Structures under Shock & Impact VI, C.A. Brebbia & N ......Structures Under Shock and Impact 17 179 Figure 2 : Model used for the shock capture In the studied application, the 3D model

Numerical analysis of the structural response of

armoured vehicles subject to ballistic impacts

B. Malherbe & E. Deletombe

Solid and Damage Mechanics Department,ONERA, France

Abstract

Ballistic impacts on armoured vehicles cause shock effects that are transmitted inthe structure to the occupants and equipment. These often exceed the human andsystems limits. For a design engineer, reducing the shock levels transmitted to theoccupant and to the onboard equipment requires the use of specific analysis toolsand methods. A complete numerical methodology has been developed byONERA-Lille to treat this problem, the main objective of which is to be easilyusable by industrials to improve their structural design. A commercial finiteelement code is used, using explicit resolution methods. For computing costreasons, the problem must be solved in several steps. In a first step, local impacton a real 3D armour geometry is simulated. The complete description of theshock transmission is extracted from this simulation by an appropriatedtechnique, in the periphery of the armour. Then, the evolution of these data isdescribed through load functions, introduced as new inputs in the model of thecomplete structure. The natural response of the structure can then be analysed, interms of stress waves on the one hand, and of shock spectrums measured at theequipment's position on the other hand.

1. Introduction

The paper deals with the development and validation of numerical methodologiesto evaluate the structural behaviour of armoured vehicles subject to ballisticimpacts, and consider global survivability issues. The acceleration levels due tohigh energy impacts could reach and exceed the human and systems limits.Preserving the structural integrity is not enough, it is also necessary to reduce the

Structures under Shock & Impact VI, C.A. Brebbia & N. Jones (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-820-1

176 Structures Under Shock and Impact 17

level of the shock transmitted to the occupant as well as to the onboardequipment.

In the frame of a DGA/SPART French research programme, ONERA/DMSEand DCE/ETAS have been investigating the capability of explicit numerical F.E.codes to model the impacts as well as the subsequent structural response ofarmoured vehicles. Even with these very specific kind of tools which are wellsuited to study the transient dynamic response of materials and structures, theproblem still consists in solving separately two different classes of problems : thevery short in time and localised impact on the one hand, and the global structuralresponse on the other hand. The second chapter of this paper presents andjustifies the successive steps of the method.

Once the numerical methodology applied, the simulation results have to beextracted and analysed. In order to improve the structural design, two kinds ofanalysis are carried out: for qualitatively understanding the structural behaviour,the global response is studied in watching the loading flow distribution, and forquantitatively valuing the equipment's vulnerability, shock levels are measuredby shock spectrum analysis deduced from local accelerations. This exploitationof the result is described in the third chapter.

2. Presentation of numerical methods

The computation of ballistic aggression on an armour and the simulation ofstructural dynamic response are two very different, but linked problems. Spaceand time scales are not of the same order. On the one hand the ballistic impactand the propagation of the resulting shock wave in the armour are less than onemillisecond, and require a very thin 3D mesh to be modelled properly. On theother hand the natural response of the structure, composed of many wavereflections, must be studied during about 100 milliseconds, a coarser surfacicmesh being enough to model it. Explicit F.E. codes (like MECALOG'sRADIOSS one, used in this study) use a time integration. For numerical stabilityreasons, the time step depends on the mesh size : the thinner the mesh(somewhere in the model), the smaller the time step and the longer the computingtime.

To allow reasonable computing costs and industrial use, both problems mustbe solved separately, though it could be solved within one step with this tools, ifcomputing costs were not considered (very thin meshes). So, to ensure thevalidity of the results, the proposed method is as close as possible to that wouldbe a single step computation. Then the model of the local impact represents thereal geometries : a 3D mesh is developed for the munition and for the completearmour block. The pulse of the shock wave is captured in a grid placed at thearmour periphery. In a second step, this information is spatially and temporallyreintroduced in the surfacic model of the structure, where the armour is notmodelled. So, the computing costs of this structural model are relatively limitedcomparatively to the first one.


Structures Under Shock and Impact 17

2.1 Local impact modelling

177

The first step of the methodology concerns the simulation of the 3D local impacton the armour. The main objective of this part is to capture the shock wavecaused by the ballistic impact, in order to obtain the load to be applied in thesecond step on the structure. For a very precise evaluation of the penetration, thedeformations and the erosion of the munition, terminal ballistic simulations oftenuse two-dimensional or axisymmetric representations. So, even with very finemesh, computing costs are reasonable. But the results of such simulations can notbe used to provide inputs for a structural study, because of both followingreasons :

- the boundary conditions are not representative of the real structuralenvironment, which influence the waves system,the loading to be applied on the structure can not be obtained directly andmust be extrapolated, according to complex rules (to be validated).

