Reflection of ultrasound from a region of cubic material nonlinearity due to harmonic generation

Two models are proposed to obtain information on the material nonlinearity of an inclusion in a solid body. Material nonlinearity is usually generated by the development of material microscale damage. When the region of nonlinear material is large, incidence of ultrasound on the interface between the perfectly joined regions of linear and nonlinear material behavior produces very useful information. Using the continuity condition of stress and displacement at the interface, the harmonics in the nonlinear region, together with the compensatory waves, yield a reflected wave whose amplitude contains the defining constant of the material nonlinearity near the interface. The compensatory waves are introduced to ensure the continuity conditions at the interface. When the nonlinear region is an inclusion, the equivalent body force induced by the material nonlinearity generates a backscattered wave. The backscattered wave is determined in a simple manner by the use of the reciprocity theorem of elastodynamics. The backscattered wave obtained in this manner yields information on the nonlinear material properties and the size of the inclusion. In addition, a model based on the superposition of back-propagated compensatory waves from the two interfaces of the nonlinear region reveals the physical mechanism of wave scattering from the nonlinear inclusion.