Constitutive model for third harmonic generation in elastic solids

Vamshi Krishna Chillara, Clifford Jesse Lissenden, III

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)69-74
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume82
DOIs
StatePublished - Jun 1 2016

Fingerprint

Harmonic Generation
Constitutive Model
Harmonic generation
Constitutive models
Harmonic
Nonlinearity
Geometric Nonlinearity
Guided Waves
Guided electromagnetic wave propagation
Nonlinear Response
Elastic Material
Model
Two Parameters
Compression
Limiting
Ultrasonics
Tend
Numerical Simulation
Computer simulation
Zero

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "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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Constitutive model for third harmonic generation in elastic solids. / Chillara, Vamshi Krishna; Lissenden, III, Clifford Jesse.

In: International Journal of Non-Linear Mechanics, Vol. 82, 01.06.2016, p. 69-74.

Research output: Contribution to journalArticle

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