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软物质中的理性连续介质力学基础

陈恩惠 杨锦鸿 李栋 赵亚溥

软物质中的理性连续介质力学基础

陈恩惠, 杨锦鸿, 李栋, 赵亚溥
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  • 本文介绍了理性连续介质力学在软物质研究中的意义与特点,简要回顾了软物质的理性连续介质力学背景与发展,重点介绍了关于软物质主要力学模型的本构关系:熵弹性、超弹性本构关系、黏弹性本构关系、多孔弹性介质本构关系、非牛顿流体本构关系,以及近年来这些模型在生物体系如细胞、肌肉、血管、脑组织,非生物体系如移动接触线、复合软材料,以及 3D/4D 打印等体系中的应用. 在此基础上,结合近几年国内外软物质力学研究进展与应用需求,提出了学科关键科学问题和前沿问题,指出了软物质理性连续介质力学在软物质-硬物质界面相互作用力学,发展活性软材料多场耦合的弹性理论模型,加强与其他相关学科的联系等方面的发展方向.
      通信作者: 赵亚溥, yzhao@imech.ac.cn
    • 基金项目: 国家自然科学基金(批准号: U1562105, 11372313)、中科院创新交叉团队项目、前沿科学研究重点计划(批准号: QYZDJ-SSWJSC019)和中国科学院战略性先导科技专项(B 类) (批准号: XDB22040401) 资助的课题.
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  • [1]

    Zhao Y P 2012 Physical Mechanics of Surfaces and Interfaces (Beijing: Science Press) (in Chinese) [赵亚溥 2012 表面与界面物理力学 (北京: 科学出版社)]

    [2]

    Ouyang Z C 2007 Innovative Sci. Tech. 5 44 (in Chinese) [欧阳钟灿 2007 创新科技 5 44]

    [3]

    Lu K Q, Liu J X 2006 Introduction to Soft Matter Physics (Beijing: Peking University Press) (in Chinese) [陆坤权, 刘寄星 2006 软物质物理学导论 (北京: 北京大学出版社)]

    [4]

    Chen D T N, Wen Q, Janmey P A, et al. 2010 Annu. Rev. Condens. Matter Phys. 1 301

    [5]

    Lu K Q, Liu J X 2009 Physics 38 453 (in Chinese) [陆坤权, 刘寄星 2009 物理 38 453]

    [6]

    Zhang G M, Yu L 2010 Physics 39 543 (in Chinese) [张广铭, 于渌 2010 物理 39 543]

    [7]

    Zhao Y P 2014 Nano and Mesoscopic Mechanics (Beijing: Science Press) (in Chinese) [赵亚溥 2014 纳米与介观力学 (北京: 科学出版社)]

    [8]

    Zhao Y P 2016 Modern Continuum Mechanics (Beijing: Science Press) (in Chinese) [赵亚溥 2016 近代连续介质力学 (北京: 科学出版社)]

    [9]

    Truesdell C 1959 Appl. Phys. Lett. 12 75

    [10]

    Eringen A C 1980 Mechanics of Continua (New York: Robert E Krieger)

    [11]

    Truesdell C, Noll W 1965 The Non-linear Field Theories of Mechanics (Berlin: Springer)

    [12]

    Eringen A C 2002 Nonlocal Continuum Field Theories (New York: Springer)

    [13]

    Eringen A C 1974-1976 Continuum Physics (Vol. IV) (New York: Academic Press)

    [14]

    Yang W 2013 Celebration of Winning the State Supreme Science and Technology Award of Cheng Chemin and Seminar of the Development of Mechanics 1 16 (in Chinese) [杨卫 2013 庆祝郑哲敏先生荣获国家最高科学技术奖暨力学学科发展研讨会 1 16]

    [15]

    Li S, Sun B 2012 Advances in Soft Matter Mechanics (Beijing: Higher Education Press)

    [16]

    Capaldi F M 2012 Continuum Mechanics: Constitutive Modeling of Structural and Biological Materials (Cambridge: Cambridge University Press)

    [17]

    Austin R H, Brody J P, Cox E C, Duke T, Volkmuth W 1997 Phys. Today 50 32

    [18]

