Blast Loads versus Point Loads: The Missing Factor

In the course of implementing and testing an efficient algorithm for the computation of the displacements (or Green's functions, or fundamental solutions) elicited by a pulsating blast source acting at some point in a laminated medium, the writer encountered what was at first an unexpected and puzzling anomaly: A benchmark test with the analytical solution for a blast source in a homogeneous, elastic full-space revealed a discrepancy by a constant factor. Since the solution for the blast source had been derived from available Green's functions for harmonic point sources, the first thought that came to mind was that there was a fault in the derivation. When a careful analysis demonstrated that the formulation was indeed correct, it became necessary to search for an alternative explanation. Finally, the cause for the mysterious discrepancy became clear: A homogeneous solid with an infinitesimally small cavity (i.e., a vanishingly small radius) is not the same as the continuous solid medium, at least not when a singularly large pressure acts within that point-like cavity. After this observation was accounted for, the differences between the numerical and analytical solutions could be fully resolved and a perfect match achieved. Since neither the problem nor its proof are obvious, the following note addresses both of these.