Acoustoelastic theory for elastic–plastic materials

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Abstract
A generalized acoustoelastic theory is presented for the determination of propagation speeds of plane waves in bodies experiencing elastic–plastic deformation. The development is carried out in the framework of an isothermal theory for the response of an elastic–plastic continuum by considering the small deformations of a propagating wave superimposed on a finite homogeneous deformation. Specific expressions for the velocities are generated by assuming an isotropic form of the free energy which includes cubic terms in the elastic strain. The velocities are first presented for a finite strain theory and then reduced to linear form for the case of infinitesimal strain.

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