Articles

Mechanical effects of circular liquid inclusions inside soft matrix: role of internal pressure change and surface tension

Expand
  • College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China

Received date: 2020-11-28

  Revised date: 2021-01-06

  Online published: 2021-03-23

Abstract

The mechanical effects of dilute liquid inclusions on the solid-liquid composite are explored, based on an analytical circular inclusion model incorporating the internal pressure change of the liquid and the surface tension of the interface. Several simple explicit dependences of the stress field and effective stiffness on the bulk modulus and the size of the liquid, the surface tension, and Poisson’s ratio of the matrix are derived. The results show that the stresses in the matrix are reduced, and the stiffness of the solid-liquid composite is enhanced with the consideration of either the surface tension or the internal pressure change. Particularly, the effective Young’s modulus predicted by the present model for either soft or stiff matrices agrees well with the known experimental data. In addition, according to the theoretical results, it is possible to stiffen a soft solid by pressured gas with the presence of the surface tension of the solid-gas interface.

Cite this article

Lei ZHANG . Mechanical effects of circular liquid inclusions inside soft matrix: role of internal pressure change and surface tension[J]. Applied Mathematics and Mechanics, 2021 , 42(4) : 501 -510 . DOI: 10.1007/s10483-021-2722-8

References

[1] GOJNY, F. H., WICHMANN, M. H. G., and FIEDLER, B. Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites-a comparative study. Composites Science and Technology, 65, 2300-2313(2005)
[2] COLEMAN, J. N., KHAN, U., and GUNKO, Y. K. Mechanical reinforcement of polymers using carbon nanotubes. Advanced Materials, 18(6), 689-706(2006)
[3] STYLE, R. W., BOLTYANSKIY, R., ALLEN, B., JENSEN, K. E., FOOTE, H. P., WETTLAUFER, J. S., and DUFRESNE, E. R. Stiffening solids with liquid inclusions. Nature Physics, 11(1), 82-87(2015)
[4] DUCLOUE, L., PITOIS, O., GOYON, J., CHATEAU, X., and OVARLEZ, G. Coupling of elasticity to capillarity in soft aerated materials. Soft Matter, 10(28), 5093-5098(2014)
[5] VINCENT, O., MARMOTTANT, P., QUINTO-SU, P. A., and OHL, C. D. Birth and growth of cavitation bubbles within water under tension confined in a simple synthetic tree. Physical Review Letters, 108(18), 184502(2012)
[6] LI, X. Y., ZHANG, J. M., and YI, X. Multimaterial microfluidic 3D printing of textured composites with liquid inclusions. Advanced Science, 6(3), 1800730(2019)
[7] STYLE, R. W., WETTLAUFER, J. S., and DUFRESNE, E. R. Surface tension and the mechanics of liquid inclusions in compliant solids. Soft Matter, 11(4), 672-679(2015)
[8] WU, J., RU, C. Q., and ZHANG, L. An elliptical liquid inclusion in an infinite elastic plane. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 474(2215), 20170813(2018)
[9] CHEN, X., LI, M., YANG, M., LIU, S., GENIN, G. M., XU, F., and LU, T. J. The elastic fields of a compressible liquid inclusion. Extreme Mechanics Letters, 22, 122-130(2018)
[10] LIANG, H., CAO, Z., and DOBRYNIN, A. V. Effect of monofluoro substitution on the optoelectronic properties of benzo[c] [1,2,5]thiadiazole based organic semiconductors. Macromolecules, 49(16), 7108-7115(2016)
[11] WANG, Y. and HENANN, D. L. Finite-element modeling of soft solids with liquid inclusions. Extreme Mechanics Letters, 9, 147-157(2016)
[12] JERISON, E. R., XU, Y., and WILEN, L. A. Deformation of an elastic substrate by a three-phase contact line. Physical Review Letters, 106(18), 186103(2011)
