混凝土动力损伤本构关系的基础理论及应用
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摘要
概括了建立混凝土动力损伤本构模型的基础理论,简述了应用这些基本理论在建立混凝土动损伤本构方面的应用,对相关研究的特点和不足做了分析,为进一步建立科学合理实用的混凝土动损伤本构提供较全面的理论总结和前瞻性启发,对相关理论的发展趋势做了展望,为这方面的工作提供指导.
Key theories and approaches on establishing dynamic damage constitutive model for concrete are outlined,which include continuum mechanics,damage mechanics,classic plasticity mechanics,continuum thermodynamics containing internal variable theory,micro-mesomechanics and endochronic theory.Constructing scientific and reasonable dynamic damage model for concrete requires knowing those theories well.Brief description has been made on applications and their characteristics as well as shortcomings.The trends for these studies are previewed.
Key theories and approaches on establishing dynamic damage constitutive model for concrete are outlined,which include continuum mechanics,damage mechanics,classic plasticity mechanics,continuum thermodynamics containing internal variable theory,micro-mesomechanics and endochronic theory.Constructing scientific and reasonable dynamic damage model for concrete requires knowing those theories well.Brief description has been made on applications and their characteristics as well as shortcomings.The trends for these studies are previewed.
引文
[1]林皋,陈健云.混凝土大坝的抗震安全评价[J].水利学报,2001(2):8-15.
[2]LIN Gao.Ase ism ic design of arch dam s[A].Proc.E-leventh W orld Conference on Earthquake Engineering[C].Acapu lco:E lsevier,1996:2020.
[3]ERHARD K,FAZEEL K.Rate(tim e)dependent de-form ation behavior:an overview of som e properties ofm etals and solids polym ers[J].Int J P lastic ity,2003,19(7):1 069-1 095.
[4]COM I C,PEREGO U.Variationally consistent general-ized variab le formu lation of the elastop lastic rate prob lem[J].M atAcc 1991,2(9):177-190.
[5]林皋,陈健云,肖诗云.混凝土的动力特性与拱坝的非线性地震响应[J].水利学报,2003(6):6-12.
[6]CHEN W F.Concrete p lastic ity:past,present and fu-ture[A].YU M H,FAN S C.Strength Theory:App li-cation,Developm ent&Prospects for 21stcentury[C].Be ijing:Sc ience Press,1998.7-47.
[7]CERNOCKY E P,Evalution of a un iaxial non linear sec-ond-order d ifferential overstress model for rate depend-ence,creep and relaxation[J].Int J Solids Structures,1983,19(9):753-766.
[8]PERZYNA P,PECHERSK I R B.Mod ified theory of vis-cop lastic ity physical foundations and identification ofm a-terial function for advanced strains[J].Arch M ech,1983,35(3):423-436.
[9]PERZYNA P.Advances in App lied M echan ics[M].New York:Academ ic Press,1966.
[10]MARTIN J B,KAUNDA M.Internal variab le formu la-tions of elastic-p lastic dynam ic prob lem s[J].Int J Im-pact Engng,1996,18(7-8):849-858.
[11]PARK SW,X IA Q,ZHOU M.Dynam ic behavior of con-crete at high strain rates and pressures II.numerical simu-lation[J].Int J Impact Engng,2001,25(9):887-910.
[12]FREDER IC R,FABR ICE G.Inelastic behavior model-ling of concrete in low and h igh strain rate dynam ics[J].Computures Structures,2003,81(12):1 287-1 299.
[13]李庆斌,张楚汉,王光纶.单轴状态下混凝土的动力损伤本构模型[J].水利学报,1994(12):55-60.
[14]李庆斌.混凝土静动、双剪损伤本构理论[J].水利学报,1995(27):27-34.
[15]李庆斌,邓宗才,张立翔.考虑初始弹模变化的砼动力损伤本构模型[J].清华大学学报,2003,43(8):1 088-1 091.
[16]LU Pe iyin,LI Q ingb in,SONG Yupu.Dam age constitu-tive of concrete under un iaxial alternate tension-com-pression fatigue load ing based on doub le bound ing sur-faces[J].Int.J.Solids Structures,2004,41(11-12):3 151-3 166.
