Cohesive elasticity and surface phenomena

Author:
Chien H. Wu

Journal:
Quart. Appl. Math. **50** (1992), 73-103

MSC:
Primary 73T05; Secondary 73B99, 73C99

DOI:
https://doi.org/10.1090/qam/1146625

MathSciNet review:
MR1146625

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Cohesive elasticity is the grade-3 theory of elasticity developed by Mindlin in 1965. It has a modulus of cohesion that gives rise to surface-tension. The concept of adhesion is introduced, and interfacial energies and energy of adhesion are defined. The interfacial energy solution may also be used to define a grain boundary energy. Also presented are the thin film energy and the concept of an interface-phase. The stretching of a thin film is analyzed in detail; and it is found that the apparent Young's modulus obtained from a film is higher than that obtained from a plate.

**[1]**B. Budiansky and J. R. Rice,*Conservation laws and energy-release rates*, J. Appl. Mech.**40**, 201-203 (1973)**[2]**J. W. Cahn and J. E. Hilliard,*Free energy of a nonuniform system*I.*Interfacial free energy*, J. Chem. Phys.**28**, 258-267 (1958)**[3]**Julian D. Cole,*Perturbation methods in applied mathematics*, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR**0246537****[4]**J. M. Doyle,*Singular solutions in elasticity*, Acta Mech.**4**, 27-33 (1966)**[5]**J. E. Dunn and J. Serrin,*On the thermomechanics of interstitial working*, Arch. Rational Mech. Anal.**88**(1985), no. 2, 95–133. MR**775366**, https://doi.org/10.1007/BF00250907**[6]**J. D. Eshelby,*The force on an elastic singularity*, Philos. Trans. Roy. Soc. London. Ser. A.**244**(1951), 84–112. MR**0048294**, https://doi.org/10.1098/rsta.1951.0016**[7]**J. D. Eshelby,*The continuum theory of lattice defects*, Solid State Physics 3, (F. Seitz and D. Turnball, eds.), Academic Press, New York, 1956, pp. 79-144**[8]**J. D. Eshelby,*The determination of the elastic field of an ellipsoidal inclusion, and related problems*, Proc. Roy. Soc. London. Ser. A.**241**(1957), 376–396. MR**0087326**, https://doi.org/10.1098/rspa.1957.0133**[9]**J. D. Eshelby,*Energy relations and the energy-momentum tensor in continuum mechanics*, Inelastic Behavior of Solids, (M. F. Kannineu, W. F. Adler, A. R. Rosenfield, and R. I. Jaffee, eds.), McGraw-Hill, New York, 1970, pp. 77-114**[10]**D. C. Gazis and R. F. Wallis,*Surface tension and surface modes in semi-infinite lattices*, Surface Science, vol. 3, 1964, pp. 19-32**[11]**L. H. Germer, A. V. MacRae, and C. D. Hartman, (110)*Nickel Surface*, J. Appl. Phys.**32**, 2432-2439 (1961)**[12]**A. E. Green and R. S. Rivlin,*Simple force and stress multipoles*, Arch. Rational Mech. Anal.**16**(1964), 325–353. MR**0182191**, https://doi.org/10.1007/BF00281725**[13]**Morton E. Gurtin,*On a nonequilibrium thermodynamics of capillarity and phase*, Quart. Appl. Math.**47**(1989), no. 1, 129–145. MR**987902**, https://doi.org/10.1090/S0033-569X-1989-0987902-4**[14]**J. K. Knowles and Eli Sternberg,*On a class of conservation laws in linearized and finite elastostatics*, Arch. Rational Mech. Anal.**44**(1971/72), 187–211. MR**0337111**, https://doi.org/10.1007/BF00250778**[15]**R. D. Mindlin,*Influence of couple-stresses on stress concentrations*, Exp. Mech.**3**, 1-7 (1963)**[16]**R. D. Mindlin,*Micro-structure in linear elasticity*, Arch. Rational Mech. Anal.**16**(1964), 51–78. MR**0160356**, https://doi.org/10.1007/BF00248490**[17]**R. D. Mindlin,*Second gradient of strain and surface-tension in linear elasticity*, Internat. J. Solids Structures**1**, 417-438 (1965)**[18]**R. D. Mindlin,*On the equations of elastic materials with micro-structure*, Internat. J. Solids Structures**1**, 73-78 (1965)**[19]**R. D. Mindlin,*Polarization gradient in elastic dielectrics*, Internat. J. Solids Structures**4**, 637-642 (1968)**[20]**R. D. Mindlin and N. N. Eshel,*On first strain-gradient theories in linear elasticity*, Internat. J. Solids Structures**4**, 109-124 (1968)**[21]**T. Mura,*Micromechanics of Defects in Solids*, Martinus Nighoff Publishers, The Hague, The Netherlands, 1982**[22]**L. E. Murr,*Interfacial Phenomena in Metals and Alloys*, Addison-Wesley, Reading, Mass., 1975**[23]**G. C. Sih and H. Liebowitz,*On the Griffith energy criterion for brittle fracture*, Internat. J. Solids Structures**3**, 1-22 (1967)**[24]**R. A. Toupin,*Elastic materials with couple-stresses*, Arch. Rational Mech. Anal.**11**(1962), 385–414. MR**0144512**, https://doi.org/10.1007/BF00253945**[25]**R. A. Toupin and D. C. Gazis,*Surface effects and initial stress in continuum and lattice models of elastic crystals, Proceedings of the International Conference on Lattice Dynamics*, Copenhagen, (R. F. Wallis, ed.), Pergamon Press, New York-Oxford, 1964, pp. 597-602**[26]**Milton Van Dyke,*Perturbation methods in fluid mechanics*, Annotated edition, The Parabolic Press, Stanford, Calif., 1975. MR**0416240**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
73T05,
73B99,
73C99

Retrieve articles in all journals with MSC: 73T05, 73B99, 73C99

Additional Information

DOI:
https://doi.org/10.1090/qam/1146625

Article copyright:
© Copyright 1992
American Mathematical Society