JZUS - Journal of Zhejiang University SCIENCE

Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.4 P.231-240

The renaissance of continuum mechanics*

Author(s): Wei-qiu Chen
Affiliation(s): . Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China
Corresponding email(s): chenwq@zju.edu.cn
Key Words: Continuum mechanics, Quantum mechanics, Engineering, Current research activities, Renaissance

Share this article to： More \|Next Article >>>

Wei-qiu Chen. The renaissance of continuum mechanics[J]. Journal of Zhejiang University Science A, 2014, 15(4): 231-240.

@article{title="The renaissance of continuum mechanics",
author="Wei-qiu Chen",
journal="Journal of Zhejiang University Science A",
volume="15",
number="4",
pages="231-240",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1400079"
}

%0 Journal Article
%T The renaissance of continuum mechanics
%A Wei-qiu Chen
%J Journal of Zhejiang University SCIENCE A
%V 15
%N 4
%P 231-240
%@ 1673-565X
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1400079

TY - JOUR
T1 - The renaissance of continuum mechanics
A1 - Wei-qiu Chen
J0 - Journal of Zhejiang University Science A
VL - 15
IS - 4
SP - 231
EP - 240
%@ 1673-565X
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1400079

Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical (or mechanical) properties are assumed to vary continuously in the spaces they occupy. continuum mechanics may be seen as the symbol of modern mechanics, which differs greatly from current physics, the two often being mixed up by people and even scientists. In this short paper, I will first try to give an illustration on the differences between (modern) mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modern science, and is much closer to physics, chemistry, biology, etc. than ever before.

连续介质力学的复兴

概要：连续介质力学，正如其名称所喻示的，研究的是所有连续介质的力学问题。所谓连续介质，就是其宏观的物理或力学性质沿空间连续变化，而不必考虑各组成原子或分子的结构及其相互作用。连续介质力学可以看作是现代力学的标志，后者与现代物理学区别明显，但经常被大众甚至科学家所混淆。在此，首先从个人理解的角度阐述了现代力学与现代物理学的区别，特别指出现代力学与重大工程应用紧密相关，这从其新兴于二十世纪的三个分支学科——断裂力学、空气动力学和有限元的发展历史即可看出。然后，基于Web of Science的检索数据（见图1），清楚揭示了二十世纪五、六十年代是连续介质力学的形成期，七、八十年代是其平稳发展期，而从九十年代起至今就是其复兴期。最后，着重从三个方面展示了连续介质力学的复兴和新发展：在纳机电领域与量子力学的衔接，在能源等领域与化学的耦合，在生物学领域由生物力学向力生物学的转变。可以看到，正如其在二十世纪的工程设计中扮演了轴心角色一样，连续介质力学将通过学科交叉（与物理、化学、生物学、医学、信息科学、社会科学等）而在现代科学的版图中持续发挥重要作用。

关键词：连续介质力学, 量子力学, 工程, 研究现状, 复兴

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

References

[1] Beyer, M.K., Clausen-Schaumann, H., 2005. Mechanochemistry: The mechanical activation of covalent bonds. Chemical Reviews, 105(8):2921-2948.

[2] Boldyrev, V.V., Tkčov, K., 2000. Mechanochemistry of solids: Past, present, and prospects. Journal of Materials Synthesis and Processing, 8(3-4):121-132.

[3] Bordag, M., Mohideen, U., Mostepanenko, V.M., 2001. New developments in the Casimir effect. Physics Reports, 353(1-3):1-205.

[4] Chen, C.Q., Shi, Y., Zhang, Y.S., 2006. Size dependence of Young’s modulus in ZnO nanowires. Physical Review Letters, 96(7):075505

[5] Chen, W.Q., 2011. Surface effect on Bleustein-Gulyaev wave in a piezoelectric half-space. Theoretical and Applied Mechanics Letters, 1(4):041001

[6] Cowin, S.C., 2004. Tissue growth and remodeling. Annual Review of Biomedical Engineering, 6(1):77-107.

[7] Cui, Z., Gao, F., Qu, J., 2012. A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries. Journal of the Mechanics and Physics of Solids, 60(7):1280-1295.