[17]LI Q B,ZHANG C H,WANG G L.Dynam ic dam ageconstitutive model of concrete in un iaxial tension[J].Engrg FractM ech,1996,53(3):449-455.
[18]刘军.混凝土损伤分析及其工程应用[D].大连:大连理工大学,2004.
[19]匡震邦.非线性连续介质力学[M].上海:上海交通大学出版社,2002.
[20]BELYSCHKO T.连续体和结构的非线性有限元[M].庄茁,译.北京:清华大学出版社,2002.
[21]黄克智,黄永刚.固体本构关系[M].北京:清华大学出版社,1999.
[22]BRUNIG M.Num erical analysis and elastic-p lasticdeform ation behavior of an isotrop ically dam aged solids[J].Int J P lastic ity,2002,18(9):1 237-1 270.
[23]BRUNIG M.An an isotrop ic ductile dam age modelbased on irreversib le thermodynam ics[J].Int.J P las-tic ity,2003,19(10):1 679-1 713.
[24]LEMAITRE J,CHABOCHE J L.固体材料力学[M].余天庆,吴玉树,译.北京:国防工业出版社,1997.
[25]VLADYSLAV P G.Non-linear one-d im ensional con-tinuum dam age theory[J].Int J Engng Sc i,1996,38(10):1 139-1 150.
[26]FAR IA R,OLIVER J,CERVERA M.A strain-basedp lastic viscous-dam age model for m assive concretestructures[J].Int J Solids Structures,1998,35(14):1 534-1 588.
[27]李兆霞.损伤力学及其应用[M].北京:科学出版社,2002.
[28]LEE J,FENVES G L.A p lastic-dam age concretemodel for earthquake analysis of dam s[J].Earthqu En-gng Struct Dyna,1998,27:937-956.
[29]CERVERA M,OLIVER J,MANZOLI O.A rate-de-pendent isotrop ic dam age model for the se ism ic analysisof concrete dam s[J].Earthqu Engng.Struct Dyna,1996,25,987-1 010.
[30]BAZANT Z P.M icrop lane ModelM4 for concrete.Part(I,II)[J].J EngngM ech,2000,126(9):944-961.
[31]W ILFR IED B K,RAINER P.E lasto-p lastic dam agetheories and elasto-p lastic fracturing theories-a com-parison[J].ComputM at Sc i,1998,13:117-131.
[32]ZHU Y Y,CESCOTTO S.A fu lly coup led elastovisco-p lastic dam age theory for an isotrop ic m aterials[J].Int JSolids Structures,1995,32(11):1 607-1 641.
[33]钟万勰,张洪武,吴承伟.参变量变分原理[M].北京:科学出版社,1997.
[34]曲圣年,殷有泉.塑性力学的D rucker公设和Iilusin公设[J].力学学报,1981,13(5):465-472.
[35]张承柱,刘信声.应变空间表述的混凝土弹塑性耦合本构模型[J].清华大学学报,1996,36(3):59-64.
[36]肖诗云,林皋,王哲.Drucker-Prager材料一致率型本构模型[J].工程力学,2003,20(4):147-151.
[37]陈健云,李静,林皋.基于速率相关混凝土损伤模型的高拱坝地震响应分析[J].土木工程学报,2003,36(10):46-50.
[38]杨桂通,熊祝华.塑性动力学[M].北京:清华大学出版社,1984.
[39]卓家寿.非线性固体力学基础[M].北京:中国水利水电出版社,1996.
[40]PUZR IN A M,HOULSBY G T.A thermom echan icalfram ework for rate-independent d issipative m aterialsw ith internal functions[J].Int J P lastic ity,2001,17(8):1 147-1 165.
[41]HOULSBY G T,PUZR IN A M.A thermom echan icalfram ework for constitutive models for rate-independentd issipative m aterials[J].Int J P lastic ity,2000,16(9):1 017-1 047.
[42]MURAKAM I S,KAM IYA K.Constitutive and dam ageevolution equations of elastic-brittle m aterials based onirreversib le thermodynam ics[J].Int M ech Sc i,1997,39(4):473-486.
[43]SIMO S C,PISTER K C.Rem arks on rate constitutiveequations for fin ite deform ation prob lem s:computationalimp lications[J].Comput M eth App l M ech Engng,1984,(46):201-215.
