Response of armour steel plates to localised air blast load : a dimensional analysis

We report on the results of dimensional analyses on the dynamic plastic response of square armour steel plates due to detonation of proximal cylindrical charges and ensued air blast loading. By assuming a generic function for the blast load, which is multiplicative comprising its spatial and temporal parts, a set of 14 dimensionless parameters, representative of the load and plate deformation, were identified and recast in the form of dimensionless functions of stand-off to charge diameter ratio. Parametric studies were performed using commercial code ABAQUS’s module of Finite Element hydrocode using MMALE and MMAE techniques, and combined with regression analyses to quantify the dimensional parameters and the expressions for dimensionless functions. A few numerical studies with various FE mesh types were also performed to validate the transient deflections against the small-scale experiments. For pulse loading due to proximal charges of small orders of stand-off/charge diameter ratio, the magnitude of the transverse deflection increased abruptly with incremental decrease in stand-off, in contradistinction to the plate deformations at higher stand-offs where variations in displacement are smooth. This confirmed the existence of a stand-off at which a transition in behaviour takes place. For stand-off values less than charge diameter, a dimensionless energy absorbing effectiveness factor was considered to investigate the prediction of rupture in the plate corresponding to different charge masses. This factor is measured as a baseline parameter to predict, using solely numerical means, the blast loads which ensue rupture on full-scale prototypes

Structural mechanics of negative stiffness honeycomb metamaterials

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 (FE) 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

Dynamic Performance of Simply Supported Rigid-Plastic Square Plates Subject to Localized Blast Loading

This paper presents the theoretical solution to the response of a square plate undergoing plastic deformation due to a generic localized blast pulse. A localized blast load function was assumed multiplicative of its spatial distribution and temporal pulse shape. The spatial distribution was representative of constant pressure over the central zone, while exponentially decaying outside that zone. Considering an appropriate moment function and ignoring the membrane, transverse shear, and rotary inertia effects, the static plastic collapse was found, whereby the analysis was extended to the dynamic case by assuming a kinematically admissible, time-dependent velocity profile. The analytical model, which was validated against the numerical results obtained through ABAQUS hydrocode, showed close correlation in terms of the permanent transverse deflection profile. In order to consider the effect of temporal pulse shape, the results were formulated for rectangular as well as exponentially and linearly decaying pulses. For blast loads of high magnitude, the pressure load was replaced by an impulsive velocity. The calculations were simplified by utilizing the dimensionless form, and the results were corroborated with theoretical and experimental results from the literature. The model showed improvements in predicting the final deformation of square plates over previous models of simplified loading function

Inelastic dynamic response of square membranes subjected to localised blast loading

Extensive shock and highly localised blast waves generated by detonation of near field explosives (such as improvised explosive devices (IEDs)) are catastrophic to structures and humans, resulting in injury or death, progressive damage, or perforation through the structure and collapse. Mitigating the effects of such waves is paramount in various aspects of design engineering. A theoretical model is presented here to predict the large inelastic deformation of ductile thin square membranes induced by a generic, short pulse pressure load, comprising a piecewise function of spatial and temporal parts. 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 expressed in terms of dimensionless form of initial kinetic energy. The effects of boundary conditions and visco-plasticity have also been investigated. The theoretical results corroborated well with various experimental results in the literature, on ductile metallic plates such as high strength ARMOX steel and mild steel

The response of mild steel and armour steel plates to localised air-blast loading-comparison of numerical modelling techniques

This paper presents a comparative study of numerical, experimental and empirical techniques on the effect of localised air blast loads on mild steel and armour steel plates. The blast load effects on monolithic plates have been accounted for by using different approaches provided in the Finite Element hydrocode ABAQUS 6.13, namely an Eulerian Lagrangian and a Coupled Eulerian Lagrangian model. In the first model, the air and the explosive were modelled using multi-material Eulerian grids while the plate was modelled using a rigid Lagrangian mesh, while in the second model the rigid target was replaced with deformable plate. The transient deformation of the plate, strain localisation, pressure distribution on the plate have been investigated in the FE models, which have been validated against small scale experimental data for a limited range of charge sizes for both the mild steel and armoured steel. Despite the lower deflection of armour steel compared to mild steel plates, both plates were shown to undergo rupture upon similar charge mass and stand-off. For this purpose, a non-dimensional analysis was carried out with consideration of stand-off distance and slenderness ratio to predict the rupture impulse

Dynamic response of blast loaded Hollow Cylindrical and Truncated Conical shells

Hollow cylindrical and truncated conical shells depict enhanced torsional and shear resistance compared to beams and plates and are ubiquitously used in structures in aeronautics, submarines, wind turbines, pressure vessels, and transmission pylons. Upon extensive localised blast, these elements undergo local and global deformation and failure. The detrimental damage to the shell depends on the stand-off and charge mass and is proportional to the emerged local dynamic stresses and inelastic deformations. Large localised translations relocate the structure’s original pivot point and induce global rotations about the new one which raises the probability of structural collapse. In this work, we examine large plastic deformations of hollow cylindrical and truncated conical shells subject to a range of pulse pressures emanated from high explosives. Fluid-Structure Interaction (FSI)-based Finite Element (FE) models were developed to discern the characteristics of blasts at various stand-offs and functions were proposed to link load parameters to structural, material, and geometric properties

