Probing hysteretic elasticity in weakly nonlinear materials

In this study, we propose an optimized NRUS measuring and data processingprotocol dedicated to small bone samples specially designed to be used in afour-point bending mechanical fatigue test. Our goal was to assess the elasticand dissipative hysteretic nonlinear parameters repeatability with the proposedprotocol using several classes of materials with weak, intermediate and highnonlinear properties. In the proposed data processing, the frequency shift f asa function of excitation drive amplitude is measured relatively to a referenceresonance peak curve f₀ (obtained at the lowest excitation level)which is repeated before each excitation drive level. Our results show that theproposed correction may be an alternative to a stringent control of temperature(which could not be achieved in this study) by increasing significantly NRUSsensitivity. With our correction procedure, we measured relative resonantfrequency shifts of 10⁵, which are below 10 ⁴, oftenconsidered as the limit to NRUS sensitivity under common experimentalconditions. In our experiments, we identified external temperature fluctuationas one of the major source of resonance frequency variation. A variation of 0.1Ccaused a frequency variation of 0.01%, which is similar to the expectednonlinear frequency shift for weakly nonlinear materials. In the absence ofcorrection, the data could not be interpreted to support the existence ofhysteretic nonlinear behavior in bone.