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Instabilities in
the free inflation of a nonlinear hyperelastic toroidal
membrane
Sairam Pamulaparthi Venkata and Prashant Saxena |
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Vol. 14 (2019), No. 4, 473–496
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Abstract |
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We study an incompressible nonlinear hyperelastic thin-walled toroidal membrane of circular cross-section subjected to inflation due to a uniform pressure, comparing three elastic constitutive models (neo-Hookean, Mooney–Rivlin, and Ogden) and different torus shapes. A variational approach is used to derive the equations of equilibrium and bifurcation. An analysis of the pressure–deformation plots shows occurrence of the well-known limit point (snap-through) instabilities in the membrane. Calculations are performed to study the elastic buckling point to predict bifurcation of the solution corresponding to the loss of symmetry. Tension field theory is employed to study the wrinkling instability that, in this case, typically occurs near the inner regions of tori with large aspect ratios. |
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Keywords
membrane, limit point, wrinkling, bifurcation, nonlinear
elasticity, finite deformation
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Mathematical Subject Classification 2010
Primary: 74B20, 74G60, 74K15
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Milestones
Received: 7 January 2019
Revised: 1 August 2019
Accepted: 7 August 2019
Published: 13 December 2019
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Authors |
| Sairam Pamulaparthi Venkata | |
| Department of Mechanical and
Aerospace Engineering, Field of Theoretical and Applied
Mechanics Cornell University Ithaca, NY United States |
Department of Mechanical and
Aerospace Engineering Indian Institute of Technology Hyderabad Telangana India |
| Prashant Saxena | |
| Glasgow Centre for Computational
Engineering James Watt School of Engineering University of Glasgow Glasgow United Kingdom |
Department of Mechanical and
Aerospace Engineering Indian Institute of Technology Hyderabad Telangana India |
