Materials such as modern armour steel, benefit from appreciably high elastic energy storage capacity prior to failure. Such a capacity contributes to absorption of the impulse generated during an extreme pulse pressure loading event such as a localised blast. As the plate deforms within the bounds of the elastic region without plastic dissipation, the probability of catastrophic failure is mitigated while large deformations compared to conventional metallic panels are encountered. No studies have proposed, to date, a closed-form solution for nonlinear elastic response of thin circular plates subject to localised pulse loads. The present work aims at deducing, from the minimization of the Fo center dot ppl-von K ' arm ' an (FVK) energy functional, explicit solutions for the response of dynamically (pulse) loaded thin clamped circular plates undergoing large deformations. The solutions were derived from a presumed kinematically admissible displacement field together with an associated stress tensor potential as an infinite polynomial series, which was truncated into a multiplicative decomposition of temporal parts and spatial parts, representative of a Multiple Degrees-of-Freedom (MDOF's) system. In the case of static loading, using the Frobenius method, an exact recursive solution to each mode of defamation was obtained. In the event of dynamic loading, useful expressions for stress tensor components were delineated, corresponding to a multimode multiplicative product, and a series of coupled Ordinary Differential Equations (ODE's) were derived, using the Ritz-Galerkin variational method. The explicit solutions were sought using the Poincare '-Lindstedt (PL) perturbation method. The closed-form solutions obtained were corroborated with FE results including the Fluid-Structure Interaction (FSI) effects and showed convergence when the first few modes were considered. The influence of higher modes, however, on the peak deformation was negligible and the solution with 3 DOF's conveniently estimated the blast response to a satisfactory level of precision. The influence of element type on the response was also examined and discussed in the context of the problem.

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.

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 of such structures is important to design and application of protective systems, limited studies are available on their response to localised blasts. The present paper aims at deducing, from the minimization of Foppl-von Korman (FVK) energy functional, the dynamic response of localised blast loaded thin elastic square plates 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 shapes (e.g. rectangular, linear, sinusoidal, exponential). A kinematically admissible displacement field and the associated stress tensor were considered as a truncated cosine series with multiple Degrees-of-Freedom (DoF's). From the prescribed displacement field, having simply supported boundary conditions, useful expressions for stress tensor components were delineated corresponding to a unique mode and a series of differential equations were derived. The explicit solutions were sought using the Poineare-Lindstedt perturbation method. The closed form solutions of each mode were corroborated with the numerical FE models and showed convergence when the first few modes were considered. The influence of higher modes, however, on the peak deformation was negligible and the solution with 3 DOF's conveniently estimated the blast response to a satisfactory precision.

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.

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.

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.

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 nu. 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 nu > 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 nu, which effect is inconsequential on both central and endpoint displacements at discontinuous interface in the range of nu > 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.

SummaryShear locking is a major issue emerging in the computational formulation of beam and plate finite elements of minimal number of degrees of freedom as it leads to artificial overstiffening. In this paper, discontinuous Timoshenko beam and Mindlin‐Reissner plate elements are developed by adopting the Hellinger‐Reissner functional with the displacements and through‐thickness shear strains as degrees of freedom. Heterogeneous beams and plates with weak discontinuity are considered, and the mixed formulation has been combined with the extended finite element method (FEM); thus, mixed enrichment functions are used. Both the displacement and the shear strain fields are enriched as opposed to the traditional extended FEM where only the displacement functions are enriched. The enrichment type is restricted to extrinsic mesh‐based topological local enrichment. The results from the proposed formulation correlate well with analytical solution in the case of the beam and in the case of the Mindlin‐Reissner plate with those of a finite element package (ABAQUS) and classical FEM and show higher rates of convergence. In all cases, the proposed method captures strain discontinuity accurately. Thus, the proposed method provides an accurate and a computationally more efficient way for the formulation of beam and plate finite elements of minimal number of degrees of freedom.

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.

Hybrid metal-to-fiber reinforced polymer (FRP) joints are being used more commonly for load bearing applications. However, these hybrid joints usually entail geometry and material discontinuities which can induce stiffness mismatch and cause local stress concentrations. The shock impedance mismatch caused by the different wave propagation characteristics can also be crucial to the structural response of the hybrid joints under impulsive loads due to sources such as an air blast or underwater explosion (UNDEX). Recent research at Imperial College London (ICL) and the U.S. Naval Academy (USNA) has focused on characterizing the behaviour and ultimate load capacity of metal-to-composite hybrid joints with different configurations under various loading conditions. This paper presents results from tensile strength testing of steel-to-vinyl ester GRP double lap joints, comparing pseudo-static strength with dynamic strength and comparing joints that exploit perforated steel plates with those manufactured with non-perforated steel plates. An intentional manufacturing flaw also was incorporated into half of the joints, both perforated and non-perforated joints, in order to assess the effect of this flaw type on joint strength. These experimental results are compared to Finite Element Analysis (FEA) results for both perforated and non-perforated joints.

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.

This article presents a three-dimensional constitutive model to replicate the dynamic response of blast-loaded fibre–metal laminates made of 2024-0 aluminium alloy and woven composite (glass fibre–reinforced polypropylene). Simulation of the dynamic response is challenging when extreme localised loads are of concern and requires reliable material constitutive models as well as accurate modelling techniques. It is well known that back layers in a fibre–metal laminate provide structural support for front layers; thus, proper modelling of constituent failure and degradation is essential to understanding structural damage and failure. The improved developed model to analyse damage initiation, progression and failure of the composite is implemented in finite element code ABAQUS, and a good correlation is observed with experimental results for displacements of the back and front faces as presented by other researchers. The model was also able to predict accurately the tearing impulses. Finally, the concepts of the ‘efficiency of the charge’ and ‘effectiveness of the target’ are proposed in the context of localised blast loading on a structure. Dimensionless parameters are introduced to quantify these parameters.

