메뉴 건너뛰기




Volumn 455, Issue 1982, 1999, Pages 437-474

Elastic surface-substrate interactions

Author keywords

Finite deformations; Nonlinear elasticity; Quasi convexity; Shell theory; Surface stress; Thin films

Indexed keywords


EID: 33746441506     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0320     Document Type: Article
Times cited : (424)

References (59)
  • 1
    • 0017534702 scopus 로고
    • On the wrinkling of a free surface
    • Andreussi, F. & Gurtin, M. E. 1977 On the wrinkling of a free surface. J. Appl. Phys. 48, 3798-3799.
    • (1977) J. Appl. Phys. , vol.48 , pp. 3798-3799
    • Andreussi, F.1    Gurtin, M.E.2
  • 2
    • 5244327400 scopus 로고
    • Simple force multipoles in the theory of deformable surfaces
    • Balaban, M. M., Green, A. E. & Naghdi, P. M. 1967 Simple force multipoles in the theory of deformable surfaces. J. Math. Phys. 8, 1026-1036.
    • (1967) J. Math. Phys. , vol.8 , pp. 1026-1036
    • Balaban, M.M.1    Green, A.E.2    Naghdi, P.M.3
  • 3
    • 0017417265 scopus 로고
    • Convexity conditions and existence theorems in nonlinear elasticity
    • Ball, J. M. 1977 Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Analysis 63, 377-403.
    • (1977) Arch. Ration. Mech. Analysis , vol.63 , pp. 377-403
    • Ball, J.M.1
  • 4
    • 0021296252 scopus 로고
    • Quasi-convexity at the boundary, positivity of the second variation and elastic stability
    • Ball, J. M. & Marsden, J. E. 1984 Quasi-convexity at the boundary, positivity of the second variation and elastic stability. Arch. Ration. Mech. Analysis 86, 251-277.
    • (1984) Arch. Ration. Mech. Analysis , vol.86 , pp. 251-277
    • Ball, J.M.1    Marsden, J.E.2
  • 5
    • 0027579132 scopus 로고
    • Buckling of a coating bonded to a round bar subjected to axial tension
    • Bert, C. W. & Birman, V. 1993 Buckling of a coating bonded to a round bar subjected to axial tension. Mech. Mater. 15, 131-138.
    • (1993) Mech. Mater. , vol.15 , pp. 131-138
    • Bert, C.W.1    Birman, V.2
  • 6
    • 0028430416 scopus 로고
    • Large strain analysis of rubber-like membranes under dead weight, gas pressure, and hydrostatic loading
    • Bufler, H. & Schneider, H. 1994 Large strain analysis of rubber-like membranes under dead weight, gas pressure, and hydrostatic loading. Computational Mech. 14, 165-188.
    • (1994) Computational Mech. , vol.14 , pp. 165-188
    • Bufler, H.1    Schneider, H.2
  • 7
    • 84901014652 scopus 로고
    • Approximations par éléments finis d'un modèle de coques minces géométriquement exact
    • Carrive-Bédouani, M., Le Tallec, P. & Mouro, J. 1995 Approximations par éléments finis d'un modèle de coques minces géométriquement exact. Rev. EUT. Élém. Finis 4, 633-661.
    • (1995) Rev. EUT. Élém. Finis , vol.4 , pp. 633-661
    • Carrive-Bedouani, M.1    Le Tallec, P.2    Mouro, J.3
  • 8
    • 0015474163 scopus 로고
    • The influence of the reference geometry on the response of elastic shells
    • Carroll, M. M. & Naghdi, P. M. 1972 The influence of the reference geometry on the response of elastic shells. Arch. Ration. Mech. Analysis 48, 302-318.
    • (1972) Arch. Ration. Mech. Analysis , vol.48 , pp. 302-318
    • Carroll, M.M.1    Naghdi, P.M.2
  • 9
    • 10044267456 scopus 로고
    • Nonlinear theory of elastic surfaces
    • Cohen, H. & DeSilva, C. N. 1966 Nonlinear theory of elastic surfaces. J. Math. Phys. 7, 246-253.
