基于Hill原理的非相关联流动法则的机理研究
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摘要
为了克服经典塑性力学中与摩擦相关的n阶齐次屈服函数的耗散功与应力状态无关,以及砂性材料的耗散功为零,后者与塑性发生时耗散功必须大于零的热力学第二定律相违背的缺陷,将真实空间的Hill最大耗散功原理推广到耗散空间的Hill最大耗散功原理.根据摩擦引起的能量耗散与真实空间正应力(或球应力)相关的机制,在耗散空间的屈服准则中引入与真实空间正应力(或球应力)相关的函数项,从而使塑性发生时材料的耗散功大于零.由于耗散空间中的屈服准则与真实应力相关,真实空间的屈服准则与塑性应变之间必须服从非相关联流动法则.
nth homogeneous yield criteria related to friction effect is independent of true stress in classical plasticity and even equal to zero for sand materials.The latter does not conform to the second law of thermodynamics,which demonstrates that the dissipative work must be bigger than zero during the appearance of plastic behavior.Hill's principle of maximum dissipative work was generalized from true stress space to dissipative stress space.According to the mechanism that the energy dissipation resulted from friction is related to normal stress(or spherical stress) of true stress,a partial function related to true stress was added into the yield function of dissipative space in order that the dissipative work is bigger than zero during the appearance of plastic behavior.Because the yield criterion of dissipative space was relative to the true stress,the relation between the yield criteria of true space and plastic strain conformed to non-associated flow rule.
nth homogeneous yield criteria related to friction effect is independent of true stress in classical plasticity and even equal to zero for sand materials.The latter does not conform to the second law of thermodynamics,which demonstrates that the dissipative work must be bigger than zero during the appearance of plastic behavior.Hill's principle of maximum dissipative work was generalized from true stress space to dissipative stress space.According to the mechanism that the energy dissipation resulted from friction is related to normal stress(or spherical stress) of true stress,a partial function related to true stress was added into the yield function of dissipative space in order that the dissipative work is bigger than zero during the appearance of plastic behavior.Because the yield criterion of dissipative space was relative to the true stress,the relation between the yield criteria of true space and plastic strain conformed to non-associated flow rule.
引文
[1]龚晓南.土塑性力学[M].杭州:浙江大学出版社,1999:91-148.
[2]朱剑锋,徐日庆,秦艳华.基于SMP准则改进Lade-Duncan模型[J].浙江大学学报:工学版,2011,45(10):1884-1888.ZHU Jian-feng,XU Ri-qing,QING Yan-hua.ImprovedLade-Duncan model based on SMP criterion[J].Journalof Zhejiang University:Engineering Science,2011,45(10):1884-1888.
[3]朱剑锋,徐日庆,王兴陈.基于扰动状态概念模型的刚性挡土墙土压力理论[J].浙江大学学报:工学版,2011,45(6):1081-1087.ZHU Jian-feng,XU Ri-qing,WANG Xing-chen.Theory ofearth pressure against rigid retaining wall based on disturbedstate concept model[J].Journal of Zhejiang University:Engineering Science,2011,45(6):1081-1087.
[4]李金柱,朱向荣,刘用海.结构性软土弹塑性损伤模型及其应用[J].浙江大学学报:工学版,2010,44(4):806-811.LI Jin-zhu,ZHU Xiang-rong,LIU Yong-hai.Elasto-plastic damage constitutive model and its application tostructural soft soil[J].Journal of Zhejiang University:Engineering Science,2010,44(4):806-811.
[5]胡亚元.从耗散率函数看黏性与塑性间的内在联系[J].浙江大学学报:工学版,2009,43(6):1090-1094.HU Ya-yuan.Inter-relationship between viscosity andplasticity as viewed from dissipative rate function[J].Journal of Zhejiang University:Engineering Science,2009,43(6):1090-1094.
[6]陈敬虞,龚晓南,邓亚虹.基于内变量理论的岩土材料本构关系研究[J].浙江大学学报:理学版,2008,35(3):355-360.CHEN Jing-yu,GONG Xiao-nan,DENG Ya-hong.Researchon the constitutive relation of geomaterials based on the theoryof internal variable[J].Journal of Zhejiang University:ScienceEdition,2008,35(3):355-360.
[7]DRUCKER D C.A more fundamental approach to plasticstress-strain relations[C]∥Proceeding of US National Con-gress of Applied Mechanics.New York:ASME,1951:487-491.
[8]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.
[9]赵彭年.松散介质力学[M].北京:地震出版社,1995:32-35.
[10]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.A proof geotechanical materials not inagreement with Druckers postulate[J].China Journal ofGeotechnical Engineering,2010,32(1):144-146.
[11]ZIEGLER H.An introduction to thermomechanical orthogo-nality[M].2nd ed.North-Holland:Amsterdam,1983.
[12]COLLINS I F,HOULSBY G T.Application of ther-momechanical principles to the modeling of geotechnicalmaterials[J].Proceedings of the Royal Society of Lon-don A,1997,45(3):1975-2001.
