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Volumn 35, Issue 3, 2001, Pages 525-548

On the numerical modeling of deformations of pressurized martensitic thin films

Author keywords

Active materials; Finite element; Martensitic transformation; Thin film

Indexed keywords


EID: 0035606872     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2001101     Document Type: Article
Times cited : (10)

References (49)
  • 1
    • 0003796630 scopus 로고
    • Academic Press, New York
    • R. Adams, Sobolev spaces. Academic Press, New York (1975).
    • (1975) Sobolev Spaces
    • Adams, R.1
  • 2
    • 0001558920 scopus 로고
    • The TUBA family of plate elements for the matrix displacement method
    • J.H. Argyris, I. Fried and D.W. Scharpf, The TUBA family of plate elements for the matrix displacement method. Aero. J. Roy. Aero. Soc. 72 (1968) 701-709.
    • (1968) Aero. J. Roy. Aero. Soc. , vol.72 , pp. 701-709
    • Argyris, J.H.1    Fried, I.2    Scharpf, D.W.3
  • 4
    • 33750297145 scopus 로고
    • Fine phase mixtures as minimizers of energy
    • J. Ball and R. James, Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Anal. 100 (1987) 13-52.
    • (1987) Arch. Rat. Mech. Anal. , vol.100 , pp. 13-52
    • Ball, J.1    James, R.2
  • 5
    • 0002854369 scopus 로고
    • Proposed experimental tests of a theory of fine microstructure and the two-well problem
    • J. Ball and R. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. R. Soc. Lond. A 338 (1992) 389-450.
    • (1992) Phil. Trans. R. Soc. Lond. A , vol.338 , pp. 389-450
    • Ball, J.1    James, R.2
  • 6
    • 84986959258 scopus 로고
    • Basis functions for general Hsieh-Clough-Tocher triangles, complete or reduced
    • M. Bernadou and K. Hassan, Basis functions for general Hsieh-Clough-Tocher triangles, complete or reduced. Internat. J. Numer. Methods Engrg. 17 (1981) 784-789.
    • (1981) Internat. J. Numer. Methods Engrg. , vol.17 , pp. 784-789
    • Bernadou, M.1    Hassan, K.2
  • 7
    • 0033098284 scopus 로고    scopus 로고
    • A theory of thin films of martensitic materials with applications to microactuators
    • K. Bhattacharya and R.D. James, A theory of thin films of martensitic materials with applications to microactuators. J. Mech. Phys. Solids 47 (1999) 531-576.
    • (1999) J. Mech. Phys. Solids , vol.47 , pp. 531-576
    • Bhattacharya, K.1    James, R.D.2
  • 8
    • 0033437538 scopus 로고    scopus 로고
    • The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation
    • K. Bhattacharya, B. Li and M. Luskin, The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation. Arch. Rat. Mech. Anal. 149 (1999) 123-154.
    • (1999) Arch. Rat. Mech. Anal. , vol.149 , pp. 123-154
    • Bhattacharya, K.1    Li, B.2    Luskin, M.3
  • 11
    • 0034396221 scopus 로고    scopus 로고
    • Stability of microstructure for tetragonal to monoclinic martensitic transformations
    • P. Bělík and M. Luskin, Stability of microstructure for tetragonal to monoclinic martensitic transformations. ESAIM: M2AN 34 (2000) 663-685.
    • (2000) ESAIM: M2AN , vol.34 , pp. 663-685
    • Bělík, P.1    Luskin, M.2
  • 12
    • 0031533725 scopus 로고    scopus 로고
    • Numerical solution of the scalar double-well problem allowing microstructure
    • C. Carstensen and P. Plecháč, Numerical solution of the scalar double-well problem allowing microstructure. Math. Comp. 66 (1997) 997-1026.
    • (1997) Math. Comp. , vol.66 , pp. 997-1026
    • Carstensen, C.1    Plecháč, P.2
  • 13
    • 0031644439 scopus 로고    scopus 로고
    • Adaptive algorithms for scalar non-convex variational problems
    • C. Carstensen and P. Plecháč, Adaptive algorithms for scalar non-convex variational problems. Appl. Numer. Math. 26 (1998) 203-216.
