n次齐次屈服函数相关联流动法则失效的机理研究
|
摘要
岩土材料一些常用的与摩擦有关的经典屈服准则,如Mohr-Coulomb屈服准则、俞茂宏广义双剪应力屈服准则、Lade-Duncan屈服准则、Matsuoka-Nakai屈服准则和沈珠江三剪应力屈服准则等,都属于n阶欧拉齐次函数。把上述屈服准则从真实空间推广到耗散空间后发现,当耗散空间中的n阶齐次屈服函数与真实应力无关时,根据耗散空间的Drucker塑性公设获得的耗散功与应力状态无关;对于砂性材料其值甚至为零,与塑性发生时熵增大于零的热力学第二定律相违背。为了克服上述缺陷,必须在耗散空间的n阶齐次屈服函数中引入与真实应力有关的函数项,然而,由此获得的真实空间屈服准则与塑性应变增量之间必须服从非相关联流动法则。由于服从相关联流动法则时耗散空间屈服准则表达式与真实空间的完全相同,故在真实空间中服从n阶齐次屈服准则的岩土摩擦材料也不适宜采用相关联流动法则。
Some commonly-used classical yield criteria related to friction effect in geomaterials belong to nth Euler homogeneous function.Such criteria refer to Mohr-Coulomb yield criterion,generalized Yu Maohong twin shear stress yield criterion,Lade-Duncan yield criterion,Matsuoka-Nakai yield criterion and Shen Zhujiang three-shear stress yield criterion.After this type of yield criteria is extended from true space to dissipative space,it is found that if nth homogeneous yield criterion in dissipative space is independent of true stress,the dissipative work based on the Drucker's plastic postulate in dissipative space will be independent of stress state,and even equal to zero for sand materials,the latter of which does not conform to the second law of thermodynamics which demonstrates that entropy production must be larger than zero during the appearance of plastic behavior.To avoid this unconformity,a partial function related to the true stress must be added into the nth homogeneous yield function in dissipative space.Therefore,the relation between the new obtained yield criterion in true space and the increment of plastic strain must conform to the non-associated flow rule.Because the expression of the yield criteria in dissipative space is the same as that in true space on the condition of the associated flow rule,the associated flow rule is invalid for geomaterials with friction effect and nth homogeneous yield criteria in true space.
Some commonly-used classical yield criteria related to friction effect in geomaterials belong to nth Euler homogeneous function.Such criteria refer to Mohr-Coulomb yield criterion,generalized Yu Maohong twin shear stress yield criterion,Lade-Duncan yield criterion,Matsuoka-Nakai yield criterion and Shen Zhujiang three-shear stress yield criterion.After this type of yield criteria is extended from true space to dissipative space,it is found that if nth homogeneous yield criterion in dissipative space is independent of true stress,the dissipative work based on the Drucker's plastic postulate in dissipative space will be independent of stress state,and even equal to zero for sand materials,the latter of which does not conform to the second law of thermodynamics which demonstrates that entropy production must be larger than zero during the appearance of plastic behavior.To avoid this unconformity,a partial function related to the true stress must be added into the nth homogeneous yield function in dissipative space.Therefore,the relation between the new obtained yield criterion in true space and the increment of plastic strain must conform to the non-associated flow rule.Because the expression of the yield criteria in dissipative space is the same as that in true space on the condition of the associated flow rule,the associated flow rule is invalid for geomaterials with friction effect and nth homogeneous yield criteria in true space.
引文
[1]DRUCKER D C.The continuum theory of plasticity on themacroscale and microscale[J].Materials,1966,1:873–910.
