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Research Papers

Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes—Part II: Experimental Validation

[+] Author and Article Information
Xuefeng Zhao

Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, The University of Iowa, Iowa City, IA 52242-1527

Xiaolin Chen

Mechanical Engineering Program, School of Engineering and Computer Science, Washington State University, Vancouver, WA 98686

Jia Lu1

Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, The University of Iowa, Iowa City, IA 52242-1527jia-lu@uiowa.edu

1

Corresponding author.

J. Appl. Mech 76(6), 061014 (Jul 27, 2009) (8 pages) doi:10.1115/1.3130810 History: Received February 05, 2008; Revised February 04, 2009; Published July 27, 2009

Following the theoretical and computational developments of the pointwise membrane identification method reported in the first part of this paper, we perform a finite inflation test on a rubber balloon to validate the method. The balloon is inflated using a series of pressurized configurations, and a surface mesh that corresponds through all the deformed states is derived using a camera-based three dimensional reconstruction technique. In each configuration, the wall tension is computed by the finite element inverse elastostatic method, and the in-plane stretch relative to a slightly pressurized configuration is computed with the aid of finite element interpolation. Based on the stress-strain characteristics, the Ogden model is employed to describe the material behavior. The elastic parameters at every Gauss point in a selected region are identified simultaneously. To verify the predictive capability of the identified material model, the deformation under a prescribed pressure is predicted using the finite element method and is compared with the physical measurement. The experiment shows that the method can effectively delineate the distributive elastic properties in the balloon wall.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A photo of the rubber balloon used in the process of 3D geometry reconstruction

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Figure 2

Reconstructed meshes of the deformed configurations

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Figure 3

Distribution of principal tensions in deformed configuration 13: (a) t1 and (b) t2

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Figure 4

The percentage difference of principal tensions under the change of elasticity parameters. Upper row: increasing both parameters μ1 and μ2 to ten times, (a) t1 and (b) t2; lower row: keeping μ1 unchanged and increasing μ2 to five times, (c) t1 and (d) t2.

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Figure 5

The distribution of the coaxiality indicator ε (in percentage) in selected configurations: (a) configuration 1 and (b) configuration 13. Both figures were scaled to fit the canvas for clarity.

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Figure 6

Identified elasticity parameters of the Ogden model: (a) μ1, (b) μ2, and (c) μ3

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Figure 7

Distribution of the ratio of μ1 to μ2

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Figure 8

Comparison between the experimental and the identified tension curves: (a) t1 and (b) t2

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Figure 9

Comparison between the deformed configuration computed from finite element method using the identified elastic parameters and the experimentally measured configuration. (a) Thin gray mesh: experimental (whole domain); thick black mesh: finite element modeled (boundary-effect-free region) and (b) distribution of the position error e=‖x−x̂‖/L.

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