    Ouyang Z C, Liu J X 1994 From Soup Bubbles to Liquid Crystalline Biomembrane (Changsha: Hunan Education Publishing House) (in Chinese) [欧阳钟灿, 刘寄星 1994 从肥皂泡到液晶生物膜 (长沙: 湖南教育出版社)]

    [19]

    Xie Y Z, Liu J X, Ouyang Z C 2003 Elastic Theory of Surfaces of Biomembrane-Vesicle (Shanghai: Shanghai Scientific and Technical Publishers) (in Chinese) [谢毓章, 刘寄星, 欧阳钟灿 2003 生物膜泡曲面弹性理论 (上海: 上海科学技术出版社)]

    [20]

    Ottosen N S, Ristinmaa M 2005 The Mechanics of Constitutive Modeling (Amsterdam: Elsevier)

    [21]

    Finger J 1894 Sitzber. Akad. Wiss. Wien. 103 1073

    [22]

    Ogden R W 1972 Proc. R. Soc. London Ser. A 326 565

    [23]

    Varga O H 1966 Stress-strain Behavior of Elastic Materials; Selected Problems of Large Deformations (New York: Wiley)

    [24]

    Mooney M 1940 J. Appl. Phys. 11 582

    [25]

    Rivlin R S, Saunders D 1951 Philos. Trans. R. Soc. London Ser. A 243 251

    [26]

    Yeoh O 1993 Rubber Chem. Technol. 66 754

    [27]

    Yin H M, Sun L Z, Wang G, Vannier M W 2004 IEEE. Trans. Bio-med. Eng. 51 1854

    [28]

    Arruda E M, Boyce M C 1993 J. Mech. Phys. Solids 41 389

    [29]

    Treloar L R G 1943 Trans. Faraday Soc. 39 241

    [30]

    Gent A 1996 Rubber Chem. Technol. 69 59

    [31]

    Flory P 1961 Trans. Faraday Soc. 57 829

    [32]

    Weber W 1841 Ann. Phys-berlin. 130 1

    [33]

    Kohlrausch F 1847 Ann. Phys-berlin. 148 353

    [34]

    Kohlrausch F 1863 Ann. Phys-berlin. 195 337

    [35]

    Kohlrausch F 1866 Ann. Phys-berlin. 28 1

    [36]

    Maxwell J C 1867 Philos. Trans. R. Soc. London 157 49

    [37]

    Meyer O E 1874 Ann. Phys-berlin. 227 108

    [38]

    Oldroyd J 1950 Proc. R. Soc. London, Ser. A 200 523

    [39]

    Boltzmann L 1874 Mathematisch-Naturwissenscha-ftliche Classe 70 275

    [40]

    Fung Y C 1972 Stress Strain History Relations of Soft Tissues in Simple Elongation (In: Biomechanics: Its Foundations And Objectives) (New Jersey: Prentice-Hall)

    [41]

    Weinbaum S, Cowin S C, Zeng Y 1994 J. Biomech. 27 339

    [42]

    Cowin S C 1999 J. Biomech. 32 217

    [43]

    Cowin S C, Cardoso L 2011 Biomech. Model. Mechan. 10 39

    [44]

    Sandino C, McErlain D D, Schipilow J, Boyd S K 2015 J. Mech. Behav. Biomed. Mater. 44 1

    [45]

    Biot M A 1941 J. Appl. Phys. 12 155

    [46]

    Biot M A 1955 J. Appl. Phys. 26 182

    [47]

    Biot M A 1956 J. Appl. Phys. 27 459

    [48]

    Biot M 1973 Indiana. U. Math. J. 23 309

    [49]

    Detournay E, Cheng A H D 1993 Fundamentals of Poroelasticity (In: Comprehensive Rock Engineering: Principles, Practice and Projects) (New York: Pergamon Press)

    [50]

    Herschel W H, Bulkley R 1926 Kolloid-Zeitschrift 39 291

    [51]

    Herschel W H, Bulkley R 1926 Proc. Am. Soc. Test.Mater. 26 621

    [52]

    de Waele A 1923 J. Oil Color Chem. Assoc. 6 33

    [53]

    Ostwald W 1925 Colloid Polym. Sci. 36 99

    [54]

    Bingham E C 1922 Fluidity and Plasticity (New York: McGraw-Hill)

    [55]

    Blair G W S 1959 Nature 183 613

    [56]

