Assessment of cortical bone fatigue using coded nonlinear ultrasound

Bone fatigue accumulation is a factor leading to bone fracture,which is a progressive process of microdamage deteriorating under long-term and repeated stress.Since the microdamage of the early stage in bone is difficult to be investigated by linear ultrasound,the second harmonic generation method in nonlinear ultrasound technique is employed in this paper,which is proved to be more sensitive to microdamage.To solve the deficiency that the second harmonic component is easily submerged by noise in traditional nonlinear measurement,a weighted chirp coded sinusoidal signal was applied as the ultrasonic excitation,while pulse inversion is implemented at the receiving side.The effectiveness of this combination to improve the signal-to-noise ratio has been demonstrated by in vitro experiment.Progressive fatigue loading experiments were conducted on the cortical bone plate in vitro for microdamage generation.There was a significant increase in the slope of the acoustic nonlinearity parameter with the propagation distance(increased by 8%and 24%respectively)when the bone specimen was at a progressive level of microdamage.These results indicate that the coded nonlinear ultrasonic method might have the potential in diagnosing bone fatigue.

A 3D Homogenized Model for Nonlinear Wave Interaction with Randomly Distributed Microcracks

This paper presents a 3D homogenized model able to simulate the nonlinear effects generated by the interaction of ultrasonic waves with microcracks.A hexahedral element with one horizontal elliptical crack is constructed as a reference model.The reference model is smeared to be orthotropic but with different moduli in tension and compression to account for stiffness asymmetry due to crack opening and closure.Different from the existing homogenized models that usually simplify the representative volume element as a homogeneous part and require only one constitutive model for the equivalent material of the whole structure,we assign the constitutive relationship of the same reference model to all the finite elements but with random principal material orientations to take randomly oriented microcracks into consideration.In this way,the randomness of distributed microcracks can be considered in the framework of continuum mechanics.In this manner,the experimentally observed nonlinear effects,such as the generation of both even and odd harmonics,can be reproduced.The developed model has been verified for a 3D bar and a 3D plate.Particularly,the influence of crack density on the amplitude of higher harmonics is analyzed.