Analytical Modelling of the Plastic Response of Thin Plates Under Impulsive Near-Field Blast Loadings

Abstract

There has been significant scientific interest in studying the response of structures when subjected to extreme dynamic loading events such as blast and impact. Over the past three decades, there has been a rise in the number of explosion incidents globally. These often involve deliberate attacks where terrorists use high explosives to cause harm to civilians and public infrastructure through devastating blast waves. Blast loads from explosions can cause loss of human lives or severe injuries due to either the direct exposure of people to blast waves and/or as consequences of partial or overall collapse of structures, or their key structural elements. Through experiments, it is observed that the resulting deformations of structures under blast loadings are mainly plastic, and the magnitudes associated with typical blasts are found to exceed, by far, the quasi-static ultimate capacities of practical civilian structures. Furthermore, blasts from detonations of high explosives at close-in distances from the structures (called near-field blasts) are found to be highly transient and spatially non-uniform. This poses challenges to the structural engineering community that is required to provide reliable designs to protect the public and vital structures from such rising unconventional loading conditions. Most of the existing analytical techniques are either inapplicable or less accurate when the explosive threat corresponds to a near-field blast loading. Due to the high variability and sensitivity of the blast load to changes in the explosive threat’s input variables, the utilisation of commercially available numerical tools (e.g., hydrocodes and sophisticated finite element solvers) is less attractive to practising blast engineers in the early phase of design due to their substantial computational costs. The present study focuses on developing a physically based and simple model to predict the plastic response of thin plates when subjected to near-field blasts so that it is fast running and hence can be made available to practising blast engineers. The developed model is based on three idealising assumptions: the blast load is impulsive; the thin plate’s material is rigid-perfectly plastic according to von Mises’s criterion of yielding; and the plate responds in a pure membrane (or catenary) mode. These assumptions are necessarily taken to deem the ultimate model simple and easy to run, and they are considered reasonable based on a detailed review of the relevant literature. The model’s accuracy is validated by comparisons to real experiments performed by others and high fidelity finite element simulations performed by the author using LS-DYNA. The model is found reasonably accurate and provides additional insights on the response of thin targets to typical near-field blast loading.