Criterion for contacting is critically important for the Generalized
Interpolation Material Point(GIMP) method. We present an improved criterion by
adding a switching function. With the method dynamical response of high melting
explosive(HMX) with cavities under shock is investigated. The physical model
used in the present work is an elastic-to-plastic and thermal-dynamical model
with Mie-Gr\"uneissen equation of state. We mainly concern the influence of
various parameters, including the impacting velocity v, cavity size R, etc,
to the dynamical and thermodynamical behaviors of the material. For the
colliding of two bodies with a cavity in each, a secondary impacting is
observed. Correspondingly, the separation distance D of the two bodies has a
maximum value Dmax in between the initial and second impacts. When the
initial impacting velocity v is not large enough, the cavity collapses in a
nearly symmetric fashion, the maximum separation distance Dmax increases
with v. When the initial shock wave is strong enough to collapse the cavity
asymmetrically along the shock direction, the variation of Dmax with v
does not show monotonic behavior. Our numerical results show clear indication
that the existence of cavities in explosive helps the creation of ``hot
spots''.Comment: Figs.2,4,7,11 in JPG format; Accepted for publication in J. Phys. D:
Applied Physic