Band 2, Heft 4

In spite of a large number of publications on shape optimization of penetrating projectiles there are no dedicated surveys of these studies. The goal of the present review is to close this gap. The review includes more than 50 studies published since 1980 and devoted to solving particular problems of shape optimization of high-speed penetrators. We analyze publications which employed analytical and numerical method for shape optimization of high-speed penetrators against concrete, metal, fiber-reinforced plastic laminate and soil shields. We present classification of the mathematical models used for describing interaction between a penetrator and a shield. The reviewed studies are summarized in the table where we display the following information: the model; indicate whether the model accounts for or neglects friction at the surface of penetrator; criterion for optimization (depth of penetration into a semi-infinite shield, ballistic limit velocity for a shield having a finite thickness, several criteria); class of considered shapes of penetrators (bodies of revolution, different classes of 3-D bodies, etc.); method of solution (analytical or numerical); in comments we present additional information on formulation of the optimization problem. The survey also includes discussion on certain methodological facets in formulating shape optimization problems for high-speed penetrators.

This paper describes the numerical investigation of the mechanical behaviour of a structural component of an aircraft wing flap support impacted by a wheel rim fragment. The support link made of composite materials was modelled in the commercial finite element code Abaqus/Explicit, incorporating intralaminar and interlaminar failure modes by adequate material models and cohesive interfaces. Validation studies were performed step by step using quasi-static tensile test data and low velocity impact test data. Finally, high velocity impact simulations with a metallic rim fragment were performed for several load cases involving different impact angles, impactor rotation and pre-stress. The numerical rim release analysis turned out to be an efficient approach in the development process of such composite structures and for the identification of structural damage and worst case impact loading scenarios.

This paper reports the application of an energy solution to a complex problem involving large inelastic deformation in thin, clamped ductile square plates with either square or circular holes under the action of transverse pulse pressure loading. The work is part of a collaborative project to study blast loading of steel plates with penetrations as used for deck plating or bulkheads that may be required to resist loading far in excess of their design limit due to the effects of an accidental explosion. A novel differential pressure loading device was used to impart dynamic loading to 1/8 scaled 0.5 m, 1.1 mm thick, clamped mild steel square plates with a central aperture up to 4% of the plate area. This data was used to validate the energy approach that considers both plastic hinge formation and extensional effects. Accounting for strain rate, scaling and dynamic effects in the tests gave more than acceptable results when compared with final deflections in the tested plates. It is concluded that the energy approach together with small-scale test validation paves the way for a versatile robust design methodology which can be used to advantage for screening purposes and/or early stage conceptual design studies.

This paper presents a general approach for analysing the response of beam, plates and shells to short duration pressure pulses typically encountered as a result of underwater explosions. The problem is formulated in terms of curvilinear coordinates and the resulting equations can then be specialized for each particular geometry. Results are presented for several examples.

This study presents an application of peridynamic theory for predicting residual strength of impact damaged building components by considering a reinforced panel subjected to multiple load paths. The validity of the approach is established first by simulating a controlled experiment resulting in mixed-mode fracture of concrete. The agreement between the PD prediction and the experimentally observed behavior is remarkable especially considering the simple material model used for the concrete. Subsequently, the PD simulation concerns damage assessment and residual strength of a reinforced panel under compression after impact due to a rigid penetrator.

A detonating explosive interacting with a deformable structure is a highly transient and non-linear event. In field blast trials of military vehicles, a standard procedure is often followed in order to reduce the uncertainties and increase the quality of the test. If the explosive is buried in the ground, the state of the soil must meet specific demands. In the present work, laboratory experiments have been performed to characterize the behaviour of a soil material. Soil may be considered a three-phase medium, consisting of solid grains, water and air. Variations between the amounts of these phases affect the mechanical properties of the soil. The experimental outcome has formed input data to represent the soil behaviour included in a three-phase elastic-plastic cap model. This unified constitutive model for soil has been used for numerical simulations representing field blast trials, where the explosive load is interacting with a deformable structure. The blast trials included explosive buried at different depths in wet or dry sand. A dependence of the soil initial conditions can be shown, both in the past field trials along with the numerical simulations. Even though some deviations exist, the simulations showed in general acceptable agreement with the experimental results.