    • (1966) J. Math. Phys. , vol.7 , pp. 246-253
    • Cohen, H.1    Desilva, C.N.2
  • 10
    • 33746414154 scopus 로고
    • On a nonlinear theory of elastic shells
    • Cohen, H. & DeSilva, C. N. 1968 On a nonlinear theory of elastic shells. J. Mécanique 7,459-464.
    • (1968) J. Mécanique , pp. 459-464
    • Cohen, H.1    Desilva, C.N.2
  • 11
    • 0021317181 scopus 로고
    • On the response and symmetry of elastic and hyperelastic membrane points
    • Cohen, H. & Wang, C.-C. 1984 On the response and symmetry of elastic and hyperelastic membrane points. Arch. Ration. Mech. Analysis 85, 343-379.
    • (1984) Arch. Ration. Mech. Analysis , vol.85 , pp. 343-379
    • Cohen, H.1    Wang, C.-C.2
  • 12
    • 53349142465 scopus 로고
    • F-convergence and the calculus of variations
    • (ed. J. P. Cecconi & T. Zolezzi). Lecture Notes in Mathematics, no. 979. Berlin: Springer.
    • De Giorgi, E. & Dal Maso, G. 1983 f-convergence and the calculus of variations. In Mathematical theories of optimization (ed. J. P. Cecconi & T. Zolezzi). Lecture Notes in Mathematics, no. 979. Berlin: Springer.
    • (1983) Mathematical Theories of Optimization
    • De Giorgi, E.1    Dal Maso, G.2
  • 13
    • 0026896925 scopus 로고
    • The symmetry group of second-grade materials
    • Elzanowski, M. & Epstein, M. 1992 The symmetry group of second-grade materials. Int. J. Non-Linear Mech. 27, 635-638.
    • (1992) Int. J. Non-Linear Mech. , vol.27 , pp. 635-638
    • Elzanowski, M.1    Epstein, M.2
  • 14
    • 33746390051 scopus 로고
    • Wave propagation in thin elastic shells
    • Ericksen, J. L. 1971 Wave propagation in thin elastic shells. Arch. Ration. Mech. Analysis 43, 167-178.
    • (1971) Arch. Ration. Mech. Analysis , vol.43 , pp. 167-178
    • Ericksen, J.L.1
  • 15
    • 0023854557 scopus 로고
    • Configuration dependent pressure potentials
    • Fisher, D. 1988 Configuration dependent pressure potentials. J. Elasticity 19, 77-84.
    • (1988) J. Elasticity , vol.19 , pp. 77-84
    • Fisher, D.1
  • 16
    • 21344486080 scopus 로고
    • A justification of nonlinear properly invariant plate theories
    • Fox, D. D., Raoult, A. & Simo, J. C. 1993 A justification of nonlinear properly invariant plate theories. Arch. Ration. Mech. Analysis 124, 157-199.
    • (1993) Arch. Ration. Mech. Analysis , vol.124 , pp. 157-199
    • Fox, D.D.1    Raoult, A.2    Simo, J.C.3
  • 18
    • 84972453494 scopus 로고
    • The Weierstrass condition for multiple integral variation problems
    • Graves, L. M. 1939 The Weierstrass condition for multiple integral variation problems. Duke Math. J. 5, 656-660.
    • (1939) Duke Math. J. , vol.5 , pp. 656-660
    • Graves, L.M.1
  • 19
    • 0016441185 scopus 로고
    • A continuum theory of elastic material surfaces
    • Gurtin, M. E. & Murdoch, A. I. 1975 A continuum theory of elastic material surfaces. Arch. Ration. Mech. Analysis 57, 291-323.
    • (1975) Arch. Ration. Mech. Analysis , vol.57 , pp. 291-323
    • Gurtin, M.E.1    Murdoch, A.I.2
  • 20
    • 0005057974 scopus 로고
    • On the inclusion of the complete symmetry group in the unimodular group
    • Gurtin, M. E. & Williams, W. O. 1966 On the inclusion of the complete symmetry group in the unimodular group. Arch. Ration. Mech. Analysis 23, 163-172.
    • (1966) Arch. Ration. Mech. Analysis , vol.23 , pp. 163-172
    • Gurtin, M.E.1    Williams, W.O.2
  • 21
    • 0031099670 scopus 로고    scopus 로고
    • Plane infinitesimal waves in elastic sheets with bending stiffness
    • Hilgers, M. G. 1997 Plane infinitesimal waves in elastic sheets with bending stiffness. Math. Mech. Solids. 2, 75-89.