[44]SIMO S C,ORTIZ M.A un ified approach to fin ite de-form ation elastop lastic analysis based on the use of hy-perelastic constitutive equations[J].ComputM eth App lM ech Engng,1985,(49):221-245.
[45]HOULSBY G T,PURZIN A M.Rate-dependent p las-tic ity models derived from potential functions[J].SocRheo,2002,46(1):113-126.
[46]黄克智.损伤与断裂[A].王仁.塑性力学进展[C].北京:中国铁道出版社,1988,31-37.
[47]SHEN X P,MROZ Z,XU B Y.Constitutive theory ofplasticity coupled with orthotropic damage for geomaterials[J].ApplMath Mech,2001,22(9):1 028-1 034.
[48]朱兆祥.塑性理论中的内变量方法[A].王仁.塑性力学进展[C].北京:中国铁道出版社,1988,21-30.
[49]RACH ID R,JEAN-FRANCO IS G,CHR ISTIAN C.Athermodynam ic approach w ith internal variab les using la-grange form alism.Part I.general fram ework[J].M echResearch Commun ications,2003,30(2):109-117.
[50]陈建康,黄筑平,白树林.含两类内变量的一种非线性黏弹性本构模型[J].扬州大学学报,1999,2(2):60-63.
[51]PURZIN A M,HOULSBY G T.Rate-dependent hy-perp lastic ity w ith internal functions[J].J EngngM ech,2003,129(3):252-263.
[52]HENRY W,HASLACH J.A non-equ ilibrium thermo-dynam ic geom etric structure for thermoviscop lastic ityw ith m aximum d issipation[J].Int J P lastic ity,2002,18(2):127-153.
[53]黄克智,孙庆平.形状记忆合金伪弹性行为的细观本构描述[A].王仁,塑性力学和细观力学文集[C].北京:北京大学出版社,1993.100-108.
[54]唐春安,朱万成.混凝土细观损伤与数值模拟[M].北京:科学出版社,2002.
[55]VALANIS K C,On the substance of rivlin’s rem arks onthe endochron ic theory[J].Int J Solids Structures,1981,17:249-265.
[56]范镜泓.本构关系的内蕴时间理论及其应用[A].王仁.塑性力学进展[C].北京:中国铁道出版社,1988.
[57]BAZANT Z P,BHAT P.Endochron ic theory of inelas-tic ity and failure of concrete[J].J EngngM ech D ivisionASCE,1976,102(EM4):701-722.
[58]BAZANT Z P,SH IEH C.Endochron ic model for non-linear triaxial behavior of concrete[J].Nuc lear EngrgDesign,1978,47,305-315.
[59]范镜泓.内蕴时间塑性理论及其新进展(上、下)[J].力学进展,1985,15(3):273-290,(4):443-457.
[60]范镜泓.内蕴时间塑性理论及其新进展(上、下)[J].力学进展,1985,15(4):443-457.
[2]LIN Gao.Ase ism ic design of arch dam s[A].Proc.E-leventh W orld Conference on Earthquake Engineering[C].Acapu lco:E lsevier,1996:2020.
[3]ERHARD K,FAZEEL K.Rate(tim e)dependent de-form ation behavior:an overview of som e properties ofm etals and solids polym ers[J].Int J P lastic ity,2003,19(7):1 069-1 095.
[4]COM I C,PEREGO U.Variationally consistent general-ized variab le formu lation of the elastop lastic rate prob lem[J].M atAcc 1991,2(9):177-190.
[5]林皋,陈健云,肖诗云.混凝土的动力特性与拱坝的非线性地震响应[J].水利学报,2003(6):6-12.
[6]CHEN W F.Concrete p lastic ity:past,present and fu-ture[A].YU M H,FAN S C.Strength Theory:App li-cation,Developm ent&Prospects for 21stcentury[C].Be ijing:Sc ience Press,1998.7-47.
[7]CERNOCKY E P,Evalution of a un iaxial non linear sec-ond-order d ifferential overstress model for rate depend-ence,creep and relaxation[J].Int J Solids Structures,1983,19(9):753-766.
[8]PERZYNA P,PECHERSK I R B.Mod ified theory of vis-cop lastic ity physical foundations and identification ofm a-terial function for advanced strains[J].Arch M ech,1983,35(3):423-436.
[9]PERZYNA P.Advances in App lied M echan ics[M].New York:Academ ic Press,1966.
