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

doi:10.7498/aps.65.188103

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.

关键词:

Abstract

Soft matter has become one of the most active fields since the 1990 s, for it has enormous interesting behaviors and a broad range of applications. Rational continuum mechanics, as a subject mainly dealing with the kinematics and deformation of materials modeled as continuous mass, is a main source of inspiration in the development of soft matter physics. Here we review the development of rational continuum mechanics and soft matter briefly, and focus on the basic mechanical models and constitutive relations relating to soft matter: entropy elasticity, hyperelasticity, viscoelasticity, poroelasticity, non-Newtonian fluid, and the constitutive equations of these models. We simultaneously introduce the applications of these equations in hot issues in recent years, such as brain, blood vessel, cartilage, muscle, gel, cell, three dimensional printing, etc. According to applications and advances in soft matter mechanics, we then propose the key scientific problems and research fronts: mechanics of the solid-liquid interfacial interactions, introducing multiple factors into constitutive equations to describe the complex behaviors of soft matter in coupling multi-physics, and enhancing connections between soft matter mechanics and soft matter physics, chemistry, biology, etc. Finally, we conclude that the rational continuum mechanics in soft matter could be further developed in energy development, fabrication and analysis of diverse soft materials, and biomedicine development areas.

Keywords:

作者及机构信息

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.

Authors and contacts

1.
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;

2.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Zhao Ya-Pu, yzhao@imech.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U1562105, 11372313), the CAS Interdisciplinary Innovation Team Project, the CAS Key Research Program of Frontier Sciences (Grant No. QYZDJ-SSWJSC019), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040401).

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施引文献

[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)
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[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)]
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[34]	Kohlrausch F 1863 Ann. Phys-berlin. 195 337
[35]	Kohlrausch F 1866 Ann. Phys-berlin. 28 1
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[37]	Meyer O E 1874 Ann. Phys-berlin. 227 108
[38]	Oldroyd J 1950 Proc. R. Soc. London, Ser. A 200 523
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[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
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[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)
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[61]	Chevalley J 1975 J. Texture Stud. 6 177
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[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]	Zhu Z D, Zhang W, Wu C W 2014 Sci. China: Tech. Sci. 57 1269
[83]	Wang L, Cheung J T M, Pu F, Li D, Zhang M, Fan Y 2011 PLoS One 6 e26490
[84]	Basser P J, Mattiello J, LeBihan D 1994 Biophys. J. 66 259
[85]	Basser P J, Mattiello J, Lebihan D 1994 J. Magn. Reson. Ser. B 103 247
[86]	Jellison B J, Field A S, Medow J, Lazar M, Salamat M S, Alexander A L 2004 Am. J. Neuroradiol. 25 356
[87]	Hunter W 1743 Philos. Trans. R. Soc. London 42 514
[88]	Mow V C, Kuei S C, Lai W M, Armstrong C G 1980 J. Biomech. Eng. 102 73
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