Dynamic fracture in brittle materials has been difficult to model and predict. Interfaces, such as those present in multi-layered glass systems, further complicate this problem. In this paper we use a simplified peridynamic model of a multi-layer glass system to simulate damage evolution under impact with a high-velocity projectile. The simulation results are compared with results from recently published experiments. Many of the damage morphologies reported in the experiments are captured by the peridynamic results. Some finer details seen in experiments and not replicated by the computational model due to limitations in available computational resources that limited the spatial resolution of the model, and to the simple contact conditions between the layers instead of the polyurethane bonding used in the experiments. The peridynamic model uncovers a fascinating time-evolution of damage and the dynamic interaction between the stress waves, propagating cracks, interfaces, and bending deformations, in three-dimensions.

Aircraft occupant crash-safety considerations require a minimum cushion thickness to limit the relative vertical motion of the seat-pelvis during high vertical impact loadings in crash landings or accidents. In military aircraft and helicopter seat design, due to the potential for high vertical accelerations in crash scenarios, the seat system must be provided with an energy absorber to attenuate the acceleration level sustained by the occupants. Because of the limited stroke available for the seat structure, the design of the energy absorber becomes a trade-off problem between minimizing the stroke and maximizing the energy absorption. The available stroke must be used to prevent bottoming out of the seat as well as to absorb maximum impact energy to protect the occupant. In this study, the energy-absorbing system in a rotorcraft seat design is investigated using a mathematical model of the occupant/seat system. Impact theories between interconnected bodies in multibody mechanical systems are utilized to study the impact between the seat pan and the occupant. Experimental responses of the seat system and the occupant are utilized to validate the results from this study for civil and military helicopters according to FAR 23 and 25 and MIL-S-58095 requirements. A model for the load limiter is proposed to minimize the lumbar load for the occupant by minimizing the relative velocity between the seat pan and the occupant’s pelvis. The modified energy absorber/load limiter is then implemented for the seat structure so that it absorbs the energy of impact in an effective manner and below the tolerable limit for the occupant in a minimum stroke. Results show that for a designed stroke, the level of occupant lumbar spine injury would be significantly attenuated using this modified energy-absorber system.

Advanced polymeric materials are finding an increasing range of industrial and defence applications. These materials have the potential to improve combat survivability, whilst reducing the cost and weight of armour systems. In this paper the results from a split Hopkinson pressure bar (SHPB) test of a high density polyethylene (HDPE) sample involving multiple stress waves is discussed with aid of a finite element model of the test. It is seen that the phenomenon of impedance mismatch at interfaces plays an important role in the levels of stress and deformation seen in the sample. A multi-layer armour system is then investigated using the finite element model. This case study illustrates the role of impedance mismatch and interface engineering in the design and optimisation of armour solutions.

The behaviour of a vehicle at high-speed crashes is enhanced by using active vehicle dynamics control systems. A 6-Degree-of-Freedom (6-DOF) mathematical model is developed to carry out this study. In this model, vehicle dynamics is studied together with vehicle crash structural dynamics. Validation of the vehicle crash structure of the proposed model is achieved to ensure that the modelling of the crumble zone and the dynamic responses are reliable. Five different speeds are selected to investigate the robustness of control system and its effect on the vehicle crash characteristics at low and high speeds with full and offset collision scenarios. A great improvement of vehicle pitch and yaw angels and accelerations at high speed collision are obtained from this analysis.

An experimental study was performed on the repeated low-velocity impact behaviour of GLARE. Damage evolution in the material constituents was characterised with successive number of impacts. Records were correlated with visual inspection, ultrasound C-scan and chemical etching. The stiffness of the plate varied when cumulating the number of impacts. Damage accumulation was limited thanks to the synthesis of unidirectional composite and metal. The glass/epoxy plies with high elastic tensile strength could withstand several impacts before perforation despite delamination growth in the vicinity of the impacted area. The damage tolerant aluminium layers prevented the penetration of the projectile and avoided the expansion of delamination. This efficient mechanism preserved the structural integrity of GLARE until first aluminium cracking at the non-impacted side. Among the different failure modes, plate deformation absorbed most of the impact energy. The findings will support the development of a generic quasi-static analytical model and numerical methods.