Four point bending end notched flexure (4ENF) tests were used to evaluate the mode II fracture toughness (GIIC) of glass fibre reinforced vinyl-ester (GFRP) specimens in order to expose the sensitivity of GIIC to loading rate. Tests were carried out at load displacement rates ranging from 1 to 6000mm/min. Finite element models were used to evaluate the correction factors that are required during data reduction in order to compensate for geometrical non-linearity in the test. A high speed video camera was used in conjunction with the digital image correlation technique to measure crack propagation during the tests. It was found that, for short crack lengths, GIIC tended to increase as loading rate was increased.

The Buncefield incident in the UK in 2005 involved an explosion of 240,000 m(3) of vapour cloud which resulted in considerable damage to properties in the surrounding area. A number of objects that can be used as overpressure indicators such as standard steel drums were located at various points around the site. These were found deformed to different levels after the explosion. These overpressure sensitive objects were used to assess the overpressure level at the locations of the objects during the incident. This study describes full scale validation tests and numerical simulations of far-field air blast loading acting on deformable steel drums in order to investigate possible forensic methods to aid the incident investigation. Subsequently, a number of numerical models are developed in order to simulate the tests. Two models with varying complexity are used in the simulations: uncoupled Eulerian-Lagrangian model and coupled Eulerian-Lagrangian approaches. These models are validated against the test data from gas detonation explosion. Comparison between the numerical and experimental results suggests that both approaches tend to over-predict the deformation of drums due to identified inaccuracies from test measurements and numerical methods. However, both methods can comparatively capture the different levels of damage arising from blast loads with various intensities. These comparative levels are in general agreement with observations from test data. Parametric studies using the validated techniques are also carried out to further examine the response of steel drums. The results are summarised in the form of pressure-impulse diagrams, and typical residual shapes of drum models are selected to complement the pressure-impulse diagrams. The methods and results presented in this paper offer a very useful tool which could be employed to aid forensic investigations of future explosion incidents involving steel drums or similar field objects. (C) 2015 Elsevier Ltd. All rights reserved.

Hybrid steel-to-composite joints are being used more commonly for load bearing applications. However, these hybrid joints usually entail geometry and material discontinuities which can induce stiffness mismatch and cause local stress concentrations. The shock impedance mismatch caused by the different wave propagation characteristics can also be crucial to the structural response of the hybrid joints under impulsive loads. Recent research at Imperial College London (ICL) and the U.S. Naval Academy (USNA) has focused on characterizing the behavior and ultimate load capacity of hybrid steel-to-composite joints with different configurations under various loading conditions. This paper presents results from tensile strength testing of steel-to-composite double lap joints, comparing pseudostatic strength with dynamic strength and comparing joints that exploit perforated steel plates with those manufactured with non-perforated steel plates. An intentional manufacturing flaw also was incorporated into half of the joints, both perforated and non-perforated joints, in order to assess the effect of this flaw type on joint strength. Finite Element Analysis (FEA) results are compared to experimental results for both perforated and non-perforated joints.

Close-range blasts pose a threat through severe damage to structures and injury or death. In this work, the spatial and temporal descriptions of a localised blast load are presented using 6 non-dimensional parameters. These are found to be solely functions of the charge stand-off distance to diameter ratio for a cylindrically-shaped charge. Numerical simulations of a localised blast are performed using AUTODYN, where the pressure variation on a rigid barrier for various charge stand-off/diameter combinations is obtained. The least-square regression is then utilised to obtain the relationship between stand-off/diameter ratio and dimensionless loading parameters. The relevant expressions and dimensionless charts are presented. The proposed equations are verified by comparing experimental data with numerical results obtained by finite element analysis (FEA) of blast loaded steel plates (using the user-defined subroutine VDLOAD implemented in the FEA package ABAQUS/Explicit). Excellent correlation of the measured permanent displacement with numerically predicted results is obtained.

Permanent plastic deformation is expected when close-in blasts due to e.g. detonation of Improvised Explosive Devices (IED's) hit thin metallic targets. A circular thin steel plate i.e. a membrane is studied in the present work subject to a general form of a localised blast loading. The spatial shape of the pulse is fixed and different temporal shapes are investigated. Dynamic analyses are conducted and the permanent transverse displacements are found for each case.For high amplitude pulse loads of short duration, it was found that the permanent transverse displacement can be found by replacing the load by an impulse without the loss of accuracy. Excellent correlation with numerical simulations obtained from ABAQUS/Explicit is achieved. The predicted final displacements for different pulse shapes are also found to be similar, thus where membrane action is dominant, the response is insensitive to pulse shape. (C) 2015 Elsevier Ltd. All rights reserved.

Predictive computational modeling of the response of armor systems to dynamic threats such as blast and impact requires understanding and quantification of the behavior of the armor materials. This paper describes the mechanical characterization of Dyneema HB26. The in-plane tensile, compressive, and shear stress-strain behavior and strength of the laminate at low rates has been determined experimentally. The tensile behavior of the Dyneema SK76 fibers, which comprise 83% of the laminate has been determined, including the effect of temperature and rate. (C) 2014 American Society of Civil Engineers.