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The development of multi-stable structural forms has attracted considerable attention in the design of architected multi-materials, metamaterials, and morphing structures, as a result of some unusual properties such as negative stiffness and, possibly, negative Poisson's ratio. Multi-stability is achieved through a morphological change of shape upon loading, and in doing so multi-stable structures undergo transitions from one equilibrium state to another. This paper investigates the structural performance of the negative stiffness honeycomb (NSH) metamaterials made of double curved beams which are emerging in various applications such as sensors, actuators, and lightweight impact protective structures with structural tunability and recoverability. An analytical treatment is pursued using the Euler-Lagrange theorem and the stability of the honeycomb has been studied. Based on a static analysis of the nonlinear elastic system, the developed tangent stiffness matrix and ensuing deformation curve were assessed through multiple phases of deformation. The closed-form solution was in good agreement with the numerical finite element model at different bistability ratios. It was shown that the bistability ratio had a pronounced effect on the overall response of the honeycomb and the desired negativity in the stiffness matrix could be achieved with high bistability ratios.

Modern armour graded thin steel plates benefit from significant elastic strength with high elastic energy storage capacity, which contributes to dissipation of total impulse from extensive blast loads within the bounds of the elastic region. Higher elastic energy storage capability mitigates the probability of catastrophic damage and ensuing large deformations compared to the conventional graded metallic panels. While blast assessment

Extensive shock and highly localised blast waves generated by detonation of near field explosives (such as Improvised Explosive Devices (IED's)) are catastrophic to structures and detrimental to humans and may result in injury or death, penetration and progressive damage, or perforation through the structure and collapse. Mitigating the effects of such waves is paramount in various aspects of design in Structural, Aeronautical, and Defense engineering, as well as being useful in Forensic Sciences. A theoretical model is presented here to predict the large inelastic deformation of ductile thin square membranes induced by a generic short duration localised pressure pulse load. The pulse loading was idealised as a multiplicative decomposition of spatial and temporal functions. The spatial part is a piecewise continuous function of axisymmetric distribution of constant pressure over a central zone of the target, then exponentially decaying beyond this zone. The temporal part may assume various shapes. Using the constitutive framework of limit analysis and incorporating the influence of finite displacements, two patterns of kinematically admissible, time dependent velocity profiles were investigated. These patterns included stationery and moving plastic hinges. The results were investigated in two cases: once with the interaction between bending moment and membrane forces retained in the analyses, and then when the response was solely governed by membrane forces. For blast loads of high magnitude, the pressure was replaced by an impulsive velocity and the results were cast as functions of dimensionless form of initial kinetic energy. The theoretical results corroborated well with the available experimental results on high strength ARMOX steel, a class of steel impervious to the phenomenon of rate sensitivity.

Localised blast loads due to proximal charges are encountered in a variety of circumstances. This paper proposes an analytical solution for the dynamic plastic response of a rigid-perfectly plastic thick square plate subject to a localised explosion. The proposed model is an extension of the analytical model proposed by Micallef et al [1] to study circular plates which is adopted and modified in order to study impulsively loaded square plates where the effect of shear deformation is included. A piecewise continuous blast load function was assumed with axisymmetric spatial distribution of constant pressure in the central zone and exponentially decaying beyond it. Using the constitutive framework of limit analysis and incorporating the interactions between bending moment and transverse shear forces in the analyses, transverse displacement and response duration were examined on three classes of plates, classified according to the length to thickness ratio parameter . The results were furnished in terms of the impulsive velocity, which is a function of the localised blast load parameters. A theoretical solution for plates with > 2 was sought for the non-impulsive blast loads. Parametric studies were performed to elucidate the effect of loading parameters and plate thickness on the permanent deformation. The theoretical solutions have been found generic and can predict, by the correct choice of the load parameters, the dynamic response of most blast load scenarios brought about by proximal or distal charges. It was found that, for proximal impulsive blasts, the effect of transverse shear becomes irrelevant for even moderate values of , which effect is inconsequential on both central and endpoint displacements at discontinuous interface in the range of > 5 . Since the short duration pulse is of concern, localised pressure loads affect only a small area of the plated structures. Thus, whilst the