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 Free Access
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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.
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R. D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, Internat. J. Solids Structures 1, 417–438 (1965)
R. D. Mindlin, On the equations of elastic materials with micro-structure, Internat. J. Solids Structures 1, 73–78 (1965)
R. D. Mindlin, Polarization gradient in elastic dielectrics, Internat. J. Solids Structures 4, 637–642 (1968)
R. D. Mindlin and N. N. Eshel, On first strain-gradient theories in linear elasticity, Internat. J. Solids Structures 4, 109–124 (1968)
T. Mura, Micromechanics of Defects in Solids, Martinus Nighoff Publishers, The Hague, The Netherlands, 1982
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B. Budiansky and J. R. Rice, Conservation laws and energy-release rates, J. Appl. Mech. 40, 201–203 (1973)
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys. 28, 258–267 (1958)
Julian D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, Mass., 1968
J. M. Doyle, Singular solutions in elasticity, Acta Mech. 4, 27–33 (1966)
J. E. Dunn and J. Serrin, On the thermodynamics of interstitial working, Arch. Rational Mech. Anal. 88, 95–133 (1985)
J. D. Eshelby, The force on an elastic singularity, Philos. Trans. Roy. Soc. London Ser. A 244, 87–112 (1951)
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
J. D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London, Ser. A 241, 376–396 (1957)
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
D. C. Gazis and R. F. Wallis, Surface tension and surface modes in semi-infinite lattices, Surface Science, vol. 3, 1964, pp. 19–32
L. H. Germer, A. V. MacRae, and C. D. Hartman, (110) Nickel Surface, J. Appl. Phys. 32, 2432–2439 (1961)
A. E. Green and R. S. Rivlin, Simple force and stress multipoles, Arch. Rational Mech. Anal. 16, 325–353 (1964)
M. E. Gurtin, On a nonequilibrium thermodynamics of capillarity and phase, Quart. Appl. Math. 47, 129–145 (1989)
J. K. Knowles and E. Sternberg, On a class of conservation laws in linearized and finite elastostatics, Arch. Rational Mech. Anal. 44, 187–211 (1972)
R. D. Mindlin, Influence of couple-stresses on stress concentrations, Exp. Mech. 3, 1–7 (1963)
R. D. Mindlin, Micro-structure in linear elasticity, Arch. Rational Mech. Anal. 16, 51–78 (1964)
R. D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, Internat. J. Solids Structures 1, 417–438 (1965)
R. D. Mindlin, On the equations of elastic materials with micro-structure, Internat. J. Solids Structures 1, 73–78 (1965)
R. D. Mindlin, Polarization gradient in elastic dielectrics, Internat. J. Solids Structures 4, 637–642 (1968)
R. D. Mindlin and N. N. Eshel, On first strain-gradient theories in linear elasticity, Internat. J. Solids Structures 4, 109–124 (1968)
T. Mura, Micromechanics of Defects in Solids, Martinus Nighoff Publishers, The Hague, The Netherlands, 1982
L. E. Murr, Interfacial Phenomena in Metals and Alloys, Addison-Wesley, Reading, Mass., 1975
G. C. Sih and H. Liebowitz, On the Griffith energy criterion for brittle fracture, Internat. J. Solids Structures 3, 1–22 (1967)
R. A. Toupin, Elastic materials with couple-stress, Arch. Rational Mech. Anal. 11, 386–414 (1962)
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
M. Van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, California, 1975
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Article copyright:
© Copyright 1992
American Mathematical Society