    • (1998) Appl. Numer. Math. , vol.26 , pp. 203-216
    • Carstensen, C.1    Plecháč, P.2
  • 14
    • 21844504886 scopus 로고
    • Numerical analysis of oscillations in multiple well problems
    • M. Chipot, C. Collins and D. Kinderlehrer, Numerical analysis of oscillations in multiple well problems. Numer. Math. 70 (1995) 259-282.
    • (1995) Numer. Math. , vol.70 , pp. 259-282
    • Chipot, M.1    Collins, C.2    Kinderlehrer, D.3
  • 15
  • 19
    • 0001800199 scopus 로고
    • Computation of twinning
    • Microstructure and phase transitions. J. Ericksen, R. James, D. Kinderlehrer and M. Luskin Eds. Springer-Verlag, New York
    • C. Collins, Computation of twinning. In Microstructure and phase transitions. J. Ericksen, R. James, D. Kinderlehrer and M. Luskin Eds. IMA Vol. Math. Applic. 54, Springer-Verlag, New York (1993) 39-50.
    • (1993) IMA Vol. Math. Applic. , vol.54 , pp. 39-50
    • Collins, C.1
  • 20
    • 0002058256 scopus 로고
    • The computation of the austenitic-martensitic phase transition
    • Partial differential equations and continuum models of phase transitions. M. Rascle, D. Serre and M. Slemrod Eds. Springer-Verlag, Berlin
    • C. Collins and M. Luskin, The computation of the austenitic-martensitic phase transition. In Partial differential equations and continuum models of phase transitions. M. Rascle, D. Serre and M. Slemrod Eds. Lect. Notes Phys. 344, Springer-Verlag, Berlin (1989) 34-50.
    • (1989) Lect. Notes Phys. , vol.344 , pp. 34-50
    • Collins, C.1    Luskin, M.2
  • 21
    • 0001830197 scopus 로고
    • Computational results for a two-dimensional model of crystalline microstructure
    • Microstructure and phase transitions. J. Ericksen, R. James, D. Kinderlehrer and M. Luskin Eds. Springer-Verlag, New York
    • C. Collins, M. Luskin and J. Riordan, Computational results for a two-dimensional model of crystalline microstructure. In Microstructure and phase transitions. J. Ericksen, R. James, D. Kinderlehrer and M. Luskin Eds. IMA Vol. Math. Applic. 54, Springer-Verlag, New York (1993) 51-56.
    • (1993) IMA Vol. Math. Applic. , vol.54 , pp. 51-56
    • Collins, C.1    Luskin, M.2    Riordan, J.3
  • 22
    • 0001459333 scopus 로고    scopus 로고
    • Numerical computation of rank-one convex envelopes
    • G. Dolzmann, Numerical computation of rank-one convex envelopes. SIAM J. Numer. Anal. 36 (1999) 1621-1635.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1621-1635
    • Dolzmann, G.1
  • 24
    • 0022076980 scopus 로고
    • k high degree efficient symmetrical Gaussian quadrature rules for the triangle
    • D.A. Dunavant, k High degree efficient symmetrical Gaussian quadrature rules for the triangle. Internat. J. Numer. Methods Engrg. 21 (1985) 1129-1148.
    • (1985) Internat. J. Numer. Methods Engrg. , vol.21 , pp. 1129-1148
    • Dunavant, D.A.1
  • 29
    • 0028380768 scopus 로고
    • Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions
    • P.-A. Gremaud, Numerical analysis of a nonconvex variational problem related to solid-solid phase transitions. SIAM J. Numer. Anal. 31 (1994) 111-127.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 111-127
    • Gremaud, P.-A.1
  • 31
    • 0034445429 scopus 로고    scopus 로고
    • Pressurized shape memory thin films
    • special issue in honor of Roger Fosdick, D. Carlson Ed.
    • R.D. James and R. Rizzoni, Pressurized shape memory thin films. J. Elasticity 59, special issue in honor of Roger Fosdick, D. Carlson Ed. (2000) 399-436.
    • (2000) J. Elasticity , vol.59 , pp. 399-436
    • James, R.D.1    Rizzoni, R.2
  • 33
    • 0000635099 scopus 로고    scopus 로고
    • Numerical approach to double well problems
