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

Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions