岩石结构超塑性损伤本构理论及热力学框架

doi:10.13722/j.cnki.jrme.2015.1063

摘要
图/表
参考文献
相关文章 (0)

全文: PDF (305 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要基于热力学势函数引入损伤理论，建立适用于深部岩体的新结构超塑性损伤本构框架。通过定义新内变量对：应变(损伤积累应变，结构重排应变)及相应广义应力、温度和熵，用4种热力学能量函数：内能，Helmholtz自由能，焓和Gibbs自由能描述岩石结构超塑性本构关系。本理论框架即能满足热力学定律具有严格物理意义又能对结构性进行较合理考虑。通过Legendre变换建立各能量形式间的转换。利用运动内变量参数及其共轭变量(广义应力)引出耗散势。给出承压变温条件下深部岩体的塑形耗散函数或屈服函数形式，可反映损伤并考虑结构重排的体变行为，两者通过Legendre变换的退化特例进行联系。构建适用深部岩体热力学本构理论框架下具体的应力–应变增量本征关系及其新应用实例，并提供应用性的判断依据。该理论对深部地下工程实践中岩石的力学分析具有借鉴意义。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章

关键词 ：岩石力学；广义热力学；损伤；结构超塑性；能量势；耗散势；屈服函数；应力&ndash, 应变本构关系

Abstract：基于热力学势函数引入损伤理论，建立适用于深部岩体的新结构超塑性损伤本构框架。通过定义新内变量对：应变(损伤积累应变，结构重排应变)及相应广义应力、温度和熵，用4种热力学能量函数：内能，Helmholtz自由能，焓和Gibbs自由能描述岩石结构超塑性本构关系。本理论框架即能满足热力学定律具有严格物理意义又能对结构性进行较合理考虑。通过Legendre变换建立各能量形式间的转换。利用运动内变量参数及其共轭变量(广义应力)引出耗散势。给出承压变温条件下深部岩体的塑形耗散函数或屈服函数形式，可反映损伤并考虑结构重排的体变行为，两者通过Legendre变换的退化特例进行联系。构建适用深部岩体热力学本构理论框架下具体的应力–应变增量本征关系及其新应用实例，并提供应用性的判断依据。该理论对深部地下工程实践中岩石的力学分析具有借鉴意义。

Key words：岩石力学；广义热力学；损伤；结构超塑性；能量势；耗散势；屈服函数；应力&ndash 应变本构关系

引用本文:

郭璇1，张顶立1，赵成刚1，张晓新2，王梦恕1，祝瑛1. 岩石结构超塑性损伤本构理论及热力学框架[J]. 岩石力学与工程学报, 2016, 35(4): 658-669.
GUO Xuan1，ZHANG Dingli1，ZHAO Chenggang1，ZHANG Xiaoxin2，WANG Mengshu1，ZHU Ying1. Constitutive theory and thermodynamic framework for hyperplastic damage of deep rock structure. , 2016, 35(4): 658-669.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2015.1063 或 https://rockmech.whrsm.ac.cn/CN/Y2016/V35/I4/658

