TY - JOUR
T1 - Constitutive model for third harmonic generation in elastic solids
AU - Chillara, Vamshi Krishna
AU - Lissenden, Cliff J.
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Award number 1300562 . Vamshi Chillara also acknowledges the support from the Penn State College of Engineering in the form of Distinguished Teaching Fellowship .
Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - In this article, we present a new constitutive model for studying ultrasonic third harmonic generation in elastic solids. The model is hyperelastic in nature with two parameters characterizing the linear elastic material response and two other parameters characterizing the nonlinear response. The limiting response of the model as the nonlinearity parameters tend to zero is shown to be the well-known St Venant-Kirchhoff model. Also, the symmetric response of the model in tension and compression and its role in third harmonic generation is shown. Numerical simulations are carried out to study third harmonic generation in materials characterized by the proposed constitutive model. Predicted third harmonic guided wave generation reveals an increasing third harmonic content with increasing nonlinearity. On the other hand, the second harmonics are independent of the nonlinearity parameters and are generated due to the geometric nonlinearity. The feasibility of determining the nonlinearity parameters from third harmonic measurements is qualitatively discussed.
AB - In this article, we present a new constitutive model for studying ultrasonic third harmonic generation in elastic solids. The model is hyperelastic in nature with two parameters characterizing the linear elastic material response and two other parameters characterizing the nonlinear response. The limiting response of the model as the nonlinearity parameters tend to zero is shown to be the well-known St Venant-Kirchhoff model. Also, the symmetric response of the model in tension and compression and its role in third harmonic generation is shown. Numerical simulations are carried out to study third harmonic generation in materials characterized by the proposed constitutive model. Predicted third harmonic guided wave generation reveals an increasing third harmonic content with increasing nonlinearity. On the other hand, the second harmonics are independent of the nonlinearity parameters and are generated due to the geometric nonlinearity. The feasibility of determining the nonlinearity parameters from third harmonic measurements is qualitatively discussed.
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U2 - 10.1016/j.ijnonlinmec.2016.02.008
DO - 10.1016/j.ijnonlinmec.2016.02.008
M3 - Article
AN - SCOPUS:84961615226
SN - 0020-7462
VL - 82
SP - 69
EP - 74
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
ER -