    • (1997) Math. Mech. Solids. , vol.2 , pp. 75-89
    • Hilgers, M.G.1
  • 23
    • 0345221732 scopus 로고    scopus 로고
    • 19926 Bending energy of highly elastic membranes
    • Hilgers, M. G. & Pipkin, A. C. 19926 Bending energy of highly elastic membranes. Q. Appl. Math. 50, 389-400.
    • Q. Appl. Math. , vol.50 , pp. 389-400
    • Hilgers, M.G.1    Pipkin, A.C.2
  • 24
    • 0027594585 scopus 로고
    • Energy minimizing deformations of elastic sheets with bending stiffness
    • Hilgers, M. G. & Pipkin, A. C. 1993 Energy minimizing deformations of elastic sheets with bending stiffness. J. Elasticity 31, 125-139.
    • (1993) J. Elasticity , vol.31 , pp. 125-139
    • Hilgers, M.G.1    Pipkin, A.C.2
  • 25
    • 0030165839 scopus 로고    scopus 로고
    • Bending energy of highly elastic membranes
    • Hilgers, M. G. & Pipkin, A. C. 1996 Bending energy of highly elastic membranes. II. Q. Appl. Math. 54, 307-316.
    • (1996) Q. Appl. Math. , vol.54 , pp. 307-316
    • Hilgers, M.G.1    Pipkin, A.C.2
  • 26
    • 0345653633 scopus 로고
    • Uniqueness criteria and extremum principles in self-adjoint problems of continuum mechanics
    • Hill, R. 1962 Uniqueness criteria and extremum principles in self-adjoint problems of continuum mechanics. J. Mech. Phys. Solids 10, 185-194.
    • (1962) J. Mech. Phys. Solids , vol.10 , pp. 185-194
    • Hill, R.1
  • 27
    • 84930244279 scopus 로고
    • Über das gleichgewicht und die bewegung einer elastischen Scheibe
    • Kirchhoff, G. 1850 Über das gleichgewicht und die bewegung einer elastischen Scheibe. J. Reine. Angew. Math. 40, 51-88.
    • (1850) J. Reine. Angew. Math. , vol.40 , pp. 51-88
    • Kirchhoff, G.1
  • 28
    • 0039149783 scopus 로고
    • Stress and microstructure in LPCVD polycrystalline silicon films: Experimental results and closed form modeling of stresses
    • (cd. W. D. Nix, J. C. Bravman, E. Arzt & L. B. Freund). Pittsburgh, PA: Materials Research Society
    • Krulevitch, P., Johnson, G. C. & Howe, R. T. 1992 Stress and microstructure in LPCVD polycrystalline silicon films: experimental results and closed form modeling of stresses. In Thin films: stresses and mechanical properties III (cd. W. D. Nix, J. C. Bravman, E. Arzt & L. B. Freund). Pittsburgh, PA: Materials Research Society.
    • (1992) Thin Films: Stresses and Mechanical Properties III
    • Krulevitch, P.1    Johnson, G.C.2    Howe, R.T.3
  • 29
    • 0000312494 scopus 로고
    • The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity
    • Le Dret, H. & Raoult, A. 1995 The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl. 74, 549-578.
    • (1995) J. Math. Pures Appl. , vol.74 , pp. 549-578
    • Le Dret, H.1    Raoult, A.2
  • 30
    • 1842611371 scopus 로고    scopus 로고
    • The membrane shell model in nonlinear elasticity: A variational asymptotic derivation
    • Le Dret, H. & Raoult, A. 1996 The membrane shell model in nonlinear elasticity: a variational asymptotic derivation. J. Nonlinear Sci. 6, 59-84.
    • (1996) J. Nonlinear Sci. , vol.6 , pp. 59-84
    • Le Dret, H.1    Raoult, A.2
  • 32
    • 0024680405 scopus 로고
    • Work-conjugate boundary conditions in the nonlinear theory of thin shells
    • Makowski, J. & Pietraszkiewicz, W. 1989 Work-conjugate boundary conditions in the nonlinear theory of thin shells. ASME J. Appl. Mech. 56, 395-402.
