Asymptotic Study on a Soft Thin Layer: The Non-Convex Case

REFERENCES

• Suquet , P. 1988 . “Discontinuities and plasticity,” . In Nonsmooth mechanics and applications , 315 – 323 . Springer-Verlag .
   Google Scholar
• Licht , C. 1992 . “Comportement asymptotique d'une bande dissipative mince de faible rigidité,” . Compte Rendu Académie des Sciences Série I. , 317 : 429 – 433 .
   Google Scholar
• Licht , C. and Michaille , G. 1996 . “Une modélisation du comportement d'un joint collé élastique,” . Compte Rendu Académie des Sciences Série I. , 322 : 295 – 300 .
   Google Scholar
• Licht , C. and Michaille , G. 1997 . “A modelling of elastic adhesive bonded joints,” . Adv. Math. Sci. Appl. , 7 : 711 – 740 .
   Google Scholar
• Ould-Khaoua , A. , Lebon , F. , Licht , C. and Michaille , G. “Thin layers in elasticity: a theoretical and numerical study,” . ASME, editor, Proceedings of the 1996 ESDA Conference, volume 4 . pp. 171 – 178 .
   Google Scholar
• Lebon , F. , Ould Khaoua , A. and Licht , C. 1997 . “Numerical study of soft adhesively bonded joints in finite elasticity,” . Comp. Mech. , 21 : 134 – 140 .
   Google Scholar
• Frémond , M . 1987 . “Matériaux á mémoire de forme,” . Compte Rendu Académie des Sciences , 304 : 239 – 214 .
   Google Scholar
• Ericksen , J. L. 1991 . “Equilibrium of bars,” . J. Elast. , 5 : 191 – 201 .
   Google Scholar
• Aberavatne , R. , Bhattacharya , K. and Knowles , J. K. 2000 . “Strain-energy functions with multiple local minima: modeling phase transformations using finite thermoelasticity,” . In Nonlinear elasticity: Theory and application , Edited by: Fu , Y. and Ogden , R. W. Cambridge University Press .
   Google Scholar
• Aberayatne , R. , Chu , C. and James , R. D. 1996 . “Kinetics of materials with wiggly energies: theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy,” . Phil. Mag. , A73 : 457 – 497 .
   Google Scholar
• Del Piero , G. and Rizzoni , R. “Weak local energy minimizers in finite elasticity,” in preparation
   Google Scholar
• Aberayatne , R. and Knowles , J. K. 1990 . “On the driving traction acting on a surface of strain discontinuity in a continuum,” . J. Mech. Phys. Solids , 38 : 345 – 360 .
   Google Scholar
• Aberayatne , R. and Knowles , J. K. 1991 . “Kinetic relations and the propagation of phase boundaries in solids,” . Arch. Rational. Mech. Anal. , 114 : 119 – 154 .
   Google Scholar
• Sanchez-Hubert , J. and Sanchez-Palencia , E. 1992 . Introduction aux méthodes asymptotiques et á l'homogénisation , Paris : Masson .
   Google Scholar
• Panagiotopoulos , P. D. 1985 . Inequality problems in mechanics and applications Convex and nonconver energy functions , Birkhauser .
   Google Scholar
• Morean , J. J. , Panagiotopoulos , P. D. and Strang , G. 1988 . Topics in nonsmooth mechanics , Birkhauser .
   Google Scholar
• Mistakidis , E. S. and Panagiotopoulos , P. D. 1997 . “Numerical treatment of problems involving nonmonotone boundary or stress-strain laws,” . Comp. and Struct. , 64 : 553 – 565 .
   Google Scholar
• Pagano , S. , Alart , P. and Maisonneuve , O. 1998 . “Solid-solid phase transition modelling. Local and global minimizations of non-convex and relaxed potetials. Isothermal case for shape memory alloys,” . International Journal of Engineering Sciences , 36 : 1143 – 1172 .
   Google Scholar
• Sagan , H. 1992 . An introduction to the calculus of variations , New York : Dover Publications .
   Google Scholar
• Lebon , F. and Rizzoni , R. “Aymptotic analysis of soft thin layers with nonconvex energy,” . 16th AIMETA Congress of Theoretical and Applied Mechanics . Ferrara.
   Google Scholar
• Dacorogna , B. 1989 . Direct methods in the calculus of variations , Berlin : Springer-Verlag .
   Google Scholar
• Klarbring , A. 1991 . “Derivation of the adhesively bonded joints by the asymptotic expansion method,” . International Journal of Engineering Science , 29 : 493 – 512 .
   Web of Science ®Google Scholar
• Lebon , F. and Ronel-Idrissi , S. 2004 . “Asymptotic analysis of Mohr-Coulomb and Drucker Prager soft thin layers,” . International Journal of Steel and Composite Structures , 4 : 133 – 148 .
   Google Scholar