大型土木结构多尺度模拟与损伤分析——从材料多尺度力学到结构多尺度力学
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摘要
从阐述重大土木工程结构安全运营面临的挑战性课题——结构多尺度力学问题开始,对多尺度力学中的材料多尺度模拟和结构多尺度模拟的工程背景、多尺度特征和关键研究内容进行比较性评述;在此基础上,重点介绍了对研究大型土木结构多尺度力学问题可能有参考价值的材料多尺度模拟和分析方法如周期性异质材料问题的平均化与渐进分析方法、单位分解法和多尺度重构核函数法,以及大型土木结构多尺度模拟与分析领域的研究现状,由此引出结构多尺度力学研究中亟待解决的关键问题并加以评述;通过认识与比较结构多尺度与材料多尺度问题的共性与个性,文中综述了在大型土木结构多尺度问题的研究进程中可供参考的理论与方法,提出了这类结构多尺度力学问题研究的几个关键科学问题为:结构多尺度模拟中的连接与跨越问题、多尺度模型的修正和验证、结构损伤的时间多尺度模拟与分析、结构强度和损伤失效过程中多尺度分析的跨尺度敏感性与随机性因素,以及适用于大型土木结构多尺度模拟和计算分析的实施策略与技术.
This paper discusses firstly a new challenge in securing safe and reliable service of large civil struc- tures:multi-scale modeling and damage analyses.Then the applications,the features of spatial multi-scales involved and the related issues for multi-scale mechanics of materials and structures are reviewed.The theo- ries and methods of multi-scale mechanics and multi-scale material modeling are briefly discussed and several methods are paid a special attention,such as asymptotic analysis of periodical heterogeneous materials,parti- tion of unity method and multi-scale reproducing kernel method.The engineering background and the current research progress for multi-scale structural modeling and damage analyses of large civil structure are summa- rized,and several key issues are proposed,among which are bridging in simulation,updating and verification of the multi-scale structural model,damage evolution in multiple temporal scales,trans-scale sensitivity in the simulation of structural deterioration and final failure,and the strategies of multi-scale modeling and simulation in engineering computation of large civil structure.
This paper discusses firstly a new challenge in securing safe and reliable service of large civil struc- tures:multi-scale modeling and damage analyses.Then the applications,the features of spatial multi-scales involved and the related issues for multi-scale mechanics of materials and structures are reviewed.The theo- ries and methods of multi-scale mechanics and multi-scale material modeling are briefly discussed and several methods are paid a special attention,such as asymptotic analysis of periodical heterogeneous materials,parti- tion of unity method and multi-scale reproducing kernel method.The engineering background and the current research progress for multi-scale structural modeling and damage analyses of large civil structure are summa- rized,and several key issues are proposed,among which are bridging in simulation,updating and verification of the multi-scale structural model,damage evolution in multiple temporal scales,trans-scale sensitivity in the simulation of structural deterioration and final failure,and the strategies of multi-scale modeling and simulation in engineering computation of large civil structure.