    • (1989) ASME J. Appl. Mech. , vol.56 , pp. 395-402
    • Makowski, J.1    Pietraszkiewicz, W.2
  • 33
    • 84968503702 scopus 로고
    • Quasiconvexity and lower semicontinuity of multiple variational integrals of any order
    • Meyers, N. G. 1965 Quasiconvexity and lower semicontinuity of multiple variational integrals of any order. Trans. Am. Math. Soc. 119, 225-249.
    • (1965) Trans. Am. Math. Soc. , vol.119 , pp. 225-249
    • Meyers, N.G.1
  • 34
    • 84972497511 scopus 로고
    • Quasiconvexity and the lower semi-continuity of multiple integrals
    • Morrey, C. B. 1952 Quasiconvexity and the lower semi-continuity of multiple integrals. Pacific J. Math. 2, 25-53.
    • (1952) Pacific J. Math. , vol.2 , pp. 25-53
    • Morrey, C.B.1
  • 35
    • 0018293488 scopus 로고
    • Symmetry considerations for materials of second grade
    • Murdoch, A. I. 1979 Symmetry considerations for materials of second grade. J. Elasticity 9, 43-50.
    • (1979) J. Elasticity , vol.9 , pp. 43-50
    • Murdoch, A.I.1
  • 36
    • 0018711606 scopus 로고
    • Symmetry considerations for material surfaces
    • Murdoch, A. I. & Cohen, H. 1979 Symmetry considerations for material surfaces. Arch. Ration. Mech. Analysis 72, 61-98.
    • (1979) Arch. Ration. Mech. Analysis , vol.72 , pp. 61-98
    • Murdoch, A.I.1    Cohen, H.2
  • 37
    • 0005016416 scopus 로고
    • Symmetry considerations for material surfaces: Addendum
    • Murdoch, A. I. & Cohen, H. 1981 Symmetry considerations for material surfaces: addendum. Arch. Ration. Mech. Analysis 76, 393-400.
    • (1981) Arch. Ration. Mech. Analysis , vol.76 , pp. 393-400
    • Murdoch, A.I.1    Cohen, H.2
  • 38
    • 0000838996 scopus 로고
    • Theory of shells and plates
    • vol. VIa/2 (ed. C. Truesdell), Berlin: Springer.
    • Naghdi, P. M. 1972 Theory of shells and plates. In Handbuch der Physik, vol. VIa/2 (ed. C. Truesdell), pp. 425-640. Berlin: Springer.
    • (1972) Handbuch Der Physik , pp. 425-640
    • Naghdi, P.M.1
  • 39
    • 34250971713 scopus 로고
    • A mathematical theory of the mechanical behavior of continuous media
    • Noll, W. 1958 A mathematical theory of the mechanical behavior of continuous media. Arch. Ration. Mech. Analysis 2, 197-226
    • (1958) Arch. Ration. Mech. Analysis , vol.2 , pp. 197-226
    • Noll, W.1
  • 41
    • 0031131250 scopus 로고    scopus 로고
    • The effect of elastic surface coating on the finite deformation and bifurcation of a pressurized circular annulus
    • Ogden, R. W., Steigmann, D. J. & Haughton, D. M. 1997 The effect of elastic surface coating on the finite deformation and bifurcation of a pressurized circular annulus. J. Elasticity 47, 121-145.
    • (1997) J. Elasticity , vol.47 , pp. 121-145
    • Ogden, R.W.1    Steigmann, D.J.2    Haughton, D.M.3
  • 42
    • 0001395212 scopus 로고
    • General theory of elastic stability
    • Pearson, C. E. 1956 General theory of elastic stability. Q. Appl. Math. 14, 133-144.
    • (1956) Q. Appl. Math. , vol.14 , pp. 133-144
    • Pearson, C.E.1
  • 43
    • 0003123789 scopus 로고
    • Geometrically nonlinear theories of thin elastic shells
    • Pietraszkiewicz, W. 1989 Geometrically nonlinear theories of thin elastic shells. Adv. Mech. 12, 52-130.
    • (1989) Adv. Mech. , vol.12 , pp. 52-130
    • Pietraszkiewicz, W.1
  • 45
    • 0002576721 scopus 로고
    • Nonlinear theories for thin shells
    • Sanders, J. L. 1963 Nonlinear theories for thin shells. Q. Appl. Math. 21, 21-36.