Finally, in the presented method, and to deal with these problems, the truegeometries of the munition and the armour are meshed with volumic elements.Figure 1 shows a cut view of the simulation of the penetration of a kineticmunition into the armour block. The modelling methodology relies on asimplified F.E. approach, conservative and representative enough in terms ofenergy and frequency domain, but efficient in terms of computing times. Themodel is composed of about 35 000 brick elements, and the time step (mesh sizedependant) is 3.5 . 10~* ms. The CPU time of a 3 ms simulation is about 24 hourson a SGI R8000 workstation.

von Mises

Time = 0.8000 - ms

Figure 1 : Cut view of the impact simulation of a kinetic munition on an armourblock.


178 Structures Under Shock and Impact VI

In the studied application for this methodological development, the armour isan homogeneous steel block. The chosen numerical approach uses a Lagrangianformulation. The munition and the armour are modelled with an elasto-plasticJohnson-Cook material law, where temperature influence and strain rate effectsare taken into account (see equation 1 below):

(7 = (̂ +6.̂ ).(H-c.ln(-̂ )).(l-r̂ ), with: 7*"= %̂L d)^0 'melt ~^0

In the considered finite element model, material can only be "eroded" when amaximal strain criterion is reached. During the penetration of the munition, verylarge strains and material melting appear here and there in the munition and thearmour. These phenomena make the contacts difficult to manage, without using avery fine mesh or an arbitrary Lagrange-Euler formulation, which seriouslyincreases the computing costs. For preserving the industrial interest, another wayis proposed : considering the trajectory of the munition, its future "footprint" ismodelled as a stamp in which the munition impacts. This rigid envelop stampsthe armour consecutively to the shock of the munition, which is "physically"modelled (the munition melts in the rigid envelop). Then the contact is relativelyeasy to be managed.

Even if this modelling is a little bit simplified, it incorporates most of thephysical phenomena: the initial kinetic energy of the munition is transmitted tothe armour through strain and kinetic energy or consumed trough thermic and(possibly) friction energy. The possibility of introducing friction between thestamp and the armour also enables to adapt the stopping distance of the munition,and by this way the shock intensity.

If further experimental results show that the approach described above is toocoarse, some of the following improvements could be considered : mesh could belocally refined, or the use of a Lagarange-Euler formulation could improve thecontact management between the munition and the armour, and allow to avoidthe artifice of the rigid envelop.

2.2 Shock transfer methods

Assuming that the impact may be regarded as a pulse (less than one millisecond)from the structural response point of view, it is then captured in the former thin3D model of the armour (series of selected nodal data versus time functions) andre-injected in the latter vehicle model. This capture is carried out at the frontierbetween the armour and the structure, and may concern different types ofvariables.

For ensuring the validity of the extracted informations, the near environmentof the area where data are captured must be geometrically representative of thereal structure, and the boundary conditions must be set far enough of this area, inorder not to generate waves interference. The time step of the extracted data mustbe chosen in order to describe the evolution of the functions precisely enoughand to be compatible with the studied frequency domain.


Structures Under Shock and Impact 17 179

Figure 2 : Model used for the shock capture

In the studied application, the 3D model of the armour is surrounded with itsreal box, modelled with shell elements. This is continued with a very simplifiedstructure supported on a rigid wall. The general dimensions and plate thicknessesof this simplified structure are representative of the real structure.

Figure 2 shows this model with only a cut view of the armour. Different typesof informations may be extracted from it, in order to be directly re-injected in thestructural model. The process aims at preserving mechanical quantities, such aslinear momentum or contact forces. This quantities can be either displacementsor velocities or concentrated forces. They can be extracted at the periphery of thearmour, or in its box, or at the interface between both in the case of contactforces. Three different transfer methods, applied on a test model, have beenvalidated. They have proved the conservation of the global energy and of thelocal accelerations measured in the structure, after having applied equivalentloads.

Nevertheless, if these methods are conservative, they often require a verylarge number of load functions to be captured. The number of those functionsdepends on the mesh size of the armour and box models. It generally exceeds10 000 functions. The consequences are that the data sets size is very large (morethan 50 Mo), and that the computation of the structural response requires a largememory capacity and a proper data allocation capacity of the F.E codes.

