Experimental Mechanics

, Volume 56, Issue 1, pp 3–23 | Cite as

Exploration of Saint-Venant’s Principle in Inertial High Strain Rate Testing of Materials

  • H. Zhu
  • F. Pierron


Current high strain rate testing procedures of materials are limited by poor instrumentation which leads to the requirement for stringent assumptions to enable data processing and constitutive model identification. This is the case for instance for the well known Split Hopkinson Pressure Bar (SHPB) apparatus which relies on strain gauge measurements away from the deforming sample. This paper is a step forward in the exploration of novel tests based on time and space resolved kinematic measurements obtained through ultra-high speed imaging. The underpinning idea is to use acceleration fields obtained from temporal differentiation of the full-field deformation maps measured through techniques like Digital Image Correlation (DIC) or the grid method. This information is then used for inverse identification with the Virtual fields Method. The feasibility of this new methodology has been verified in the recent past on a few examples. The present paper is a new contribution towards the advancement of this idea. Here, inertial impact tests are considered. They consist of firing a small steel ball impactor at rectangular free standing quasi-isotropic composite specimens. One of the main contributions of the work is to investigate the issue of through-thickness heterogeneity of the kinematic fields through both numerical simulations (3D finite element model) and actual tests. The results show that the parasitic effects arising from non-uniform through-the-thickness loading can successfully be mitigated by the use of longer specimens, making use of Saint-Venant’s principle in dynamics.


Virtual fields method High strain rates Inertial effects Full-field measurements Grid method 



This work is supported by China Scholarship Council (CSC) through the government grant of Haibin Zhu. Professor Pierron gratefully acknowledges support from the Royal Society and the Wolfson Foundation through a Royal Society Wolfson Research Merit Award. The authors would like to acknowledge Mr Brian Speyer from Speyer Photonics Ltd and Dr. Markus Ortlieb from Shimadzu Europa GmbH for lending the camera and helping out with the experiments. They would also like to thank Dr. Nicola Symonds and Dr. Liam Goodes from the nCATS group at the University of Southampton for their help with the impact rig.

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Copyright information

© Society for Experimental Mechanics 2015

Authors and Affiliations

  1. 1.LASMIS Université de Technologie de TroyesTroyes CedexFrance
  2. 2.Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

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