Elastic theory of unconstrained non-Euclidean plates

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 4, 2009, Pages 762-775

  Efrati, E ^a   Sharon, E ^a   Kupferman, R ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Hyper elasticity; Metric; Non Euclidean; Residual stress; Thin plates

Indexed keywords

ELASTICITY; RESIDUAL STRESSES; STRENGTH OF MATERIALS;

BUCKLING TRANSITIONS; ELASTIC BODIES; ELASTIC STRUCTURES; ELASTIC THEORIES; EQUILIBRIUM SHAPES; EXTERNAL CONSTRAINTS; EXTERNAL FORCES; HYPER-ELASTICITY; INTRINSIC GEOMETRIES; LARGE DISPLACEMENTS; LINEAR ELASTICITIES; MATHEMATICAL FRAMEWORKS; METRIC; NON-EUCLIDEAN; PLATE THEORIES; PLATE THICKNESS; SMALL STRAINS; THIN PLATE THEORIES; THIN PLATES;

PLATES (STRUCTURAL COMPONENTS);

EID: 61549105950     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.12.004     Document Type: Article

References (29)

1. Audoly B., and Boudaoud A. Self-similar structures near boundaries in strained systems. Phys. Rev. Lett. 91 (2003) 086105
2. Behl, M., Lendlein, A., 2007. Soft matter gets smart. Materials Today 10, 4, 2007.
3. Ben Amar M., and Goriely A. Growth and instabilities in elastic tissues. J. Mech. Phys. Solids 53 (2005) 2284-2319
4. Cerda E., and Mahadevan L. Geometry and physics of wrinkling. Phys. Rev. Lett. 90 (2003) 074302-1
5. Ciarlet P.G. Mathematical Elasticity vol. 2 (1997), North-Holland, Amsterdam
6. Ciarlet P.G. An Introduction to Differential Geometry with Applications to Elasticity (2005), Springer, Dordrecht, The Netherlands
7. Efimenko K., Rackaitis M., Manias E., Vaziri A., Mahadevan L., and Genzer J. Nested self-similar wrinkling patterns in skins. Nat. Mat. 4 (2005) 293-297
8. Forterre Y., Skotheim J.M., Dumais J., and Mahadevan L. How the Venus flytrap snaps. Nature 433 (2005) 421-425
9. Friesecke G., James R.D., and Müller S. A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Arch. Ration. Mech. Anal. 180 (2006) 183-236
10. Goriely A., and Ben-Amar M. On the definition and modeling of incremental, cumulative, and continuous growth laws in morphoelasticity. Biomechan. Model Mechanobiol. 6 (2007) 289-296
11. Green A.E., and Naghdi P.M. Some remarks on elastic-plastic deformation at finite strain. Int. J. Eng. Sci. 9 12 (1971) 1219-1229
12. Hoger A. Residual stress in an elastic body: a theory for small strains and arbitrary rotation. J. Elasticity 31 (1993) 1-24
13. Holmes D.P., and Crosby A.J. Snapping surfaces. Adv. Mater. 19 (2007) 3589-3593
14. Huang J., Juszkiewicz M., de Jeu W.H., Cerda E., Emrick T., and Menon N. Capillary wrinkling of floating thin polymer films. Science 317 (2007) 650-653
15. John F. Estimates for the derivatives of the stresses in thin shell and interior shell equation. Commun. Pure Appl. Math. 18 (1965) 235-267
16. Klein Y., Efrati E., and Sharon E. Shaping of elastic sheets by prescription of non-Euclidean metrics. Science 315 (2007) 1116-1120
17. Koiter W.T. On the nonlinear theory of thin elastic shells. Proc. Kon. Ned. Acad. Wetensch. B69 (1966) 1-54
18. Koiter W.T. Comment on: The linear and non-linear equilibrium equations for thin elastic shells according to the Kirchhoff-Love hypotheses. Int. J. Mech. Sci. 12 (1970) 663-664
19. Love A.E.H. The Mathematical Theory of Elasticity (1906), Cambridge University Press, Cambridge
20. Marder M., and Papanicolaou N. Geometry and elasticity of strips and flowers. J. Stat. Phys. 125 (2006) 1065-1092
21. Mora T., and Boudaoud A. Buckling of swelling gels. Eur. Phys. J. E Soft Matter 20 2 (2006) 119-124
22. Park J.S., Chu J.S.F., Cheng C., Chen F., Chen D., and Li S. Differential effects of equiaxial and uniaxial strain on mesenchymal stem cells. Biotechnol. Bioeng. 88 (2004) 359-368
23. Sharon E., Roman B., Marder M., Shin G.S., and Swinney H.L. Mechanics: buckling cascades in free sheets. Nature 419 (2002) 579-580
24. Sharon E., Marder M., and Swinney H.L. Leaves, flowers and garbage bags: making waves. Am. Sci. 92 (2004) 254-261
25. Sidoroff F. Incremental constitutive equation for large strain elasto plasticity. Int. J. Eng. Sci. 20 1 (1982) 19-26
26. Sidoroff F., and Dogui A. Thermodynamics and duality in finite elastoplasticity. Continuum Thermomech. (2002) 389-400
27. Truesdell C. The mechanical foundations of elasticity and fluid dynamics. Indiana Univ. Math. J. 1 (1952) 125-300
28. Venkataramani S.C. Lower bounds for the energy in a crumpled elastic sheet-a minimal ridge. Nonlinearity 17 (2004) 301-312
29. Willmore T.J. Reimannian Geometry (1993), Oxford University Press, Oxford