    • M. Kružík, Numerical approach to double well problems. SIAM J. Numer. Anal. 35 (1998) 1833-1849.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1833-1849
    • Kružík, M.1
  • 35
    • 0040170655 scopus 로고    scopus 로고
    • Finite element analysis of microstructure for the cubic to tetragonal transformation
    • B. Li and M. Luskin, Finite element analysis of microstructure for the cubic to tetragonal transformation. SIAM J. Numer. Anal. 35 (1998) 376-392.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 376-392
    • Li, B.1    Luskin, M.2
  • 36
    • 0032364336 scopus 로고    scopus 로고
    • Nonconforming finite element approximation of crystalline microstructure
    • B. Li and M. Luskin, Nonconforming finite element approximation of crystalline microstructure. Math. Comp. 67 (1998) 917-946.
    • (1998) Math. Comp. , vol.67 , pp. 917-946
    • Li, B.1    Luskin, M.2
  • 37
    • 0033456348 scopus 로고    scopus 로고
    • Approximation of a martensitic laminate with varying volume fractions
    • B. Li and M. Luskin, Approximation of a martensitic laminate with varying volume fractions. ESAIM: M2AN 33 (1999) 67-87.
    • (1999) ESAIM: M2AN , vol.33 , pp. 67-87
    • Li, B.1    Luskin, M.2
  • 38
    • 0031322111 scopus 로고    scopus 로고
    • Simultaneous numerical approximation of microstructures and relaxed minimizers
    • Z. Li, Simultaneous numerical approximation of microstructures and relaxed minimizers. Numer. Math. 78 (1997) 21-38.
    • (1997) Numer. Math. , vol.78 , pp. 21-38
    • Li, Z.1
  • 40
    • 0030353296 scopus 로고    scopus 로고
    • Approximation of a laminated microstructure for a rotationally invariant, double well energy density
    • M. Luskin, Approximation of a laminated microstructure for a rotationally invariant, double well energy density. Numer. Math. 75 (1996) 205-221.
    • (1996) Numer. Math. , vol.75 , pp. 205-221
    • Luskin, M.1
  • 41
    • 0347284844 scopus 로고    scopus 로고
    • On the computation of crystalline microstructure
    • M. Luskin, On the computation of crystalline microstructure. Acta Numer. 5 (1996) 191-257.
    • (1996) Acta Numer. , vol.5 , pp. 191-257
    • Luskin, M.1
  • 42
    • 0026843542 scopus 로고
    • Analysis of the finite element approximation of microstructure in micromagnetics
    • M. Luskin and L. Ma, Analysis of the finite element approximation of microstructure in micromagnetics. SIAM J. Numer. Anal. 29 (1992) 320-331.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 320-331
    • Luskin, M.1    Ma, L.2
  • 43
    • 0000650634 scopus 로고
    • The triangular equilibrium element in the solution of plate bending problems
    • L.S.D. Morley, The triangular equilibrium element in the solution of plate bending problems. Aero. Quart. 19 (1968) 149-169.
    • (1968) Aero. Quart. , vol.19 , pp. 149-169
    • Morley, L.S.D.1
  • 44
    • 0030508310 scopus 로고    scopus 로고
    • On the numerical analysis of non-convex variational problems
    • P. Pedregal, On the numerical analysis of non-convex variational problems. Numer. Math. 74 (1996) 325-336.
    • (1996) Numer. Math. , vol.74 , pp. 325-336
    • Pedregal, P.1
  • 46
    • 21744444554 scopus 로고    scopus 로고
    • Numerical approximation of relaxed variational problems
    • T. Roubíček, Numerical approximation of relaxed variational problems. J. Convex Anal. 3 (1996) 329-347.
    • (1996) J. Convex Anal. , vol.3 , pp. 329-347
    • Roubíček, T.1
  • 47
  • 49
    • 0039862786 scopus 로고
    • Error estimates of Morley element
    • Z. Shi, Error estimates of Morley element. Chinese J. Num. Math. Appl. 12 (1990) 102-108.
    • (1990) Chinese J. Num. Math. Appl. , vol.12 , pp. 102-108
    • Shi, Z.1


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