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

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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。

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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(04): 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(04): 658-669.

链接本文:

http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2015.1063 或 http://www.rockmech.org/CN/Y2016/V35/I04/658

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