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Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we introduce a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), to explicitly simulate the crack induced nonlinear elasticity in solids with both horizontal and inclined cracks. In the FDEM model, the solid is discretized into finite elements to capture the wave propagation in the bulk material, and the finite elements along the two sides of the crack also behave as discrete elements to track the normal and tangential interactions between crack surfaces. The simulation results show that for cracked models, nonlinear elasticity is generated only when the excitation amplitude is large enough to trigger the contact between crack surfaces, and the nonlinear behavior is very sensitive to the crack surface contact. The simulations reveal the influence of normal and tangential contact on the nonlinear elasticity generation. Moreover, the results demonstrate the capabilities of FDEM for decoding the causality of nonlinear elasticity in cracked solid and its potential to assist in Non-Destructive Testing (NDT)., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Non-linear resonant ultrasound spectroscopy (NRUS) is a technique exploiting the significant non-linear behavior of damaged materials, related to the presence of damage. This study shows for the first time the feasibility of this technique for damage assessment in bone. Two samples of bovine cortical bone were subjected to a progressive damage experiment. Damage accumulation was progressively induced in the samples by mechanical testing. For independent assessment of damage, X-ray CT imaging was performed at each damage step, but only helped in the detection of the prominent cracks. Synchrotron micro-CT imaging and histology using epifluorescence microscopy were performed in one of the two samples at the last damage step and allowed detection of micro-cracks for this step. As the quantity of damage accumulation increased, NRUS revealed a corresponding increase in the non-linear response. The measured change in non-linear response is much more sensitive than the change in elastic modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique where bone access will be a challenging problem.