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Research Papers

Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes—Part I: Theoretical and Computational Developments

[+] Author and Article Information
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

Xuefeng Zhao

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

1

Corresponding author.

J. Appl. Mech 76(6), 061013 (Jul 27, 2009) (10 pages) doi:10.1115/1.3130805 History: Received February 05, 2008; Revised February 04, 2009; Published July 27, 2009

We present an innovative method for characterizing the distributive elastic properties in nonlinear membranes. The method hinges on an inverse elastostatic approach of stress analysis that can compute the wall stress in a deformed convex membrane structure using assumed elastic models without knowing the realistic material parameters. This approach of stress analysis enables us to obtain the wall stress data independently of the material in question. The stress and strain data collected during a finite inflation motion are used to delineate the elastic property distribution in selected regions. In this paper, we discuss the theoretical and computational underpinnings of the method and demonstrate its feasibility using numerical simulations involving a saclike structure of known material property.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic illustration of the kinematic map

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Figure 2

Undeformed geometry and finite element mesh of the membrane sac: (a) perspective view and (b) bottom view

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Figure 3

The distribution of principal stresses in the membrane sac: (a) t1 and (b) t2

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Figure 4

The percentage difference in principal stresses under the change of elasticity parameters. Upper row: increasing both parameters μ1 and μ2 by 10 times: (a) t1 and (b) t2; lower row: increasing both parameters μ1 and μ2 by 100 times: (c) t1 and (d) t2.

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Figure 5

Identified elasticity parameters of model A knowing the reference metric: (a) μ1 and (b) μ2

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Figure 6

Absolute values of the relative error (in percentage) between identified elasticity parameters and true parameters of model A knowing the reference metric: (a) μ1 and (b) μ2

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Figure 7

Identified elasticity parameters of model A without knowing the reference metric: (a) μ1 and (b) μ2

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Figure 8

Absolute values of the relative error (in percentage) between identified elasticity parameters and true parameters of model A without knowing the reference metric: (a) μ1 and (b) μ2

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Figure 9

Identified elasticity parameters of model B knowing the reference metric: (a) ν1 and (b) ν2

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Figure 10

Identified elasticity parameters of model B without knowing the reference metric: (a) ν1 (b) ν2

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Figure 11

Comparison between the “experimental” stress invariants and the predictions of model B: (a) J1 and (b) J2

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