[8] Duan, H.L., Wang, J., Karihaloo, B.L., 2008. Theory of elasticity at the nanoscale. Advances in Applied Mechanics, 42(1):1-68.

[9] Ekinci, K.L., Roukes, M.L., 2005. Nanoelectromechanical systems. Review of Scientific Instruments, 76(6):061101

[10] Epstein, M., 2010. , London: Cambridge University Press,:

[11] Eringen, A.C., 1980. Mechanics of Continua. Robert E. Krieger Publishing Co.,Huntington, New York :

[12] Fish, J., 2006. Bridging the scales in nano engineering and science. Journal of Nanoparticle Research, 8(5):577-594.

[13] Freund, L.B., 2009. Characterizing the resistance generated by a molecular bond as it is forcibly separated. Proceedings of the National Academy of Sciences of the United States of America, 106(22):8818-8823.

[14] Fukada, E., 1968. Piezoelectricity in polymers and biological materials. Ultrasonics, 6(4):229-234.

[15] Fung, Y.C., 1990. Biomechanics: Motion, Flow, Stress and Growth. Springer,Berlin :

[16] Fung, Y.C., 1993. Biomechanics: Mechanical Properties of Living Tissues. Springer,Berlin :

[17] Fung, Y.C., 1996. Biomechanics: Circulation. Springer,Berlin :

[18] Gilman, J.J., 1996. Mechanochemistry. Science, 274(5284):65

[19] Girard, P.P., Cavalcanti-Adam, E.A., Kemkemer, R., 2007. Cellular chemomechanics at interfaces: Sensing, integration and response. Soft Matter, 3(3):307-326.

[20] Griffith, A.A., 1921. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 221(582):163-198.

[21] Harik, V.M., 2001. Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods. Solid State Communications, 120(7-8):331-335.

[22] Herglotz, G., 1911. Über die mechanik des deformierbaren körpers vom standpunkte der relativitätstheorie. Annalen der Physik, (in German),341(13):493-533.

[23] Hu, H.C., 1955. On some variational principles in the theory of elasticity and the theory of plasticity. Scientia Sinica, 4(1):33-54.

[24] Hu, L.B., Hueckel, T., 2007. Coupled chemo-mechanics of intergranular contact: Toward a three-scale mode. Computers and Geotechnics, 34(4):306-327.

[25] Huang, Z., Boulatov, R., 2011. Chemomechanics: Chemical kinetics for multiscale phenomena. Chemical Society Reviews, 40(5):2359-2384.

[26] Humphrey, J.D., 2003. Continuum biomechanics of soft biological tissues. Proceedings of the Royal Society of London A, 459(2029):3-46.

[27] Ingber, D.E., 2006. Cellular mechanotransduction: Putting all the pieces together again. The FASEB Journal, 20(7):811-827.

[28] Janmey, P.A., McCulloch, C.A., 2007. Cell mechanics: Integrating cell responses to mechanical stimuli. Annual Review of Biomedical Engineering, 9(1):1-34.

[29] Kim, D.H., Lu, N.S., Ma, R., 2011. Epidermal electronics. Science, 333(6044):838-843.

[30] Li, B., Cao, Y.P., Feng, X.Q., 2012. Mechanics of morphological instabilities and surface wrinkling in soft materials: A review. Soft Matter, 8(21):5728-5745.

[31] Liu, D.Y., Chen, W.Q., Zhang, C.Z., 2013. Improved beam theory for multilayer graphene nanoribbons with interlayer shear effect. Physics Letters A, 377(18):1297-1300.

[32] Liu, Y.M., Zhang, Y.H., Chow, M.J., 2012. Biological ferroelectricity uncovered in aortic walls by piezoresponse force microscopy. Physical Review Letters, 108(7):078103

[33] Maugin, G.A., 2013. Continuum Mechanics through the Twentieth Century. Springer,Berlin :

[34] Mller, I., 2007. A History of Thermodynamics. Springer,Berlin :

[35] Prandtl, L., 1904. Über Flüssigkeitsbewegungen bei sehr kleiner Reibung. , Lecture on International Congress of Mathematicians, Heidelberg, :

[36] Qian, D., Wagner, G.J., Liu, W.K., 2002. Mechanics of carbon nanotubes. Applied Mechanics Reviews, 55(6):495-533.

