A scaled framework for strain rate sensitive structures subjected to high rate impact loading

The ability to perform scaled high impact, energy absorption type experimentation is practically impeded for rate-sensitive materials by an inherently nonlinear response that changes markedly structural behaviour at scale. The issue is re-examined in this paper where equivalent models for structures subjected to high rate axial impact are proposed founded on the recently discovered concept of finite similitude. Finite similitude has been proven to exist for continuum mechanics and is defined by proportional corresponding transport equations on synchronised control volumes in full-scale and scaled spaces. The theory provides a means for performing tests on scaled models instead of the original full-sized sample. Focus in this paper is on the high-rate loading of tubes leading to elastic-plastic buckling behaviour, which is recognised to be inherently scale dependent. The finite-similitude approach allows scaled models to be projected into the full-scale physical space for direct comparison. Different projections are tested by means of the finite element software LS-Dyna in which the strain rate effect is accounted for using Cowper-Symonds or Johnson-Cook constitutive equations. It is confirmed in the paper that scaled models for tube buckling exist and although exact similitude is not generally possible, good accuracy is nevertheless achievable.