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research-article

Mapping the Viscoelastic Behavior of Soft Solids from Time Harmonic Motion

[+] Author and Article Information
Yue Mei

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843
meiyue1989@gmail.com

Sevan Goenezen

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843
sevangoenezen@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4038966 History: Received October 06, 2017; Revised January 08, 2018

Abstract

We present a non-destructive 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, however for low frequencies, the mapped loss modulus is of inferior quality. To explain this observation, we analyze two simple one dimensional models theoretically. The analysis reveals that the known displacement amplitude is insensitive to the loss modulus value at low frequencies. Thus, we conclude that the inverse algorithm 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 the right range of frequencies are utilized.

Copyright (c) 2018 by ASME
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