Pressure–impulse diagrams for elastic-plastic-hardening and softening single-degree-of-freedom models subjected to blast loading

Pressure–impulse (P–I) diagrams are commonly used in the preliminary design of protective structures to establish safe response limits for given blast-loading scenarios. In this paper, P–I diagrams of an elastic-plastic-hardening and an elastic-plastic-softening single-degree-of-freedom model are studied. The formal analytical procedure to establish P–I diagrams of such a system is explained. A dimensionless parameter has been used to categorize the response into elastic, elastic-plastic-hardening, elastic-plastic-softening, rigid-plastic-hardening and rigid-plastic-softening. Two different methods to derive and use P–I diagrams have been explained. The feasibility of representing the resistance function as bilinear has been studied with regard to resistance at yield and total area under the resistance curve as system characteristics and maximum displacement as response. An example is included to verify this simplification. Inverse ductility and hardening/softening indexes have been introduced as dimensionless parameters to generalize the solution to all elastic-plastic-hardening and softening systems. Parametric studies have been conducted on the influence of inverse ductility and hardening/softening index on P–I diagrams and it was observed that the blast energy per unit of maximum displacement increases as inverse ductility increases or as hardening index increases (softening index decreases). Small variations in P–I diagrams have been observed with respect to softening index which implies low sensitivity of P–I diagrams with respect to this parameter in the studied range.