Vol. 14, No. 4, 2019

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Instabilities in the free inflation of a nonlinear hyperelastic toroidal membrane

Sairam Pamulaparthi Venkata and Prashant Saxena

Vol. 14 (2019), No. 4, 473–496
Abstract

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.

Keywords
membrane, limit point, wrinkling, bifurcation, nonlinear elasticity, finite deformation
Mathematical Subject Classification 2010
Primary: 74B20, 74G60, 74K15
Milestones
Received: 7 January 2019
Revised: 1 August 2019
Accepted: 7 August 2019
Published: 13 December 2019
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