A unifying model of weakly nonlinear elastic waves; large on large theory

Christopher M. Kube, Anubhav Roy, Daniel S. Jensen, Darren W. Branch

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This article reconsiders traditional topics in nonlinear elastic waves and nonlinear ultrasonics. Herein, higher-order coupling between finite initial deformation and finite amplitude waves are considered. To allow for coupling, a large-on-large deformation model is developed and used to generate the equations of motion relative to the deformed and undeformed material configurations. Thus, the equations of motion provide a single setting to describe topics in nonlinear elastic waves such as acoustoelasticity, second harmonic generation, and coupling relations between these topics. The model is evaluated to recover the traditional linearized acoustoelastic relations and predicted second harmonic amplitudes. Then, the so-called large acoustoelasticity theory is developed for anisotropic materials with specific results given for isotropic materials. Last, the stress influence on second harmonic generation is presented.

Original languageEnglish (US)
Pages (from-to)1294-1310
Number of pages17
JournalJournal of the Acoustical Society of America
Issue number2
StatePublished - Feb 1 2022

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


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