An investigation into finite similitude for high-rate loading processes: Advantages in comparison to dimensional analysis and its practical implementation

Hamed Sadeghi, Keith Davey, Rooholamin Darvizeh, Reza Rajabiehfard, Abolfazl Darvizeh

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Exploration of the behaviour of large-scale structures under impact and explosive loading can in principle be achieved by means of scaled experimentation. In practice however, scaled experiments can be unrepresentative of high-rate phenomena due to non-scalable strain-rate effects and altered material behaviours. Critical is proper experimental design but this is presently impeded by the inability of dimensional analysis to cater for the absence of exact similarity in high-rate loading scenarios. This paper re-examines the place of high-rate scaled experimentation in the light of a new similarity theory founded on the distortion of space (called finite similitude), which has recently appeared in the open literature. The advantage of finite similitude over dimensional-analysis based techniques is demonstrated in the paper, which is able cope (to some extent) with the breakdown in similarity with an approximate approach called inexact-finite similitude. It is shown to be independent of loading type (unlike competing methods), which is a feature demonstrated through the analysis of a scaled plate subject to a free-air explosion. The work presented here provides the first attempt to test the practical importance of the new theory through detailed experimental trials. The experimental investigations reaffirm the theoretical studies and reveal that the developed inexact-finite similitude theory can practically be used for predicting full-scale behaviour by conducting experimental tests on trial models of different sizes and even different materials. For this purpose, circular tubes subjected to high loading rate axial impact using a gas-gun apparatus are chosen as case studies. It is shown that in most cases, scaled experimentation provides superior predictions of buckling shapes, shortenings, temporal response of axial force and peak loads in comparison with numerical simulation. Analytical outputs for mean force and peak load are also shown to be significantly inferior to those returned through scaled experimentation.

Original languageEnglish
Article number103554
JournalInternational Journal of Impact Engineering
Early online date26 Feb 2020
Publication statusPublished - Jun 2020


  • Experimental results
  • Finite similitude
  • High loading rate processes
  • Scaling


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