[10]MARTIN J B,KAUNDA M.Internal variab le formu la-tions of elastic-p lastic dynam ic prob lem s[J].Int J Im-pact Engng,1996,18(7-8):849-858.
[11]PARK SW,X IA Q,ZHOU M.Dynam ic behavior of con-crete at high strain rates and pressures II.numerical simu-lation[J].Int J Impact Engng,2001,25(9):887-910.
[12]FREDER IC R,FABR ICE G.Inelastic behavior model-ling of concrete in low and h igh strain rate dynam ics[J].Computures Structures,2003,81(12):1 287-1 299.
[13]李庆斌,张楚汉,王光纶.单轴状态下混凝土的动力损伤本构模型[J].水利学报,1994(12):55-60.
[14]李庆斌.混凝土静动、双剪损伤本构理论[J].水利学报,1995(27):27-34.
[15]李庆斌,邓宗才,张立翔.考虑初始弹模变化的砼动力损伤本构模型[J].清华大学学报,2003,43(8):1 088-1 091.
[16]LU Pe iyin,LI Q ingb in,SONG Yupu.Dam age constitu-tive of concrete under un iaxial alternate tension-com-pression fatigue load ing based on doub le bound ing sur-faces[J].Int.J.Solids Structures,2004,41(11-12):3 151-3 166.
[17]LI Q B,ZHANG C H,WANG G L.Dynam ic dam ageconstitutive model of concrete in un iaxial tension[J].Engrg FractM ech,1996,53(3):449-455.
[18]刘军.混凝土损伤分析及其工程应用[D].大连:大连理工大学,2004.
[19]匡震邦.非线性连续介质力学[M].上海:上海交通大学出版社,2002.
[20]BELYSCHKO T.连续体和结构的非线性有限元[M].庄茁,译.北京:清华大学出版社,2002.
[21]黄克智,黄永刚.固体本构关系[M].北京:清华大学出版社,1999.
[22]BRUNIG M.Num erical analysis and elastic-p lasticdeform ation behavior of an isotrop ically dam aged solids[J].Int J P lastic ity,2002,18(9):1 237-1 270.
[23]BRUNIG M.An an isotrop ic ductile dam age modelbased on irreversib le thermodynam ics[J].Int.J P las-tic ity,2003,19(10):1 679-1 713.
[24]LEMAITRE J,CHABOCHE J L.固体材料力学[M].余天庆,吴玉树,译.北京:国防工业出版社,1997.
[25]VLADYSLAV P G.Non-linear one-d im ensional con-tinuum dam age theory[J].Int J Engng Sc i,1996,38(10):1 139-1 150.
[26]FAR IA R,OLIVER J,CERVERA M.A strain-basedp lastic viscous-dam age model for m assive concretestructures[J].Int J Solids Structures,1998,35(14):1 534-1 588.
[27]李兆霞.损伤力学及其应用[M].北京:科学出版社,2002.
[28]LEE J,FENVES G L.A p lastic-dam age concretemodel for earthquake analysis of dam s[J].Earthqu En-gng Struct Dyna,1998,27:937-956.
[29]CERVERA M,OLIVER J,MANZOLI O.A rate-de-pendent isotrop ic dam age model for the se ism ic analysisof concrete dam s[J].Earthqu Engng.Struct Dyna,1996,25,987-1 010.
[30]BAZANT Z P.M icrop lane ModelM4 for concrete.Part(I,II)[J].J EngngM ech,2000,126(9):944-961.
[31]W ILFR IED B K,RAINER P.E lasto-p lastic dam agetheories and elasto-p lastic fracturing theories-a com-parison[J].ComputM at Sc i,1998,13:117-131.
[32]ZHU Y Y,CESCOTTO S.A fu lly coup led elastovisco-p lastic dam age theory for an isotrop ic m aterials[J].Int JSolids Structures,1995,32(11):1 607-1 641.
[33]钟万勰,张洪武,吴承伟.参变量变分原理[M].北京:科学出版社,1997.
[34]曲圣年,殷有泉.塑性力学的D rucker公设和Iilusin公设[J].力学学报,1981,13(5):465-472.
[35]张承柱,刘信声.应变空间表述的混凝土弹塑性耦合本构模型[J].清华大学学报,1996,36(3):59-64.
