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

  • Shuai Wang
  • Fei XuEmail author
  • Zhen Dai


A group of dimensionless numbers, termed density–length–velocity (DLV) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham \(\Pi \) theorem with an essential basis. The distinct features of this group of dimensionless numbers are that it relates physical quantities of the impacted structures to essential basis of the density, the length and the velocity, and thus it can represent the scaled influence of material property, geometry characteristic and velocity on the behavior of structure. The newly 15 proposed dimensionless numbers reflect three advantages: (1) the intuitively clear physical significance of these dimensionless numbers, such as the ratios of force intensity, force, moment of inertia to the corresponding dynamic quantities, the Johnson’s damage number \(D_{n}\) and Zhao’s response number \(R_{n}\), are naturally included; (2) the property of directly matching the dimensionless expression of response equations of dynamic problems with these dimensionless numbers through simple equation analysis; (3) the addressing ability of non-scaling problems for different materials and strain-rate-sensitive materials through adjusting impact velocity of the scaled model or adjusting density of the scaled model, as well as the VSG (initial impact velocity–dynamic flow stress–impact mass G) system. Four classical impact models are used to verify the directly matching property and the non-scaling addressing ability of the DLV system by equation analysis. The results show that the proposed dimensionless number system is simple, clear and efficient, and we suggest using it to represent the scaled behavior of structures under impact loads.


Dimensionless numbers Structural impact Scaling Similarity Johnson’s damage number Zhao’s response number 



The authors would like to acknowledge Mr. Xiaochuan Liu, Mr. Xulong Xi and Mr. Jijun Liu (Aviation Key Laboratory of Science Research Institute of China, Xi’an 710065, China) for their writing assistance. This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.Institute for Computational Mechanics and Its ApplicationsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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