Maximising impact protection of fibre reinforced plastic (FRP) laminated composite structures and predicting and preventing the negative effects of impact on these structures are paramount design criteria for ground and space vehicles. In this paper the low velocity impact response of these structures will be investigated. The current work is based on the application of explicit finite element software for modelling the behaviour of laminated composite plates under low velocity impact loading and it explores the impact, post impact and failure of these structures. Three models, namely thick shell elements with cohesive interface, solid elements with cohesive interface, and thin shell elements with tiebreak contact, were all developed in the explicit nonlinear finite element code LS-DYNA. The FEA results in terms of force and energy are validated with experimental studies in the literature. The numerical results are utilized in providing guidelines for modelling and impact simulation of FRP laminated composites, and recommendations are provided in terms of modelling and simulation parameters such as element size, number of shell sub-laminates, and contact stiffness scale factors.

The mechanical behavior of elastomeric foam, in particular, Ethylene Propylene Diene Methyle (EPDM) and crushable foams, in particular, Expanded Poly-Propylene (EPP) and Poly Urthane Rigid (PUR), under low-velocity impact are studied experimentally and numerically. At first, these foams were loaded under quasi-static loading in compression. In order to study the dependence of their behavior on strain rate, the loadings were performed in two rates, 3 mm/min and 100 mm/min. The low-velocity impact tests were applied using a drop hammer testing machine. The drop heights of projectile in all tests were 0.5 and 1 m. The thickness effect of specimens on absorption of energy and parameters such as, contact force and displacement of specimens are discussed. Then, the dynamic factors of force and energy for three types of foam are investigated. Since, EPP showed an insensitive property to the thickness of specimen in the impact tests, it is possible to define dynamic factors for different thickness of this type of foam. Finally, all test results are compared with numerical results through implementation of ABAQUS finite element package. Good agreements between numerical results and experimental data show the capability of numerical modeling to fulfill the experimental investigation.

In the present study, impact behavior of Kevlar/Epoxy composite plates has been carried out experimentally by considering different thicknesses and lay-up sequences and compared with analytical results. The effect of thickness, lay-up sequence on energy absorbing capacity has been studied for high velocity impact. Four lay-up sequences and four thickness values have been considered. Initial velocities and residual velocities are measured experimentally to calculate the energy absorbing capacity of laminates. Residual velocity of projectile and energy absorbed by laminates are calculated analytically. The results obtained from analytical study are found to be in good agreement with experimental results. It is observed from the study that 0/90 lay-up sequence is most effective for impact resistance. Delamination area is maximum on the back side of the plate for all thickness values and lay-up sequences. The delamination area on the back is maximum for 0/90/45/-45 laminates compared to other lay-up sequences.

This paper address the examination of spall damage in medium carbon steel subjected to a repeated impact testing. The experiments were performed well below the threshold spall-stress of 2.6 GPa and the damage introduced in the subsurface volume was investigated using the low frequency scanning acoustic microscopy. Based on B- and C-scan images (the images taken along and perpendicular to the impact surface) we made a qualitative and semi-quantitative evaluation of the damage type (voids in a ductile material or cracks in a brittle one) and its distribution. We found the spall damage development dependent on the amplitude and the duration of the stress pulses. In particular, we proved that the high, long stress pulses induce damage that resembles tensile failure of material, in which voids or cracks nucleate along the spall plane to form macro-cracks. This explains why spall-damage is not seen when the first impact is below the characteristic threshold spall-stress. However, when the tests consist of more than four impacts the spall damage is produced already under stress below the threshold-value.

Construction of spherical vessel in various dimensions is known as one of the frequent problems for construction and production engineers, since conventional methods of shell construction require mold and press which leads to higher costs of production. Therefore, current work has tried to investigate a new method based on explosive forming without using molds. In this technique, final shape of the shell can be achieved by explosion inside a prefabricated structure called four cones. This structure is produced from combination and welding of four truncated cones two of which are paired in each side. Initial shape of the tank is then used to transform this structure into a more complete sphere using explosives at its center. This paper aims to study the amount of explosives needed for this process in terms of vessel’s diameter and thickness. In this regard, simulation was run by LS-DYNA software and the resultant outputs were evaluated with those of experimental tests. The results shows that the required charge of forming varies exponentially with thickness.