[36]肖诗云,林皋,王哲.Drucker-Prager材料一致率型本构模型[J].工程力学,2003,20(4):147-151.
[37]陈健云,李静,林皋.基于速率相关混凝土损伤模型的高拱坝地震响应分析[J].土木工程学报,2003,36(10):46-50.
[38]杨桂通,熊祝华.塑性动力学[M].北京:清华大学出版社,1984.
[39]卓家寿.非线性固体力学基础[M].北京:中国水利水电出版社,1996.
[40]PUZR IN A M,HOULSBY G T.A thermom echan icalfram ework for rate-independent d issipative m aterialsw ith internal functions[J].Int J P lastic ity,2001,17(8):1 147-1 165.
[41]HOULSBY G T,PUZR IN A M.A thermom echan icalfram ework for constitutive models for rate-independentd issipative m aterials[J].Int J P lastic ity,2000,16(9):1 017-1 047.
[42]MURAKAM I S,KAM IYA K.Constitutive and dam ageevolution equations of elastic-brittle m aterials based onirreversib le thermodynam ics[J].Int M ech Sc i,1997,39(4):473-486.
[43]SIMO S C,PISTER K C.Rem arks on rate constitutiveequations for fin ite deform ation prob lem s:computationalimp lications[J].Comput M eth App l M ech Engng,1984,(46):201-215.
[44]SIMO S C,ORTIZ M.A un ified approach to fin ite de-form ation elastop lastic analysis based on the use of hy-perelastic constitutive equations[J].ComputM eth App lM ech Engng,1985,(49):221-245.
[45]HOULSBY G T,PURZIN A M.Rate-dependent p las-tic ity models derived from potential functions[J].SocRheo,2002,46(1):113-126.
[46]黄克智.损伤与断裂[A].王仁.塑性力学进展[C].北京:中国铁道出版社,1988,31-37.
[47]SHEN X P,MROZ Z,XU B Y.Constitutive theory ofplasticity coupled with orthotropic damage for geomaterials[J].ApplMath Mech,2001,22(9):1 028-1 034.
[48]朱兆祥.塑性理论中的内变量方法[A].王仁.塑性力学进展[C].北京:中国铁道出版社,1988,21-30.
[49]RACH ID R,JEAN-FRANCO IS G,CHR ISTIAN C.Athermodynam ic approach w ith internal variab les using la-grange form alism.Part I.general fram ework[J].M echResearch Commun ications,2003,30(2):109-117.
[50]陈建康,黄筑平,白树林.含两类内变量的一种非线性黏弹性本构模型[J].扬州大学学报,1999,2(2):60-63.
[51]PURZIN A M,HOULSBY G T.Rate-dependent hy-perp lastic ity w ith internal functions[J].J EngngM ech,2003,129(3):252-263.
[52]HENRY W,HASLACH J.A non-equ ilibrium thermo-dynam ic geom etric structure for thermoviscop lastic ityw ith m aximum d issipation[J].Int J P lastic ity,2002,18(2):127-153.
[53]黄克智,孙庆平.形状记忆合金伪弹性行为的细观本构描述[A].王仁,塑性力学和细观力学文集[C].北京:北京大学出版社,1993.100-108.
[54]唐春安,朱万成.混凝土细观损伤与数值模拟[M].北京:科学出版社,2002.
[55]VALANIS K C,On the substance of rivlin’s rem arks onthe endochron ic theory[J].Int J Solids Structures,1981,17:249-265.
[56]范镜泓.本构关系的内蕴时间理论及其应用[A].王仁.塑性力学进展[C].北京:中国铁道出版社,1988.
[57]BAZANT Z P,BHAT P.Endochron ic theory of inelas-tic ity and failure of concrete[J].J EngngM ech D ivisionASCE,1976,102(EM4):701-722.
[58]BAZANT Z P,SH IEH C.Endochron ic model for non-linear triaxial behavior of concrete[J].Nuc lear EngrgDesign,1978,47,305-315.
[59]范镜泓.内蕴时间塑性理论及其新进展(上、下)[J].力学进展,1985,15(3):273-290,(4):443-457.
[60]范镜泓.内蕴时间塑性理论及其新进展(上、下)[J].力学进展,1985,15(4):443-457.
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