Experimental Mechanics

, Volume 52, Issue 7, pp 865–880 | Cite as

Membrane Curvatures and Stress-strain Full Fields of Axisymmetric Bulge Tests from 3D-DIC Measurements. Theory and Validation on Virtual and Experimental results

  • G. Machado
  • D. FavierEmail author
  • G. Chagnon


The bulge test is mostly used to analyze equibiaxial tensile stress state at the pole of inflated isotropic membranes. Three-dimensional digital image correlation (3D-DIC) technique allows the determination of three-dimensional surface displacements and strain fields. In this paper, a method is proposed to determine also the membrane stress tensor fields for in-plane isotropic materials, independently of any constitutive equation. Stress-strain state is then known at any surface point which enriches greatly experimental data deduced from the axisymmetric bulge tests. Our method consists, first in calculating from the 3D-DIC experimental data the membrane curvature tensor at each surface point of the bulge specimen. Then, curvature tensor fields are used to investigate axisymmetry of the test. Finally in the axisymmetric case, membrane stress tensor fields are determined from meridional and circumferential curvatures combined with the measurement of the inflating pressure. Our method is first validated for virtual 3D-DIC data, obtained by numerical simulation of a bulge test using a hyperelastic material model. Afterward, the method is applied to an experimental bulge test performed using as material a silicone elastomer. The stress-strain fields which are obtained using the proposed method are compared with results of the finite element simulation of this overall bulge test using a neo-Hookean model fitted on uniaxial and equibiaxial tensile tests.


Bulge test Biaxial tensile test 3D image correlation Membrane Curvatures 



We would like to thank the French ANR for supporting this work through the project RAAMO (“Robot Anguille Autonome pour Milieux Opaques”).


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Copyright information

© Society for Experimental Mechanics 2011

Authors and Affiliations

  1. 1.Laboratoire 3SRUniversité de Grenoble/CNRSGrenoble Cedex 9France

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