  We experimentally characterize the impact response of concentrated
suspensions consisting of cornstarch and water. We observe that the suspensions
support a large normal stress -- on the order of MPa -- with a delay after the
impactor hits the suspension surface. We show that neither the delay nor the
magnitude of the stress can yet be explained by either standard rheological
models of shear thickening in terms of steady-state viscosities, or impact
models based on added mass or other inertial effects. The stress increase
occurs when a dynamically jammed region of the suspension in front of the
impactor propagates to the opposite boundary of the container, which can
support large stresses when it spans between solid boundaries. We present a
constitutive relation for impact rheology to relate the force on the impactor
to its displacement. This can be described in terms of an effective modulus,
but only after the delay required for the dynamically jammed region to span
between solid boundaries. Both the modulus and the delay are reported as a
function of impact velocity, fluid height, and weight fraction. We report in a
companion paper to this one on the structure of the dynamically jammed region
when it spans between the impactor and the opposite boundary
(arXiv:1709.01133). In a direct follow-up, we show that this constitutive model
can be used to quantitatively predict, for example, the trajectory and
penetration depth of the foot of a person walking or running on cornstarch and
water.
