  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).
