Research Papers

Identification of Material Parameters of a Hyper-Elastic Body With Unknown Boundary Conditions

[+] Author and Article Information
M. Hajhashemkhani

Department of Mechanical Engineering,
Shiraz University,
Shiraz 71936, Iran
e-mail: m-hajhashemkhani@shirazu.ac.ir

M. R. Hematiyan

Department of Mechanical Engineering,
Shiraz University,
Shiraz 71936, Iran
e-mail: mhemat@shirazu.ac.ir

S. Goenezen

Department of Mechanical Engineering,
Texas A & M University,
College Station, TX 77843
e-mail: sgoenezen@tamu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 1, 2017; final manuscript received January 27, 2018; published online March 12, 2018. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 85(5), 051006 (Mar 12, 2018) (13 pages) Paper No: JAM-17-1659; doi: 10.1115/1.4039170 History: Received December 01, 2017; Revised January 27, 2018

Identification of material properties of hyper-elastic materials such as soft tissues of the human body or rubber-like materials has been the subject of many works in recent decades. Boundary conditions generally play an important role in solving an inverse problem for material identification, while their knowledge has been taken for granted. In reality, however, boundary conditions may not be available on parts of the problem domain such as for an engineering part, e.g., a polymer that could be modeled as a hyper-elastic material, mounted on a system or an in vivo soft tissue. In these cases, using hypothetical boundary conditions will yield misleading results. In this paper, an inverse algorithm for the characterization of hyper-elastic material properties is developed, which takes into consideration unknown conditions on a part of the boundary. A cost function based on measured and calculated displacements is defined and is minimized using the Gauss–Newton method. A sensitivity analysis is carried out by employing analytic differentiation and using the finite element method (FEM). The effectiveness of the proposed method is demonstrated through numerical and experimental examples. The novel method is tested with a neo–Hookean and a Mooney–Rivlin hyper-elastic material model. In the experimental example, the material parameters of a silicone based specimen with unknown boundary condition are evaluated. In all the examples, the obtained results are verified and it is observed that the results are satisfactory and reliable.

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Fig. 1

Reference and deformed configuration for a deformable solid

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Fig. 2

(a) target material attached to an unknown material and (b) separate illustration of deformed target material after applying external forces for inverse analysis

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Fig. 3

The geometry of the direct problem and its boundary conditions

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Fig. 4

The geometry of the inverse problem with some controlling and sampling points

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Fig. 7

The inverse problem under plane strain conditions with two controlling points and eight sampling points

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Fig. 5

The deformed shape of the interface AB obtained by the inverse analysis for the neo–Hookean model with one controlling point and six sampling points under plane strain conditions

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Fig. 6

The deformed shape of the interface AB obtained by the inverse analysis for the neo–Hookean model with one controlling point and eight sampling points under plane strain conditions

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Fig. 8

The deformed shape of the interface AB obtained by the inverse analysis for the neo–Hookean model with two controlling points and eight sampling points under plane strain conditions

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Fig. 17

Sampling points used for inverse analysis

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Fig. 10

Nominal stress–stretch curves for the Mooney–Rivlin hyper-elastic material with constants μ1 = 80 Pa, μ2 = 20 Pa, and K1 = 2000 and the material parameters reported in Table 8

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Fig. 11

A part of the speckle pattern on the sample surface and a unique feature in a facet

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Fig. 12

(a) Dimensions of the rectangular sample and (b) the sample with sandpaper at both ends and random gray pattern on its surface

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Fig. 13

Force-stretch curve of the rectangular silicone sample

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Fig. 14

(a) Dimensions of the silicone sample and (b) the silicone sample molded in the customized wooden mold

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Fig. 15

The silicone sample under tension with INSTRON 5567

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Fig. 16

The part of the sample used for inverse analysis

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Fig. 18

Force-stretch curve of the neo–Hookean model obtained from the inverse analysis in comparison with the experimental curve

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Fig. 19

(a) Displacement contour in the member obtained from ISTRA 4D software in mm and (b) displacement contour corresponding to the results of the inverse analysis in m

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Fig. 20

Comparison of the deformed shape of the interface AB in the experiment and reconstructed from the inverse analysis

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Fig. 9

The inverse problem with three controlling points and ten sampling points for the plane stress condition



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