Smart controllable wave dispersion in acoustic metamaterials using magnetorheological elastomers

The success in the flexible design of smart acoustic metamaterials is crucially contingent upon the degree of control over the parameters that uniquely define the spectrum of band structure and morphology of dispersion surfaces. In this work, we have studied the driving physical mechanisms, the control of which makes possible operating, in real-time, on the set of band gaps formed in 3D metamaterials based on magneto elastomers. In such acoustic structures, the stiffness of the medium in which unit cells are immersed, as well as the stiffness of the shells surrounding multi-particle cores depend on the induction, B(t), of an external magnetic field. The results obtained are systematized through the qualitative analysis of diversе scenarios for the evolution of the frequency characteristics of the metamaterial and summarized in the following complete physical picture of their dynamics. Variation of the stiffness of the medium/shells changes the wavelength of the shell's surface waves at characteristic frequencies of the core vibrations and, as a result, the level of coupling between the vibration modes of the flexible shells and cores. Consequently, with an increase/decrease in the stiffnesses of the shells/medium, the dispersion surfaces of the entire acoustic system shift up/down along the frequency axis with noticeably different ‘mobilities’ that reversibly lead either to the formation of the band gaps in initially dense frequency spectrum or to the transformation of the band gaps formed into pass bands. The tuning of the set of dispersion surfaces depending on the range of changes in the magnetic field induction can be carried out in dynamic, quasi-stationary, and over-critical regimes when some of the dispersion surfaces degenerate into planes. In anisotropic metamaterials, simultaneously with creating full band gaps, it is possible to create tunable directional band gaps with adjustable frequency and angular widths. The results obtained, within the framework of the idealized discrete mass-spring model, are in good agreement with the data presented in the available experimental works and can be useful in the design of acoustic systems with desirable properties

Plastic dynamic response of simply supported thick square plates subject to localised blast loading

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 ν. 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 ν > 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 ν which effect is inconsequential on both central and endpoint displacements at discontinuous interface in the range of ν > 5. Since the short duration pulse is of concern, localised pressure loads affect only a small area of the plated structures. Thus, whilst the theoretical treatments also examine the fully clamped plates, the boundary conditions in such loads do not influence the overall response of the structure compared to the static or global blast loads

Large elastic-plastic deformation of square membranes subjected to localised pulse pressure loads

Ductile isotropic materials are widely used in protective systems against transient pulse pressure loads, such as those of localised blasts. This is due to the combined elastic-plastic response which contributes to dissipation of total impulse from extensive loading as the energy stored elastically limits deformation while the energy expended plastically limits the level of transferred forces in the structure. In the case of thin, modern armour graded steel plates, the tailored metallurgy helps the structure store energy within the bounds of elastic region, which may be dissipated at a later stage as damping kills it off in subsequent cycles. On the other hand, the plastic work is almost entirely converted to heat and dissipates.The present work focuses on the elastic and plastic energies in the membrane and aims at deducing, from the minimization of Föppl-Von-Kármán (FVK) energy functional combined with enforcing the constitutive relations of limit analysis, the dynamic elastic-plastic response of localised blast loaded square membranes undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various temporal shapes (e.g. rectangular, linear, exponential).Considering the elastic response, a single-degree-of-freedom model was developed from the prescribed displacement field and associated stress tensor having clamped and simply supported boundary conditions. The explicit closed form solutions were sought by using the Ritz-Galerkin’s variational method as well as the Poincaré-Lindstedt perturbation method. The theoretical solutions of rigid-perfectly plastic square membranes subjected to the same blast scenarios were then discussed. From the combined effects we deduce the load displacement curves representing the trajectory of the nonlinear elastic-perfectly plastic structure.Key words: localised blast, square membrane, Ritz-Galerkin method.Pages of the article in the issue: 126-133Language of the article: Englis

Dynamic plastic response of beams subjected to localised pulse loads

Localised blast loads give rise to high gradients of overpressure detrimental to structural elements as beams and plates. This article presents an analytical study on the dynamic plastic response of beams made of a ductile metallic material due to close-in pulse pressure loading. The close-in pressure load is characterised by a spatially varying function constant over a central region and exponentially decaying beyond it. The temporal pulse shape is assumed to take different forms. The exact static plastic collapse load was obtained for the characteristic load using the framework of plastic limit analysis, whereby the analysis was then extended to the dynamic case by considering the appropriate yield surface and inclusion of inertia forces. The yield surfaces considered were representative of pure bending, the interactions between the bending moment and transverse shear, and bending moment and membrane force, each corresponding to a special case depending on the geometry of the beam. A time-dependent, kinematically admissible velocity profile was assumed to treat the dynamic formulations in interaction of each phenomenon. A study on the strain-rate sensitivity was also presented, and existence of a critical pressure triggering the apparition of travelling plastic hinges was hence highlighted. For blast loads of high magnitude, the expressions for normalised deflection were furnished in terms of the impulsive velocity. The analytical models were validated by performing a parametric study on the two-dimensional representative of the beam model in commercial finite element software ABAQUS 6.14. The numerical results show a good correlation with the analytical results in each case