We present a nondestructive approach to map the heterogeneous viscoelastic moduli from time harmonic motion via a constrained optimization strategy under the framework of finite element techniques. The adjoint equations are carefully derived to determine the gradient of the objective function with respect to the viscoelastic moduli. The feasibility of this inverse scheme is tested with simulated experiments under various driving frequencies. We observe that the overall strategy results in well-reconstructed moduli. For low frequencies, however, the mapped loss modulus is of inferior quality. To explain this observation, we analyze two simple one-dimensional (1D) models theoretically. The analysis reveals that the known displacement amplitude is less sensitive to the loss modulus value at low frequencies. Thus, we conclude that the inverse method is incapable of finding a well-reconstructed loss modulus distribution for low driving frequencies in the presence of noisy data. Overall, the inverse algorithms presented in this work are highly robust to map the storage and loss modulus with high accuracy given that a proper range of frequencies are utilized.
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April 2018
Research-Article
Mapping the Viscoelastic Behavior of Soft Solids From Time Harmonic Motion
Yue Mei,
Yue Mei
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
Texas A&M University,
College Station, TX 77843
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Sevan Goenezen
Sevan Goenezen
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: sevangoenezen@gmail.com
Texas A&M University,
College Station, TX 77843
e-mail: sevangoenezen@gmail.com
Search for other works by this author on:
Yue Mei
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
Texas A&M University,
College Station, TX 77843
Sevan Goenezen
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: sevangoenezen@gmail.com
Texas A&M University,
College Station, TX 77843
e-mail: sevangoenezen@gmail.com
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 6, 2017; final manuscript received January 8, 2018; published online February 2, 2018. Assoc. Editor: Yihui Zhang.
J. Appl. Mech. Apr 2018, 85(4): 041003 (11 pages)
Published Online: February 2, 2018
Article history
Received:
October 6, 2017
Revised:
January 8, 2018
Citation
Mei, Y., and Goenezen, S. (February 2, 2018). "Mapping the Viscoelastic Behavior of Soft Solids From Time Harmonic Motion." ASME. J. Appl. Mech. April 2018; 85(4): 041003. https://doi.org/10.1115/1.4038966
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