引文
1工程技术发展研究综合专题组．2020年的中国工程技术发展研究(送审稿)——中国科协“2020年的中国科学和技术发展研究”综合专题之九研究报告，2004年2月
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3白以龙．工程结构损伤的两个重要科学问题——分布式损伤和尺度效应．华南理工大学学报(自然科学版)，2002，30(1)：11～14
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5 Auweraer H V,Peeters B.International research projects on structural health monitoring:an overview.Structural Health Monitoring,2003,2(4):341～358
6 Chong K P.NSF research in mechanics,computational & other areas.In:Sih G C,Tu S T,Wang Z,eds.Multiscale Damage Related to Environment Assisted Cracking.2005. 323～332
7 Lee J,Chcn Y P,Eskandarian A,et al.Multiscale material modeling:theories and applications.In:Sih G C,Tu S T, Wang Z,eds.Multiscale Damage Related to Environment Assisted Cracking.2005.301～310
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13 Cui J Z,Shin T M,Wang Y L.The two-scale analysis method for bodies with small periodic configurations.Struc- tural Engineering and Mechanics,1999.17:601～614
14崔俊芝，曹礼群．基于双尺度渐进分析的有限元算法．计算数学，1998．20：89～102
15 Fish J,Schwob C.Towards constitutive model based on atomistics.International Journal of Multiscale Computa- tional Bngineering,2003,1:43～56
16 Chen W,Fish J.Mathematical homogenization perspective of virial stress.International Journal for Numerical Meth- ods in Engineering,2006,67:189～207
17 Fish J,Chen W.Higher-order homogenization of initial/boundary-value problem.Journal of Engineering Mechanics,2001,127:1223～1230
18 Broughton J Q,Abraham F F,Bernstein N,Kaxiras E.Con- current coupling of length scales:methodology and applica- tion.Physics Review B,1999,60:2391～2403
19 Qian D,Wagner G J,Liu W K,et al.Mechanics of carbon nanotubes.Applied Mechanics Reviews,2002,55:495～532
20 Miller R E,Tadmor E B.The quasi-continuum method: overview,application and current derection.Journal of Computer-Aided Material Design,2002,9:203～239
21 Knap J,Ortiz M.An analysis of the quasi-continuum method.Journal of the Mechanics and Physics of Solids, 2001,49:1899～1923
22 Tadmor E B,Smith G S,Bernstein N,Kaxiras E.Mixed fi- nite element and atomistic formulation for complex crystals. Physics Review B,1999,59:235～245
23 Belytschko T,Xiao S P.Coupling methods for continuum model with molecular model.International Journal of Mul- tiscale Computational Engineering,2003,1:115～126
24 Wagner G J,Liu W K.Coupling of atomic and continuum simulations using a bridge scale decomposition.Journal of Computational Physics,2003,190:249～274
25 Curtin W A,Miller R E.Atomistic/continuum coupling in computational material science.Modeling and Simulation in Materials Science and Engineering,2003,11:R33～R68
26 Chen Y P,Lee J.Connecting molecular dynamics to micro- morphic theory(Ⅰ):Instantaneous and averaged mechanical variables.Physica A,2003,322:359～376
27 Chen Y P,Lee J.Connecting molecular dynamics to micro- morphic theory(Ⅱ):Balance laws.Physica A,2003,322: 377～392
28 Chen Y P,Lee J,Eskandarian A.Atomistic viewpoint of the applicability of microcontinuum theories.International Journal of Solids and Structures,2004,41:2085～2097
29 Chen Y P,Lee J.Multiscale modeling of polycrystalline sil- icon.International Journal of Engineering Science,2004, 42:987～1000
30 Bai Y L,Wang H Y,Xia M F,et al.Statistical mesomechan- ics of solid,linking coupled multiple space and time scales. Applied Mechanics Reviews,2005,58:372～388
31 Bazant Z,Chen E P.Scaling of structural failure.Applied Mechanics Reviews,1997,50(10):593～627
32 Sih G C.Implication of scaling hierarchy associated with nonequilibrium:field and particulate.Theoretical and Ap- plied Fracture Mechanics.2001,37:335～369
33白以龙，汪海英，夏蒙棼等．固体的统计细观力学——连接多个耦合的时空尺度．力学进展，2006，36(2)：286～305
34 Bazant Z，Chen E P．结构破坏的尺度率．力学进展，1999，29：383～433
35薛昌明，唐雪松．与非平衡问题相关的尺度效应：场与微粒．力学进展，2004，34(2)：145～170
36白以龙，汪海英，柯孚久等．从“哥伦比亚”号悲剧看多尺度力学问题．力学与实践，2005，26(3)：1～6
37何国威，夏蒙棼，柯孚久等．多尺度耦合现象：挑战与机遇．自然科学进展，2004，14：121～124
38 Sih G C,Tu S T,Wang Z D,eds.Structural Integrity and Materials Aging:Fracture Mechanics and Applications. Shanghai:East China University of Science and Technology Press,2003
39 Sih G C,Tu S T,Wang Z D,eds.Environment Effects on Fracture and Damage:Fracture Mechanics and Applica- tions.Hangzhou:Zhejiang University Press,2004
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