[2]陈惠发.极限分析与土体塑性[M].詹世斌,译.北京:高等教育出版社,1995.(CHEN W F.Limit analysis and soilplasticity[M].ZHAN Shi-bin,trans.Beijing:ElsevierScientific Publishing Company,1975.(in Chinese))
[3]沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2):11–19.(SHEN Zhu-jiang.Rationalform of elasto-plastic stress-strain relation for soil[J].ChineseJournal of Geotechnical Engineering,1980,2(2):11–19.(inChinese))
[4]赵彭年.松散介质力学[M].北京:地震出版社,1995:32–35.(ZHAO Peng-nian.Mechanics of media[M].Beijing:China Seismic Press,1995:32–35.(in Chinese))
[5]郑颖人,沈珠江,龚晓南.岩土塑性力学原理[M].北京:中国建筑工业出版社,2002.(ZHENG Ying-ren,SHENZhu-jiang,GONG Xiao-nan.Principle of geotechnical plasticmechanics[M].Beijing:China Architecture and BuildingPress,2002.(in Chinese))
[6]杨光华.岩土材料不符合Drucker公设的一个证明[J].岩土工程学报,2010,32(1):144–146.(YANG Guang-hua.Aproof geotechanical materials not in agreement withDrucker’s postulate[J].Chinese Journal of GeotechnicalEngineering,2010,32(1):144–146.(in Chinese))
[7]龚晓南.土塑性力学[M].杭州:浙江大学出版社,1999:91–148.(GONG Xiao-nan.Soil plasticity[M].Hangzhou:Zhejiang University Press,1999:91–148.(in Chinese))
[8]ZIEGLER H.An introduction to thermomechanics[M].2nd ed.North-Holland:Amsterdam,1983.
[9]COLLINS I F,HOULSBY G T.Application ofthermomechanical principles to the modeling of geotechnicalmaterials[J].Proceedings of the Royal Society of London A,1997,45(3):1975–2001.
[10]COLLINS I F.Associated and non-associated aspects of theconstitutive laws for coupled elastic/plastic materials[J].TheInternational Journal of Geomechanicals,2002(2):259–267.
[11]HOULSBY G T,PUZRIN A M.A thermomechanicalframework for rate-independent dissipative materials withinternal functions[J].The International Journal of Plasticity,2001,17:1147–1165.
[12]胡亚元.关于率无关塑性力学和广义塑性力学的评述[J].岩土工程学报,2005,27(1):128–131.(HU Ya-yuan,Comment on rate-independent plasticity and generalizedplasticity[J].China Journal of Geotechnical Engineering,2005,27(1):128–131.(in Chinese))
[13]秦理曼.基于能量耗散土的本构模型研究[D].大连:大连理工大学,2006.(QIN Li-man.Soil constitutive modelsbased on energy dissipation[D].Dalian:Dalian University ofTechnology,2006.(in Chinese))
[14]赵成刚,刘艳.连续孔隙介质土力学及其在非饱和土本构关系中的应用[J].岩土工程学报,2009,31(9):1214–1335.(ZHAO Cheng-gang,LIU Yan.Continuum porousmedium soil mechanics and its application in constitutiverelationship of unsaturated soils[J].Chinese Journal ofGeotechnical Engineering,2009,31(9):1214–1335.(inChinese))
[15]孔亮,李学丰,赵占兵.土体热力学本构模型的改进、验证及有限元分析.岩土工程学报,2009,31(10):1595–1601.(KONG Liang,LI Xue-feng,ZHAO Zhan-bing.Improvement,verification and FEM analysis ofthermomechanical model for soil[J].Chinese Journal ofGeotechnical Engineering,2009,31(10):1595–1601.(inChinese))
[16]胡亚元.多重耗散函数率无关塑性力学在黏土模型中的应用[J].岩土力学,2005,26(增刊1):9–12.(HU Ya-yuan.Application of multiple dissipation potentials functionsrate-independent plasticity model with applications to clay[J].Soil and rock mechanics,2005,26(S1):9–12.(in Chinese))
