Continuum Mechanics and Thermodynamics

, Volume 29, Issue 6, pp 1291–1311 | Cite as

A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis

  • Vamshi Krishna Chillara
Original Article


We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions—one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measurables like accumulated plastic strain is obtained.


Nonlinear ultrasonics Damage prognosis Structural health monitoring 


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The author would like to thank Prof. Cliff J Lissenden and Prof. Francesco Costanzo, Penn State, for their invaluable comments on an earlier version of the manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg (Outside the USA) 2017

Authors and Affiliations

  1. 1.Materials Physics and Applications, MPA 11Los Alamos National LaboratoryLos AlamosUSA

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