Estimating the blast response in Elastic-Plastic-Hardening-Softening Structures

In this paper, the Elastic-Plastic-Hardening-Softening (E-P-S-H) material model is described by a non-smooth piecewise linear system. The blast response is determined via a Single Degree of Freedom (SDOF) method. The hardening and softening parameters are introduced by which the stiffness of the structure is described in 3 regions. These are elastic, plastic hardening, and plastic softening regions with different governing equations in each region. The blast force is also designated by an unsymmetrical triangular pulse force in 3 different time ranges. Therefore, to obtain the blast response, a solution of 9 linear equations is required. In each Plastic Dynamic Load Factor DLFR, the ratio of (Td/T) simulation is done, and the maximum amplitude is picked up that indicates the damage of the blast. In a practical example, the SDOF results are then validated via FEM analysis of a blast wall structure. It is shown that in any yield stress, the hardening-softening behaviour of the material and structure causes less damage in comparison with the Elastic-Perfectly-Plastic (E-P-P) model. Thereby, only a correction factor has been determined, and the non-smoothness (piecewise linearity) in the system and loading does not produce a non-smooth response. It is shown that for steel structures, where the hardening and softening parameters are small, the overestimation in the E-P-P model is not significant. Therefore, the existing approaches that are based on the E-P-P model can be used with an acceptable conservativeness. Moreover, if the pulse index is small, the results of the E-P-P model for linearly decreasing pulse can be used to keep the conservativeness for design purposes.