The study of asymptotically fine wrinkling in nonlinear elasticity using a boundary layer analysis

Journal of the Mechanics and Physics of Solids

Volumn 61, Issue 8, 2013, Pages 1691-1711

  Maclaurin, James ^a   Chapman, Jon ^a   Wyn Jones, Gareth ^b   Roose, Tiina ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Bifurcation; Boundary layer; Nonlinear elasticity; Perturbation expansion; Wrinkling

Indexed keywords

BOUNDARY LAYER ANALYSIS; ELASTO-STATIC PROBLEM; ELECTRONIC SUPPLEMENTARY MATERIALS; INCOMPRESSIBLE ELASTICITY; NONLINEAR ELASTICITY; PERTURBATION EXPANSIONS; POSTBUCKLING BEHAVIOUR; WRINKLING;

BIFURCATION (MATHEMATICS); BOUNDARY LAYERS; BUCKLING; ELASTICITY; ORDINARY DIFFERENTIAL EQUATIONS;

NONLINEAR ANALYSIS;

EID: 84879844948     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2013.04.003     Document Type: Article

References (23)

1. M.A. Biot Fundamental skin effect in anisotropic solid mechanics Int. J. Solids Struct. 2 1966 645 663
2. Fabian Brau, Hugues Vandeparre, Abbas Sabbah, Christophe Poulard, Arezki Boudaoud, and Pascal Damman Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators Nat. Phys. 7 2011 56 60
3. Y. Cao, and J.W. Hutchinson From wrinkles to creases in elastomers: the instability and imperfection-sensitivity of wrinkling Proc. R. Soc. A 468 2012 94 115
4. Ciprian Coman Global asymptotic approximations for wrinkling of polar orthotropic annular plates in tension Int. J. Solids Struct. 47 2010 1572 1579
5. Ciprian D. Coman, and Andrew Bassom On the wrinkling of a pre-stressed annular thin film in tension J. Mech. Phys. Solids 55 2007 1601 1617
6. Julien Dervaux, and Martine Ben Amar Buckling condensation in constrained growth J. Mech. Phys. Solids 59 2011 538 560
7. Michel Destrade, Aisling Ni Annaidh, and Ciprian D. Coman Bending instabilities of soft biological tissues Int. J. Solids Struct. 46 2009 4322 4330
8. Lawrence Evans Partial Differential Equations 1998 American Mathematical Society
9. Alain Goriely, R. Vandiver, and M. Destrade Nonlinear euler buckling Proc. R. Soc. A 464 2008 3003 3019
10. D. Haughton, and A. Orr On the eversion of compressible elastic cylinders Int. J. Solids Struct. 34 1997 1893 1914
11. Evan Hohlfeld, and L. Mahadevan Unfolding the sulcus Phys. Rev. Lett. 106 2011
12. W.T. Koiter Elastic Stability of Solids and Structures 2009 Cambridge University Press
13. Bo Li, Yan-Ping Cao, and Xi-Qiao Feng Growth and surface folding of esophageal mucosa: a biomechanical model Journal of Biomechanics 44 2011 182 188
14. Bo Li, Yan-Ping Cao, Xi-Qiao Feng, and Huajian Gao Surface wrinkling of mucosa induced by volumetric growth: theory, simulation and experiment J. Mech. Phys. Solids 59 2011 758 774
15. MacLaurin, James, 2012. The buckling of capillaries in tumours. Ph.D. thesis. University of Oxford.
16. MacLaurin, James, Chapman, Jon, Jones, Gareth Wyn, Roose, Tiina, 2012. The buckling of capillaries in solid tumours. Proc. R. Soc. A.
17. Jerrold E. Marsden, and Thomas J.R. Hughes Mathematical Foundations of Elasticity 1983 Dover
18. Derek Moulton, and Alain Goriely Circumferential buckling instability of a growing cylindrical tube J. Mech. Phys. Solids 59 2011 525 537
19. Derek Moulton, and Alain Goriely Possible role of differential growth in airway wall remodeling in asthma J. Appl. Physiol. 110 2011 1003 1012
20. Pablo V. Negron-Marrero, and Errol Montes-Pizarro The complementing condition and its role in a bifurcation theory applicable to nonlinear elasticity N.Y. J. Math. 17a 2011 1 12
21. Pablo V. Negron-Marrero, and Errol Montes-Pizarro Violation of the complementing condition and local bifurcation in nonlinear elasticity J. Elasticity 107 2012 151 178
22. B.S. Ng, and W.H. Reid The compound matrix method for ordinary differential systems J. Comput. Phys. 58 1985 209 228
23. R. Ogden Non-Linear Elastic Deformations 1984 Ellis Horwood Limited