[2]陈惠发.极限分析与土体塑性[M].詹世斌,译.北京:高等教育出版社,1995.(CHEN W F.Limit analysis and soilplasticity[M].ZHAN Shi-bin,trans.Beijing:ElsevierScientific Publishing Company,1975.(in Chinese))
[3]沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2):11–19.(SHEN Zhu-jiang.Rationalform of elasto-plastic stress-strain relation for soil[J].ChineseJournal of Geotechnical Engineering,1980,2(2):11–19.(inChinese))
[4]赵彭年.松散介质力学[M].北京:地震出版社,1995:32–35.(ZHAO Peng-nian.Mechanics of media[M].Beijing:China Seismic Press,1995:32–35.(in Chinese))
[5]郑颖人,沈珠江,龚晓南.岩土塑性力学原理[M].北京:中国建筑工业出版社,2002.(ZHENG Ying-ren,SHENZhu-jiang,GONG Xiao-nan.Principle of geotechnical plasticmechanics[M].Beijing:China Architecture and BuildingPress,2002.(in Chinese))
[6]杨光华.岩土材料不符合Drucker公设的一个证明[J].岩土工程学报,2010,32(1):144–146.(YANG Guang-hua.Aproof geotechanical materials not in agreement withDrucker’s postulate[J].Chinese Journal of GeotechnicalEngineering,2010,32(1):144–146.(in Chinese))
[7]龚晓南.土塑性力学[M].杭州:浙江大学出版社,1999:91–148.(GONG Xiao-nan.Soil plasticity[M].Hangzhou:Zhejiang University Press,1999:91–148.(in Chinese))
[8]ZIEGLER H.An introduction to thermomechanics[M].2nd ed.North-Holland:Amsterdam,1983.
[9]COLLINS I F,HOULSBY G T.Application ofthermomechanical principles to the modeling of geotechnicalmaterials[J].Proceedings of the Royal Society of London A,1997,45(3):1975–2001.
[10]COLLINS I F.Associated and non-associated aspects of theconstitutive laws for coupled elastic/plastic materials[J].TheInternational Journal of Geomechanicals,2002(2):259–267.
[11]HOULSBY G T,PUZRIN A M.A thermomechanicalframework for rate-independent dissipative materials withinternal functions[J].The International Journal of Plasticity,2001,17:1147–1165.
[12]胡亚元.关于率无关塑性力学和广义塑性力学的评述[J].岩土工程学报,2005,27(1):128–131.(HU Ya-yuan,Comment on rate-independent plasticity and generalizedplasticity[J].China Journal of Geotechnical Engineering,2005,27(1):128–131.(in Chinese))
[13]秦理曼.基于能量耗散土的本构模型研究[D].大连:大连理工大学,2006.(QIN Li-man.Soil constitutive modelsbased on energy dissipation[D].Dalian:Dalian University ofTechnology,2006.(in Chinese))
[14]赵成刚,刘艳.连续孔隙介质土力学及其在非饱和土本构关系中的应用[J].岩土工程学报,2009,31(9):1214–1335.(ZHAO Cheng-gang,LIU Yan.Continuum porousmedium soil mechanics and its application in constitutiverelationship of unsaturated soils[J].Chinese Journal ofGeotechnical Engineering,2009,31(9):1214–1335.(inChinese))
[15]孔亮,李学丰,赵占兵.土体热力学本构模型的改进、验证及有限元分析.岩土工程学报,2009,31(10):1595–1601.(KONG Liang,LI Xue-feng,ZHAO Zhan-bing.Improvement,verification and FEM analysis ofthermomechanical model for soil[J].Chinese Journal ofGeotechnical Engineering,2009,31(10):1595–1601.(inChinese))
[16]胡亚元.多重耗散函数率无关塑性力学在黏土模型中的应用[J].岩土力学,2005,26(增刊1):9–12.(HU Ya-yuan.Application of multiple dissipation potentials functionsrate-independent plasticity model with applications to clay[J].Soil and rock mechanics,2005,26(S1):9–12.(in Chinese))
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心