Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation

International Journal of Mechanical Sciences

Volumn 65, Issue 1, 2012, Pages 18-23

  Pamplona, D C ^a   Mota, D E J S ^a  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Circular membrane; Elastic foundation; Finite deformations; Hyperelastic material; Inflation

Indexed keywords

CIRCULAR MEMBRANES; ELASTIC FOUNDATION; FINITE DEFORMATIONS; HYPERELASTIC MATERIALS; INFLATION;

BIOLOGICAL ORGANS; BIOMECHANICS; DEFORMATION; LIQUIDS; RUNGE KUTTA METHODS; SILICONES;

MEMBRANES;

EID: 84870060196     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2012.08.010     Document Type: Article

References (23)

1. A.E. Green, and J.E. Adkins Large elastic deformations and non-linear continuum mechanics 2nd ed 1960 Clarendon Press Oxford
2. A.H. Corneliussen, and R.T. Shield Finite deformation of elastic membranes with application to the stability of an inflated and extended tube Archive for Rational Mechanics and Analysis 7 1961 273 304
3. H. Alexander The tensile instability of inflated cylindrical membrane as effected by an axial load International Journal of Engineering Science 5 1970 177 193
4. D.M. Haughton, and R.W. Ogden On the incremental equations in non-linear elasticity II: bifurcation of pressurized spherical shells Journal of the Mechanics and Physics of Solids 26 2 1978 111 138
5. A.M. Ratner Tensile stability of cylindrical membranes International Journal of Non-Linear Mechanics 18 1983 133 147
6. X. Li, and D.J. Steigmann Finite plane twist of an annular membrane The Quarterly Journal of Mechanics and Applied Mathematics 46 1993 601 625
7. E.M. Haseganu, and D.J. Steigmann Theoretical flexure of a pressurized cylindrical membrane International Journal of Solids and Structures 31 1994 27 50
8. Y. Chen Stability and bifurcation of inflated cylindrical elastic membranes L.A. Godoy, S.R. Idelshon, P.A.A. Laura, D.T. Mook, Applied mechanics in the Americas 1 1995 A.A.M Associacion Argentina de Mecanica Computacional Buenos Aires, Argentina 404 409
9. P.B. Gonçalves, R.M. Soares, and D.C. Pamplona Nonlinear vibrations of a radially stretched circular hyperelastic membrane Journal of Sound and Vibration 327 2009 231 248
10. T. Sohail, and B. Nadler On the contact of an inflated spherical membrane-fluid structure with a rigid conical indenter Acta Mechanica 218 3-4 2011 225 235
11. R.W. Ogden Non-Linear Elastic Deformations 4th ed. 1997 Dover Publications Mineola, NY
12. R.W. Ogden Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids Proceedings of the Royal Society of London A326 1972 565 584
13. H. Alexander Tensile instability of initially spherical balloons International Journal of Engineering Sciences 9 1971 151 162
14. D. Pamplona, and L. Bevilacqua Large deformations under axial force and moment load of initially flat membranes International Journal of Non-Linear Mechanics 27 1992 639 650
15. D. Pamplona, P.B. Gonçalves, M. Davidovich, and H.I. Weber Finite axisymmetric deformations of an initially stressed fluid-filled cylindrical membrane International Journal of Solids and Structures 38 2001 2033 2047
16. D. Pamplona, P.B. Gonçalves, and S.R.X. Lopes Finite deformations of cylindrical membrane under internal pressure International Journal of Mechanical Sciences 48 6 2006 683 696
17. R.W. Ogden, and D.M. Haughton Bifurcation of inflated circular cylinders of elastic material under axial loading I. membrane theory for thin-walled tubes Journal of the Mechanics and Physics of Solids 27 1979 179 212
18. A.C. Pipkin Integration of an equation in membrane theory Zeitschrift für Angewandte Mathematik und Physik 19 1968 818 819
19. M. Aleksandrov, and V. Salamatova The bending of a circular membrane on a linearly deformed foundation Journal of Applied Mathematics and Mechanics 75 2011 472 475
20. D.C. Pamplona, C.R. Carvalho, H. Radwanski, and I. Pitanguy Changes in the Characterization of the human scalp due to the process of successive skin expansion H.S. Costa Mattos, M. Alves, Mechanics of Solids in Brazil 2009 2009 ABCM publishing Rio de Janeiro 425 436
21. M. Hetenyi Beams on elastic foundation: theory with applications in the fields of civil and mechanical engineering 1st ed. 1974 University of Michigan Press Ann Arbor
22. D.M. Haughton Axially elastic membranes subjected to fluid loads IMA Journal of Applied Mathematics 56 1996 303 320
23. Pamplona DC, Carvalho CR, Characterization of human skin through skin expansion, Journal of Mechanics of Materials and Structures. (2012) in press.