[37] Saha, R., Nix, W.D., 2002. Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Materialia, 50(1):23-38.

[38] Schwab, K.C., Roukes, M.L., 2005. Putting mechanics into quantum mechanics. Physics Today, 58(7):36-42.

[39] Shenoy, V.B., 2005. Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Physical Review B, 71(9):094104

[40] Shi, X.H., von dem Bussche, A., Hurt, R.H., 2011. Cell entry of one-dimensional nanomaterials occurs by tip recognition and rotation. Nature Nanotechnology, 6(6):714-719.

[41] Silling, S.A., Lehoucq, R.B., 2010. Peridynamic theory of solid mechanics. Advances in Applied Mechanics, 44(1):73-166.

[42] Skalak, R., Dasgupta, G., Moss, M., 1982. Analytical description of growth. Journal of Theoretical Biology, 94(3):555-577.

[43] Stoltz, J.F., Wang, X., 2002. From biomechanics to mechanobiology. Biorheology, 39(1):5-10.

[44] Taber, L., 1995. Biomechanics of growth, remodeling and morphogenesis. Applied Mechanics Reviews, 48(8):487-545.

[45] Tadmor, E.B., Phillips, R., Ortiz, M., 1996. Mixed atomistic and continuum models of deformation in solids. Langmuir, 12(19):4529-4534.

[46] Truesdell, C.A., Toupin, R.A., 1960. The Classical Field Theories. Bd. III/1 in Handbuch der Physik. Springer,Berlin :

[47] Truesdell, C.A., Noll, W., 1965. The Non-linear Field Theories of Mechanics. Bd. III/3 in Handbuch der Physik. Springer,Berlin :

[48] Tsien, H.S., 1953. Physical mechanics, a new field in engineering science. Journal of the American Rocket Society, 23(1):14-16.

[49] Turner, M.J., Clough, R.W., Martin, H.C., 1956. Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences, 25(9):805-823.

[50] Volokh, K.Y., 2013. Challenge of biomechanics. Molecular & Cellular Biomechanics, 10(2):107-135.

[51] Wang, Q., 2005. Wave propagation in carbon nanotubes via nonlocal continuum mechanics. Journal of Applied Physics, 98(12):124301

[52] Wilson, J.S., Virag, L., Di Achille, P., 2013. Bio-chemomechanics of intraluminal thrombus in abdominal aortic aneurysms. Journal of Biomechanical Engineering, 135(2):021011

[53] Wong, E.W., Sheehan, P.E., Lieber, C.M., 1997. Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes. Science, 277(5334):1971

[54] Xiao, X., Liu, P., Verbrugge, M.W., 2011. Improved cycling stability of silicon thin film electrodes through patterning for high energy density lithium batteries. Journal of Power Sources, 196(3):1409-1416.

[55] Yakobson, B.I., Brabec, C.J., Bernholc, J., 1996. Nanomechanics of carbon tubes: Instabilities beyond linear response. Physical Review Letters, 76(14):2511-2514.

[56] Young, R.J., Kinlocha, I.A., Gong, L., 2012. The mechanics of graphene nanocomposites: A review. Composites Science and Technology, 72(12):1459-1476.

[57] Zhang, P., Huang, Y., Geubelle, P.H., 2002. The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials. International Journal of Solids and Structures, 39(13-14):3893-3906.

[58] Zhang, W.L., Lin, Y., Qian, J., 2013. Tuning molecular adhesion via material anisotropy. Advanced Functional Materials, 23(37):4729-4738.

[59] Zhang, X., Jiao, K., Sharma, P., 2006. An atomistic and non-classical continuum field theoretic perspective of elastic interactions between defects (force dipoles) of various symmetries and application to graphene. Journal of the Mechanics and Physics of Solids, 54(11):2304-2329.

[60] Zhao, K.J., Pharr, M., Vlassak, J.J., 2011. Inelastic hosts as electrodes for high-capacity lithium-ion batteries. Journal of Applied Physics, 109(1):016110

Similar articles

- Go to

连续介质力学的复兴

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

References