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A group of dimensionless numbers, termed DLV (Density-Length-Velocity)system, is put forward to represent the scaled behavior of structures underimpact loads. It is obtained by means of the Buckingham Pi theorem with analternative basis. The distinct features of this group of dimensionless numbersare that it relates physical quantities of the impacted structure withessential basis of the Density, the Length and the Velocity, and thus it canrepresent the scaled influence of material property, geometry characteristicand velocity on the behavior of structures. The newly 15 proposed dimensionlessnumbers reflect three advantages. (1) The intuitively clear physicalsignificance of these dimensionless numbers, such as the ratios of forceintensity, force, moment of inertia to the corresponding dynamic quantities,the Johnson's damage number Dn and Zhao's response number Rn etc. are naturallyincluded. (2) The property of direct matching the dimensionless expression ofresponse equations of dynamic problems with these dimensionless numbers throughsimple equation analysis; (3) The ability of addressing non-scaling problemsfor different materials and strain-rate-sensitive as well as the VSG (initialimpact Velocity-dynamic flow Stress-impact mass G) system. Four classicalimpact models are used to verify the direct matching property and thenon-scaling addressing ability of the DLV system by equation analysis. Theresults show that the proposed dimensionless number system is simple, clear andefficient, and we suggest using it to represent the scaled behavior ofstructures under impact loads.

Suggestion of the DLV dimensionless number system to represent the scaled behavior of structures under impact loads