛行为。A linear rheological solid model with a fractional order derivative was obtained by replacing the dashpot in a standard linear solid model with a Koeller spring-pot unit.Its dynamic viscoelasticity characterized by a storage modulus,a loss modulus and a loss factor,and static viscoelasticity characterized by a creep compliance and a relaxation modulus,were derived.The stress relaxation characteristic of polypropylene（PP） was modeled using the fractional linear rheological solid model,a standard linear solid model and a five-element solid model.Moreover,the truncation error in the summation calculation of a Mittag-Leffler function was discussed.It is demonstrated that the fractional linear rheological solid model can more adequately reproduce the stress relaxation behavior of the PP sample than other two models.

关 键 词：黏弹性 本构模型 分数阶导数 弹壶 标准线性固体 五参量固体 应力松弛 

分 类 号：O345[理学—固体力学]