On the theoretical basis of rational continuum mechanics in softmatter

Chen En-Hui; Yang Jin-Hong; Li Dong; Zhao Ya-Pu

doi:10.7498/aps.65.188103

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:

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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Cited By

[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]	Schmid-Schnbein G W, Sung K L, Tzeren H, Skalak R, Chien S 1981 Biophys. J. 36 243
[67]	Sato M, Theret D P, Wheeler L T, Ohshima N, Nerem R M 1990 J. Biomech. Eng. 112 263
[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]	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
[89]	Mow V C, Holmes M H, Lai W M 1984 J. Biomech. 17 377
[90]	Mow V C, Lai W M 1979 Annu. Rev. Fluid. Mech. 11 247
[91]	Sakai N, Hagihara Y, Furusawa T, Hosoda N, Sawae Y, Murakami T 2012 Tribol. Int. 46 225
[92]	Veronda D R, Westmann R A 1970 J. Biomech. 3 111
[93]	Joanny J F, de Gennes P G 1984 J. Chem. Phys. 81 552
[94]	Nadkarni G D, Garoff S 1992 Europhys. Lett. 20 523
[95]	Wang P F, Zhao X H, Lin M, Lu T J, Xu F 2014 Adv. Mech. 44 201411 (in Chinese) [王鹏飞, 赵兴红, 林敏, 卢天健, 徐峰 2014 力学进展 44 201411]
[96]	Yoon J, Cai S, Suo Z, Hayward R C 2010 Soft Matter 6 6004
[97]	Cai S, Hu Y, Zhao X, Suo Z 2010 J. Appl. Phys. 108 113514
[98]	Hu Y, Suo Z 2012 Acta Mech. Solida. Sin. 25 441
[99]	Hu Y, Zhao X, Vlassak J J, Suo Z 2010 Appl. Phys. Lett. 96 121904
[100]	Ji B, Gao H 2004 J. Mech. Phys. Solids. 52 1963
[101]	https://en. wikipedia. org/wiki/3D_printing
[102]	Tallinen T, Chung J Y, Rousseau F, Girard N, Lefevre J, Mahadevan L 2016 Nature Phys. 12 588
[103]	Eckel Z C, Zhou C, Martin J H, Jacobsen A J, Carter W B, Schaedler T A 2016 Science 351 58
[104]	Gibson L J, Ashby M F 1997 Cellular Solids: Structure and Properties (Cambridge: Cambridge University Press)
[105]	Giorgio I, Grygoruk R, dell'Isola F, Steigmann D J 2015 Mech. Res. Commun. 69 164
[106]	Qi G, Conner K D, Qi H J, Martin L D 2014 Smart Mater. Struct. 23 094007
[107]	Gladman A S, Matsumoto E A, Nuzzo R G, Mahadevan L, Lewis J A 2016 Nat. Mater. 15 413
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Vol. 65, Issue 18 - 2016-09-20

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