    Reiner M, Blair G S 1959 Nature 184 354

    [57]

    Casson N 1957 Bull. Br. Soc. Rheol. 2 5

    [58]

    Casson N 1959 A Flow Equation for Pigment-oil Suspensions of the Printing Ink Type (In: Rheology of Disperse Systems) (London: Pergamon Press)

    [59]

    Steiner E H 1958 Rev. Int. Chocolat. 13 290

    [60]

    Heinz W 1959 Mater. Prfung 1 311

    [61]

    Chevalley J 1975 J. Texture Stud. 6 177

    [62]

    Li J, Han D, Zhao Y P 2014 Sci. Rep. 4 3910

    [63]

    Lim C T, Zhou E H, Quek S T 2006 J. Biomech. 39 195

    [64]

    Yeung A, Evans E 1989 Biophys. J. 56 139

    [65]

    Dong C, Skalak R, Sung K L P, Schmid-Schonbein G W, Chien S 1988 J. Biomech. Eng. 110 27

    [66]

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    [67]

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    [68]

    Bambardekar K, Clment R, Blanc O, Chards C, Lenne P F 2015 P. Natl. Acad. Sci. USA 112 1416

    [69]

    Zhang K, Siegmund T, Chan R W 2006 J. Acoust. Soc. Am. 119 1050

    [70]

    Chan R W, Siegmund T, Zhang K 2009 Logop. Phoniatr. Voco. 34 181

    [71]

    Smith S L, Hunter E J 2014 J. Acoust. Soc. Am. 135 2041

    [72]

    Grasa J, Ramrez A, Osta R, Muoz M, Soteras F, Calvo B 2011 Biomech. Model. Mechan. 10 779

    [73]

    Martins J A C, Pires E B, Salvado R, Dinis P B 1998 Comput. Method. Appl. M 151 419

    [74]

    Hill A V 1922 J. Physiol. 56 19

    [75]

    Ehret A E, Bl M, Itskov M 2011 J. Mech. Phys. Solids 59 625

    [76]

    Holzapfel G A, Gasser T C, Ogden R W 2000 J. Elasticity 61 1

    [77]

    Kyriacou K S, Mohamed A, Miller K, Neff S 2002 Biomech. Model. Mech. 1 151

    [78]

    Pamidi M R, Advani S H 1978 J. Biomech. Eng. 100 44

    [79]

    Mendis K K, Stalnaker R L, Advani S H 1995 J. Biomech. Eng. 117 279

    [80]

    Miller K, Chinzei K 1997 J. Biomech. 30 1115

    [81]

    Rashid B, Destrade M, Gilchrist M D 2014 J. Mech. Behav. Biomed. Mater. 33 43

    [82]

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  • 收稿日期:  2016-08-09
  • 修回日期:  2016-09-12
  • 刊出日期:  2016-09-05

软物质中的理性连续介质力学基础

  • 1. 中国科学院力学研究所, 非线性国家重点实验室, 北京 100190;
  • 2. 中国科学院大学工程科学学院, 北京 100049
  • 通信作者: 赵亚溥, yzhao@imech.ac.cn
    基金项目: 

    国家自然科学基金(批准号: U1562105, 11372313)、中科院创新交叉团队项目、前沿科学研究重点计划(批准号: QYZDJ-SSWJSC019)和中国科学院战略性先导科技专项(B 类) (批准号: XDB22040401) 资助的课题.

摘要: 本文介绍了理性连续介质力学在软物质研究中的意义与特点,简要回顾了软物质的理性连续介质力学背景与发展,重点介绍了关于软物质主要力学模型的本构关系:熵弹性、超弹性本构关系、黏弹性本构关系、多孔弹性介质本构关系、非牛顿流体本构关系,以及近年来这些模型在生物体系如细胞、肌肉、血管、脑组织,非生物体系如移动接触线、复合软材料,以及 3D/4D 打印等体系中的应用. 在此基础上,结合近几年国内外软物质力学研究进展与应用需求,提出了学科关键科学问题和前沿问题,指出了软物质理性连续介质力学在软物质-硬物质界面相互作用力学,发展活性软材料多场耦合的弹性理论模型,加强与其他相关学科的联系等方面的发展方向.

English Abstract

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