2.3 Structural response modelling

This «equivalent structural loading» method once validated, the structuralresponse can be studied in a couple of hours. Indeed, the structure can bemodelled without the munition and the armour, that provides a quite coarsemodel.



The main further use of the simulation results being to study local shockspectrums, the model must be compatible with the targeted frequency domain. Inthe frame of this study, this domain goes from 10 Hz up to 10 kHz. Then somemesh rules must be considered. One the one hand, the time step of thecomputation (mesh size dependant) must allow to extract enough data forreaching high frequencies. 10 kHz means a maximal time step of 2.5 . 10"̂ s. Onthe other hand, high frequencies must not be filtered by too coarse a mesh. To besure to be geometrically representative of a bending mode, ten finite elements bywavelength are required. For steel material, 10 kHz means a maximal mesh sizeof 50 mm.

The armoured vehicle is modelled using only shell elements (see figure 3). Itincludes less than 20 000 elements, that is to say about twice less than the localimpact model. Another interest is that the time step is about 70 times longer thanin the local impact model, because of the much larger mesh size. So, thecomplete simulation of a 100 ms response needs only 9 CPU hours on a SGIR8000 workstation.

Without considering accurate mechanical properties, equipments are rigidlymodelled, tied up on the structure meshing. Their mass is taken into account.Seats are modelled (see figure 4), in order that, to study shock effects on theoccupants, numerical dummies could be used in the future.

Figure 3 : F.E model of the armoured vehicle


Structures Under Shock and Impact 17 181

Figure 4 : Seat model

3. Analysis tools

3.1 Loading flow analysis

Due to its reasonable computing costs, the presented structural model is avery well suited analysis tool, from an industrial point of view. In order to protectthe equipments from the shock effects, the structural design may be improvednumerically. It relies on a preliminary understanding of global mechanismsobserved in the structure. It is provided by an analysis of the stress distribution,that indicates the main loading paths in the structure. A possible easy use of suchanalysis could be to propose and test to shift some equipments in a less criticalarea.

3.2 Shock spectrum analysis

Shock resistance of electronic equipments is mainly linked to the accelerationlevels that they support. Those data can be measured either directly on thestructure or at the centre of gravity of the equipment. The first position is themost often used in experimental studies. In the numerical model, accelerationversus time curves can be extracted on each node. An example of resulting curveis given in figure 5. Such curves are difficult to be directly analysed, and do notenable to evaluate the consequences of the shock on the equipments easily.

For those reasons, shock spectrum analyses are processed. The techniquerelies on considering the equipment as a mass-spring system, linked to the



structure. The transfer function of the equipment being unknown, the oscillator isexcited with the locally measured acceleration signal, and its basic springcharacteristics are varied to cover the sought frequency domain. Differentdamping values are introduced in the spring. Automatic processing tools havebeen developed. An example of a result curve is shown in figure 6.

Then, shock resistance of the equipment can be analysed regarding a generalcriterion, which indicates for each frequency the vulnerability degree of theequipment.

Acceleration

80 10040 60Temps

Figure 5 : Example of an acceleration / time curve measured in the structure

1.00E+01 1.00E+02 1.00E+03Frequence • Hz

Figure 6 : Example of a shock spectrum computed in the structure


Structures Under Shock and Impact \'l 183

4. Conclusion

This paper has presented a complete numerical methodology, the main objectiveof which being to study the effects of ballistic shocks on the equipments. Theresolution relies on a 3-steps method :

local impact simulation, using a Lagrangian formulation,pulse capture on the periphery of the armour,computation of the structural response.

Concerning the CPU costs, the first step is the most expensive (about 24 CPUhours on a SGI R8000 workstation), but is performed only once for a consideredimpact. The simulation of the complete structural response, which is the mainpoint of interest, requires only 9 CPU hours on the same platform. This CPU timecould be now highly reduced in using up-to-date computers.

The main interest of the developed methodology is its direct and systematicaspect. It makes it possible indeed to solve the overall problem using a singletool, and sticking to the 3D real geometry of the structure. It also enables toperform series of structural computations varying or optimising parts of thevehicle to reduce the shock level.

The actual co-operation with DGA/SPART and DCE/ETAS has already madepossible the methodological development presented here. Its continuation aims toperform its ultimate validation in the one hand, and to be extended to otherproblematics, such as blast effects on the structures, in the other hand.


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Structures under Shock & Impact VI, C.A. Brebbia & N ......Structures Under Shock and Impact 17 179 Figure 2 : Model used for the shock capture In the studied application, the 3D model