[1] FENG X T，HUDSON J A. Specifying the information required for rock mechanics modelling and rock engineering design[J]. International Journal of Rock Mechanics and Mining Sciences，2010，47(2)：179–194. [2] HOULSBY G T. A study of plasticity theories and their applicability to rocks[Ph. D. Thesis][D]. Cambridge：University of Cambridge，1981. [3] COLLINS I F，KELLY P A. A thermomechanical analysis of a family of rock models[J]. Geotechnique，2002，52(7)：507–518. [4] COLLINS I F，HOULSBY G T. Application of thermomechanical principles to the modeling of geomaterials[C]// Proceedings of the Royal Society of London，Series A：Mathematical，Physical and Engineering Sciences. London：The Royal Society，1997：1 975–2 001. [5] 赵成刚，张雪东，郭璇. 土的本构方程与热力学[J]. 力学进展，2006，35(4)：611–618.(ZHAO Chenggang，ZHANG Xuedong，GUO Xuan. Constitutive equations of rock and thermodynamics[J]. Advances in Mechanics，2006，35(4)：611–618.(in Chinese)) [6] ZIEGLER H. An Introduction to Thermomechanics[M]. 2nd ed. [S. l.]：North-Holland Publishing Company，1983：8. [7] COLLINS I F. Associated and non-associated aspects of the constitutive laws for coupled elastic/plastic materials[J]. The International Journal of Geomechanics，2002，2(2)：259–267. [8] COLLINS I F，MUHUNTHAN B. On the relationship between stress-dilatancy，and plastic dissipation for granular materials[J]. Geotechnique，2003，53(7)：611–618. [9] COLLINS I F. The concept of stored plastic work for frozen elastic energy in rock mechanics[J]. Geotechnique，2005，55(5)：373–382. [10] ZIEGLER H，WEHRLI C. The derivation of constitutive relations from the free energy and the dissipation function[J]. Advances in Applied Mechanics，1987，25：183–238. [11] HOULSBY G T，PUZRIN A M. Rate-dependent plasticity models derived from potential functions[J]. Journal of Rheology，2001，46(6)：113–126. [12] PUZRIN A M，HOULSBY G T. Rat-dependent hyperplasticity with internal functions[J]. Journal of Engineering Mechanics，2003，129(3)：252–263. [13] PUZRIN A M，HOULSBY G T. Fundamentals of kinematic hardening hyper plasticity[J]. International Journal of Solids and Structures，2001，38(21)：3 771–3 794. [14] PUZRIN A M，HOULSBY G T. On the non-intersection dilemma in multi-surface plasticity[J]. Geotechnique，2001，51(4)：369–372. [15] ZIENKIEWICZ O C，CHAN A H C，PASTOR M，et al. Computational geomechanics with special reference to earthquake engineering[M]. [S. l.]：John Wiley and Sons Ltd.，1999：86–90. [16] ZIENKIEWICZ O C，TAYLOR R L. The finite element method- Volume 1 Basic formulation and linear problem[M]. 4th ed. London：McGraw- Hill Book Company，1989：65–75. [17] ZIENKIEWICZ O C，TAYLOR R L. The finite element method-Volume 2 Solid and fluid mechanics，Dynamic and non- linearity[M]. 4th ed. London：McGraw-Hill Book Company，1991：31–43. [18] HOULSBY G T，PUZRIN A M. A thermomechanical framework for constitutive models for rate-independent dissipative materials[J]. International Journal of Plasticity，2000，16(9)：1 017–1 047. [19] PUZRIN A M，HOULSBY G T. A thermomechanical framework for rate-independent dissipative materials with internal functions[J]. International Journal of Plasticity，2001，17(8)：1 147–1 165. [20] COLLINS I F，HILDER T. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests[J]. International Journal for Numerical Analytical Methods in Geomechanics，2002，26(11)：1 313–1 347. [21] GUO X，ZHAO C G，YUAN D J，et al. A thermomechanical damage approach to constitutive models for rate-independent dissipative Geomaterials[J]. Acta Mechanica Solida Sinica，2008，21(1)：73–84. [22] GUO X，ZHAO C G，YUAN D J，et al. A dual-surface damage model and evaluation for natural rocks within the thermomechanical framework[J]. Acta Mechanica Solida Sinica，2008，21(1)：85–94. [23] HOULSBY G T，AMOROSI A，ROJAS E. Elastic moduli of rocks dependent on pressure：a hyperelastic formulation[J]. Geotechnique，2005，(5)：383–392. [24] LEMAITRE J L，CHABOCHE J L. Mechanics of solid materials[M]. Cambridge：Cambridge University Press，1990：66–79. [25] BEEN K，JEFFERIES M G，HACHEY J. The critical state of sands[J]. Geotechnique，1991，41(3)：365–381. [26] LUBLINER J. On the thermodynamic foundation of non-linear solid mechanics[J]. International Journal Non-Linear Mechanics，1972，7(3)：237–254. [27] MAUGIN G A. The thermomechanics of plasticity and fracture[M]. Cambridge：Cambridge University Press，1992：16–25. [28] MAUGIN G A. The thermomechanics of nonlinear irreversible behaviors[M]. Singapore：World Scientific Press，1999：75–82.