Finite similitude in high rate dynamic behavior of structures under impact loads

At present paper, an equivalent model with different dimensions and also with different dimensions and material in comparison with main body for strain rate sensitive structures subjected to high rate loading is presented by using the novel finite similitude method. The finite similitude method provides performing a test on the model instead of the original sample. This method is used to obtain the properties of model and to reverse the obtained results for model to main body by using the principles of nature (the law of conservation of mass, the law of conservation of momentum, the law of conservation of energy and the law of conservation of entropy) which is always true for any system. The relationships for both pure dimensional and simultaneously dimensional/material scaling of strain rate sensitive structures are presented. To evaluate the efficiency of the proposed relationships, the numerical results are obtained for impacted circular plates. It should be mentioned that the numerical results are obtained by using the finite element software LS-Dyna in which the strain rate effects are considered into account by using the Cowper-Symonds and Johnson-Cook constitutive equations. The results indicate that the scaled plate to one tenth of its original dimensions and also made of different material in comparison with original plate predicts the response characteristics of the original plate with a very good accuracy.