[13]COLLINS I F.Associated and non-associated aspectsof the constitutive laws for coupled elastic/plastic ma-terials[J].The International Journal of Geomechani-cals,2002(2):259-267.
[14]HOULSB G T,PUZRIN A M.A thermomechanicalframework for rate-independent dissipative materialswith internal functions[J].The International Journalof Plasticity,2001,17:1147-1165.
[15]胡亚元.多重耗散函数率无关塑性力学在粘土模型中的应用[J].岩土力学,2005,26(suppl.1):9-12.HU Ya-yuan.Application of multiple dissipation po-tentials functions rate-independent plasticity modelwith applications to clay[J].Soil and Rock Mechanics,2005,26(suppl.1):9-12.
[16]胡亚元.关于岩土热力学本构理论几个基本概念的认识[J].温州大学学报,2010,31(增1):343-349.HU Ya-yuan.An introduction to some basic concept ofgeotechnical thermo-dynamic constitutive theory[J].Jour-nal of Wenzhou University,2010,31(suppl.1):343-349.
[2]朱剑锋,徐日庆,秦艳华.基于SMP准则改进Lade-Duncan模型[J].浙江大学学报:工学版,2011,45(10):1884-1888.ZHU Jian-feng,XU Ri-qing,QING Yan-hua.ImprovedLade-Duncan model based on SMP criterion[J].Journalof Zhejiang University:Engineering Science,2011,45(10):1884-1888.
[3]朱剑锋,徐日庆,王兴陈.基于扰动状态概念模型的刚性挡土墙土压力理论[J].浙江大学学报:工学版,2011,45(6):1081-1087.ZHU Jian-feng,XU Ri-qing,WANG Xing-chen.Theory ofearth pressure against rigid retaining wall based on disturbedstate concept model[J].Journal of Zhejiang University:Engineering Science,2011,45(6):1081-1087.
[4]李金柱,朱向荣,刘用海.结构性软土弹塑性损伤模型及其应用[J].浙江大学学报:工学版,2010,44(4):806-811.LI Jin-zhu,ZHU Xiang-rong,LIU Yong-hai.Elasto-plastic damage constitutive model and its application tostructural soft soil[J].Journal of Zhejiang University:Engineering Science,2010,44(4):806-811.
[5]胡亚元.从耗散率函数看黏性与塑性间的内在联系[J].浙江大学学报:工学版,2009,43(6):1090-1094.HU Ya-yuan.Inter-relationship between viscosity andplasticity as viewed from dissipative rate function[J].Journal of Zhejiang University:Engineering Science,2009,43(6):1090-1094.
[6]陈敬虞,龚晓南,邓亚虹.基于内变量理论的岩土材料本构关系研究[J].浙江大学学报:理学版,2008,35(3):355-360.CHEN Jing-yu,GONG Xiao-nan,DENG Ya-hong.Researchon the constitutive relation of geomaterials based on the theoryof internal variable[J].Journal of Zhejiang University:ScienceEdition,2008,35(3):355-360.
[7]DRUCKER D C.A more fundamental approach to plasticstress-strain relations[C]∥Proceeding of US National Con-gress of Applied Mechanics.New York:ASME,1951:487-491.
[8]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.
[9]赵彭年.松散介质力学[M].北京:地震出版社,1995:32-35.
[10]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.A proof geotechanical materials not inagreement with Druckers postulate[J].China Journal ofGeotechnical Engineering,2010,32(1):144-146.
[11]ZIEGLER H.An introduction to thermomechanical orthogo-nality[M].2nd ed.North-Holland:Amsterdam,1983.
[12]COLLINS I F,HOULSBY G T.Application of ther-momechanical principles to the modeling of geotechnicalmaterials[J].Proceedings of the Royal Society of Lon-don A,1997,45(3):1975-2001.
[13]COLLINS I F.Associated and non-associated aspectsof the constitutive laws for coupled elastic/plastic ma-terials[J].The International Journal of Geomechani-cals,2002(2):259-267.
[14]HOULSB G T,PUZRIN A M.A thermomechanicalframework for rate-independent dissipative materialswith internal functions[J].The International Journalof Plasticity,2001,17:1147-1165.
[15]胡亚元.多重耗散函数率无关塑性力学在粘土模型中的应用[J].岩土力学,2005,26(suppl.1):9-12.HU Ya-yuan.Application of multiple dissipation po-tentials functions rate-independent plasticity modelwith applications to clay[J].Soil and Rock Mechanics,2005,26(suppl.1):9-12.
[16]胡亚元.关于岩土热力学本构理论几个基本概念的认识[J].温州大学学报,2010,31(增1):343-349.HU Ya-yuan.An introduction to some basic concept ofgeotechnical thermo-dynamic constitutive theory[J].Jour-nal of Wenzhou University,2010,31(suppl.1):343-349.
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