Globally smooth expressions for shock pressure decay in impacts

Abstract

Hypervelocity meteorite impacts on planets subject the target to very high shock pressures. The isobars in the affected region are approximately spherical and centered on a point at a certain depth below the point of impact. The decay of the shock pressure with increasing distance from that center is usually represented in the form lg p=a+n lg(r/R), where p is the shock pressure, r is the distance from the center of the sphere, R is the radius of the impactor, and a and n are fitting constants; a similar relation is also used for the particle velocity. Although its simplicity seems to speak in its favor, this form has some problems: it is not bounded from above, thus necessitating an imposed maximum value that depends on additional assumptions; the slope of the decay is not accurately described by a single n for all r; the transition between domains with different decay parameters introduces kinks into p(r) at poorly defined points. It is therefore proposed to replace the decay law with other functional forms that are bounded and smooth and can be fully derived from data from numerical experiments. The proposed functions are applied to data of dunite-on-dunite impacts from the literature.