  In this paper, we present numerical simulations with local and nonlocal
models under dynamic loading conditions. We show that for finite element (FE)
computations of high-velocity, impact problems with softening material models
will result in spurious post-bifurcation mesh dependency solutions. To
alleviate numerical instability associated within the post-bifurcation regime,
a characteristic length scale was added to the constitutive relations based on
calibration of the series of different notch specimen tests. This work aims to
assess the practical relevance of the modified model to yield mesh independent
results in the numerical simulations of high-velocity impact problems. To this
end, we consider the problem of a rigid projectile moving at a range of
velocities between 89-107 m/s, colliding against a 6061-T6 Aluminum disk. A
material model embedded with a characteristic length scale in the manner
proposed by Pijaudier-Cabot and Bazant (1987), but in the context of concrete
damage, was utilized to describe the damage response of the disk. The numerical
result shows that the addition of a characteristic length scale to the
constitutive model does eliminate the pathological mesh dependency and shows
excellent agreements between numerical and experimental results. Furthermore,
the application of a nonlocal model for higher strain rate behavior shows the
ability of the model to address intense localized deformations, irreversible
flow, softening, and final failure.
