Multimode Nonlinear Resonant Ultrasound Spectroscopy (NRUS): From the 1D to 3D Characterization of the Elastic Nonlinearity

International audienceNonlinear Resonant Ultrasound Spectroscopy (NRUS) has been used extensively over the last two decades to quantify, through the nonlinear parameter α, the hysteretic nonlinearity of materials for geophysical, biomedical, and civil engineering applications. This technique relies on the variations of the damping and frequency of a resonance mode with the amplitude of this mode. A typical NRUS experiment is conducted on a long bar using its first longitudinal mode. In some experiments, higher order modes have been used because the nonlinearity was more pronounced but the type of motion involved has not been characterized. The parameter α measured from these experiments is then used to calibrate a 1D model of the non-classical nonlinearity. As a first step towards extending this model from 1D to 3D, experiments were conducted on long bar samples (assumed to be macroscopically isotropic) where modes are excited selectively and the type of motion involved in each mode is well characterized. In this simple isotropic case, longitudinal and torsional motions are decoupled in order to find the α11 and α44 parameters that correspond to the compression (C11) and shear (C44) moduli, respectively. A first set of NRUS experiments is conducted using only the longitudinal modes of the sample to compute the α11 parameter. The value of α11 with respect to the order of the longitudinal mode selected for the analysis is also studied. A second set of NRUS experiments is conducted using only the torsional modes of the sample to compute the α44 parameter. Last, a discussion is given on the possibility to predict what value of the α parameter would be measured using a bending mode of the bar, since longitudinal and torsional motions coexist in such a mode