    • (1963) Q. Appl. Math. , vol.21 , pp. 21-36
    • Sanders, J.L.1
  • 46
    • 0021936321 scopus 로고
    • The strain energy density of rubber-like shells
    • Simmonds, J. G. 1985 The strain energy density of rubber-like shells. Int. J. Solids Struct. 21, 67-77.
    • (1985) Int. J. Solids Struct. , vol.21 , pp. 67-77
    • Simmonds, J.G.1
  • 47
    • 0022880338 scopus 로고
    • Proof of a conjecture in elastic membrane theory
    • Steigmann, D. J. 1986 Proof of a conjecture in elastic membrane theory. ASME J. Appl. Mech. 53, 955-956.
    • (1986) ASME J. Appl. Mech. , vol.53 , pp. 955-956
    • Steigmann, D.J.1
  • 49
    • 0013404357 scopus 로고
    • A note on pressure potentials
    • Steigmann, D. J. 1991 A note on pressure potentials. J. Elasticity 26, 87-93.
    • (1991) J. Elasticity , vol.26 , pp. 87-93
    • Steigmann, D.J.1
  • 50
    • 0026698362 scopus 로고
    • Equilibrium of prestressed networks
    • Steigmann, D. J. 1992 Equilibrium of prestressed networks. IMA Jl Appl. Math. 48, 195-215.
    • (1992) IMA Jl Appl. Math. , vol.48 , pp. 195-215
    • Steigmann, D.J.1
  • 51
    • 0027682447 scopus 로고
    • Variational theory for spatial rods
    • Steigmann, D. J. & Faulkner, M. G. 1993 Variational theory for spatial rods. J. Elasticity 33, 1-26.
    • (1993) J. Elasticity , vol.33 , pp. 1-26
    • Steigmann, D.J.1    Faulkner, M.G.2
  • 52
    • 0002713545 scopus 로고    scopus 로고
    • Plane deformations of elastic solids with intrinsic boundary elasticity
    • Steigmann, D. J. & Ogden, R. W. 1997a Plane deformations of elastic solids with intrinsic boundary elasticity. Proc. R. Soc. Lond. A 453, 853-877.
    • (1997) Proc. R. Soc. Lond. a , vol.453 , pp. 853-877
    • Steigmann, D.J.1    Ogden, R.W.2
  • 53
    • 0031094604 scopus 로고    scopus 로고
    • 19976 a necessary condition for energy-minimizing plane deformations of elastic solids with intrinsic boundary elasticity
    • Steigmann, D. J. & Ogden, R. W. 19976 A necessary condition for energy-minimizing plane deformations of elastic solids with intrinsic boundary elasticity. Math. Mech. Solids 2, 3-16.
    • Math. Mech. Solids , vol.2 , pp. 3-16
    • Steigmann, D.J.1    Ogden, R.W.2
  • 55
    • 0010467529 scopus 로고
    • (notes by R. W. Dickey). New York: Courant Institute of Mathematical Sciences.
    • Stoker, J. J. 1964 Topics in nonlinear elasticity (notes by R. W. Dickey). New York: Courant Institute of Mathematical Sciences.
    • (1964) Topics in Nonlinear Elasticity
    • Stoker, J.J.1
  • 56
    • 0023166895 scopus 로고
    • Plane deformations of nets with bending stiffness
    • Wang, W.-B. & Pipkin, A. C. 1986 Plane deformations of nets with bending stiffness. Acta Mechanica 65, 263-279.
    • (1986) Acta Mechanica , vol.65 , pp. 263-279
    • Wang, W.-B.1    Pipkin, A.C.2
  • 58
    • 0001134913 scopus 로고
    • Two-dimensional tensor function representation for all kinds of material symmetry
    • Zheng, Q.-S. 1993 Two-dimensional tensor function representation for all kinds of material symmetry. Proc. R. Soc. Lond. A 443, 127-138.
    • (1993) Proc. R. Soc. Lond. a , vol.443 , pp. 127-138
    • Zheng, Q.-S.1
  • 59
    • 77956820531 scopus 로고
    • On the concept of elastic stability
    • Ziegler, H. 1956 On the concept of elastic stability. Adv. Appl. Mech. 4, 351-403.
    • (1956) Adv. Appl. Mech. , vol.4 , pp. 351-403
    • Ziegler, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.