基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

张泷, 刘耀儒, 杨强, 吕庆超

张泷, 刘耀儒, 杨强, 吕庆超. 基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程[J]. 工程力学, 2015, 32(9): 34-41. DOI: 10.6052/j.issn.1000-4750.2014.02.0120
引用本文: 张泷, 刘耀儒, 杨强, 吕庆超. 基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程[J]. 工程力学, 2015, 32(9): 34-41. DOI: 10.6052/j.issn.1000-4750.2014.02.0120
ZHANG Long, LIU Yao-ru, YANG Qiang, LÜ Qing-chao. A VISCOELASTIC-VISCOPLASTIC CONSTITUTIVE EQUATION OF ROCK BASED ON IRREVERSIBLE INTRNAL STATE VARIABLE THERMODYNAMICS[J]. Engineering Mechanics, 2015, 32(9): 34-41. DOI: 10.6052/j.issn.1000-4750.2014.02.0120
Citation: ZHANG Long, LIU Yao-ru, YANG Qiang, LÜ Qing-chao. A VISCOELASTIC-VISCOPLASTIC CONSTITUTIVE EQUATION OF ROCK BASED ON IRREVERSIBLE INTRNAL STATE VARIABLE THERMODYNAMICS[J]. Engineering Mechanics, 2015, 32(9): 34-41. DOI: 10.6052/j.issn.1000-4750.2014.02.0120

基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

基金项目: 国家自然科学基金项目(11172150,51279086); 水沙科学与水利水电工程国家重点实验室课题项目(2013-KY-2); 教育部新世纪优秀; 人才支持计划项目(NCET-13-0323)
详细信息
    作者简介:

    刘耀儒(1974―),男,河北人,副教授,博士,从事水工结构和岩石力学研究(E-mail: liuyaoru@tsinghua.edu.cn); 杨 强(1964―),男,云南人,教授,博士,博导,从事水工结构和岩石力学研究(E-mail: yangq@tsinghua.edu.cn); 吕庆超(1986―),男,吉林人,博士生,从事水工结构和岩石力学研究(E-mail: lvqc05@gmail.com).

A VISCOELASTIC-VISCOPLASTIC CONSTITUTIVE EQUATION OF ROCK BASED ON IRREVERSIBLE INTRNAL STATE VARIABLE THERMODYNAMICS

  • 摘要: 岩石材料的粘弹性和粘塑性变形是与时间相关的能量耗散行为。在Rice不可逆内变量热力学框架下,引入两组内变量分别用来描述在粘弹性和粘塑性变形过程中材料的内部结构调整。通过给定比余能的具体形式和内变量的演化方程,推导出内变量粘弹-粘塑性本构方程。粘弹性本构方程具有普遍性,能涵盖Kelvin-Voigt和Poynting-Thomson在内的经典粘弹性模型的本构方程。并指出热力学力与应力呈线性关系是组合元件模型为线性模型的根本原因。粘塑性本构方程能较好地刻画岩石材料在粘塑性变形过程中的硬化现象。对模拟岩石的模型相似材料进行单轴加卸载蠕变试验,将蠕变过程中的粘弹性和粘塑性变形分离并根据试验数据对本构方程的材料参数进行辨识。试验数据和理论曲线对比结果表明该文提出的本构方程能很好地模拟材料的蠕变行为。该类型的本构方程能为岩石工程的长期稳定性的预测、评价以及加固分析提供基础。
    Abstract: The viscoelastic and viscoplastic deformations of geo-materials are time-dependent energy dissipation behaviors. Within the framework of Rice irreversible internal state variable thermodynamics, two sets of internal state variables are introduced to describe structural rearrangement within solids during viscoelastic and viscoplastic deformation processes, respectively. The specific complementary energy function and the kinetic functons of internal state variables are presented, and the viscoelastic-viscoplastic constitutive equations are derived. The proposed viscoelastic constitutive equation has universality and can contain constitutive equations from classical viscoelastic models, such as the Kelvin-Voigt model and Poynting-Thomson model. The opinion that the linearity relationship between thermodynamic force and stress is the essential reason that the component model is linear is presented. The hardening effect of viscoplastic deformation can also be described accurately by the viscoplastic constitutive equation. A uniaxial creep test of an analogue material used to model geo-materials is conducted by loading and unloading paths. This method can separate viscoelastic and viscopalstic deformations in creep process. Then parameter identification is conducted through test data. Comparison between test data and theoretical curves indicates that the proposed constitutive equation can describe the creep behavior accurately, and can be a fundamental basis for forecasting and evaluating the long-term stability and analyzing the reinforcement of geo-material projects.
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    其他类型引用(11)

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出版历程
  • 收稿日期:  2014-02-19
  • 修回日期:  2014-08-31
  • 刊出日期:  2015-09-24

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