[13] STYLE, R. W. and DUFRESNE, E. R. Static wetting on deformable substrates, from liquids to soft solids. Soft Matter, 8(27), 7177-7184(2012)
[14] STYLE, R. W., HYLAND, C., BOLTYANSKIY, R., WETTLAUFER, J. S., and DUFRESNE, E. R. Surface tension and contact with soft elastic solids. Nature Communications, 4, 2728(2013)
[15] STYLE, R. W., JAGOTA, A., HUI, C. Y., and DUFRESNE, E. R. Elastocapillarity:surface tension and the mechanics of soft solids. Annual Review of Condensed Matter Physics, 8, 99-118(2017)
[16] STYLE, R. W. and XU, Q. The mechanical equilibrium of soft solids with surface elasticity. Soft Matter, 14(22), 4569-4576(2018)
[17] MANCARELLA, F., STYLE, R. W., and WETTLAUFER, J. S. Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 472(2189), 20150853(2016)
[18] MANCARELLA, F. and WETTLAUFER, J. S. Surface tension and a self-consistent theory of soft composite solids with elastic inclusions. Soft Matter, 13(5), 945-955(2017)
[19] BOBO, E., LEFEZ, B., and CAUMON, M. C. Evidence of two types of fluid inclusions in single crystals. CrystEngComm, 18(28), 5287-5295(2016)
[20] BARTLETT, M. D., FASSLER, A., and KAZEM, N. Stretchable, high-k dielectric elastomers through liquid-metal inclusions. Advanced Materials, 28(19), 3726-3731(2016)
[21] CHIPARA, A. C., OWUOR, P. S., and BHOWMICK, S. Structural reinforcement through liquid encapsulation. Advanced Materials Interfaces, 4(2), 1600781(2017)
[22] CAMPAS, O., MAMMOTO, T., and TADANORI, H. S. Quantifying cell-generated mechanical forces within living embryonic tissues. Nature Methods, 11(2), 183-189(2014)
[23] OWUOR, P. S., HIREMATH, S., and CHIPARA, A. C. Nature inspired strategy to enhance mechanical properties via liquid reinforcement. Advanced Materials Interfaces, 4(16), 1700240(2017)
[24] DAI, M., LI, M., and SCHIAVONE, P. Plane deformations of an inhomogeneity-matrix system incorporating a compressible liquid inhomogeneity and complete Gurtin-Murdoch interface model. Journal of Applied Mechanics-Transactions of the ASME, 85(12), 121010(2018)
[25] DAI, M., HUA, J., and SCHIAVONE, P. Compressible liquid/gas inclusion with high initial pressure in plane deformation:modified boundary conditions and related analytical solutions. European Journal of Mechanics A-Solids, 82, 104000(2020)
[26] ENGLAND, A. H. Complex Variable Methods in Elasticity, Wiley, New York (1971)
[27] CHEN, T., CHIU, M. S., and WENG, C. N. Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. Journal of Applied Physics, 100(7), 074308(2006)
[28] DAI, M., GAO, C. F., and RU, C. Q. Surface tension-induced stress concentration around a nanosized hole of arbitrary shape in an elastic half-plane. Meccanica, 49(12), 2847-2859(2014)
[29] BOWER, A. F. Applied Mechanics of Solids, CRC Press, Boca Raton (2009)
[30] RU, C. Q. Interface design of neutral elastic inclusions. International Journal of Solids and Structures, 35, 559-572(1998)
[31] BUCKMANN, T., THIEL, M., and KADIC, M. An elasto-mechanical unfeelability cloak made of pentamode metamaterials. Nature Communications, 5, 4130(2014)
[32] ESHELBY, J. D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal of London Series A-Mathematical and Physical Sciences, 241(1226), 376-396(1957)
[33] YANG, F. Size-dependent effective modulus of elastic composite materials:spherical nanocavities at dilute concentrations. Journal of Applied Physics, 95(7), 3516-3520(2004)
[34] MANCARELLA, F., STYLE, R. W., and WETTLAUFER, J. S. Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids. Soft Matter, 12(10), 2744-2750(2016)
Outlines

/

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals