Introduction of an Electromagnetism Module in LS-DYNA for Coupled Mechanical-Thermal-Electromagnetic Simulations

Transcription

1 Metal Foming Intoduction of an Electomagnetism Module in LS-DYNA fo Coupled Mechanical-Themal-Electomagnetic Simulations Piee L Eplattenie ), Gant Cook ), Cleve Ashcaft ), Mike Buge ), Jose Imbet 2) and Michael Woswick 2) ) Livemoe Softwae Technology Copoation, 7374 Las Positas Road, Livemoe, CA 9455, USA, Piee@lstc.com 2) Depatment of Mechanical and Mechatonics Engineeing, Univesity of Wateloo, Wateloo, Ontaio, Canada A new electomagnetism module is being developed in LS-DYNA fo coupled mechanical/themal/electomagnetic simulations. One of the main applications of this module is Electomagnetic Metal Foming. The electomagnetic fields ae solved using a Finite Element Method fo the conductos coupled with a Bounday Element Method fo the suounding ai/insulatos. Both methods use elements based on discete diffeential foms fo impoved accuacy. The physics, numeical methods and capabilities of this new module ae pesented in detail as well as its coupling with the mechanical and themal solves of LS-DYNA. This module is then illustated on two Electomagnetic Metal Foming cases, the foming of an aluminum sheet on a conical die using a spial coil, and the foming of an aluminum sheet on a v-shaped die using a double pancake coil. The expeimental setups ae pesented as well as compaisons between expeimental and numeical esults. Keywods: Modelling, Finite Element Method (FEM), Bounday Element Method (BEM), Electomagnetic Metal Foming (EMF). DOI:.2374/SRI8SP52; submitted on 9 Septemebe 28, accepted on 2 Januay 29 Intoduction LS-DYNA is a highly advanced geneal-pupose nonlinea finite element pogam that is capable of simulating complex eal wold poblems. It is suitable to investigate phenomena that involve lage defomations, sophisticated mateial models and complex contact conditions []. LS-DYNA allows unning an analysis explicitly o implicitly and combining diffeent disciplines such as coupled themal analysis, fluid dynamics, fluidstuctue inteaction, SPH (smooth Paticle Hydodynamics), EFG (Element Fee Galekin). Metal foming is one of LS-DYNA s main applications, with capabilities that allow one to simulate olling, extusion, foging, casting, spinning, ioning, supe-plastic foming, sheet metal stamping, pofile olling, deep dawing, hydofoming, multi-stage pocessing, spingback, hemming. An electomagnetism (EM) module is unde development in LS-DYNA in ode to pefom coupled mechanical/themal/electomagnetic simulations [2]. This module allows us to intoduce some souce electical cuents into solid conductos, and to compute the associated magnetic field, electic field, as well as induced cuents. These fields ae computed by solving the Maxwell equations in the eddy-cuent appoximation. The Maxwell equations ae solved using a Finite Element Method (FEM) [3] fo the solid conductos coupled with a Bounday Element Method (BEM) [4] fo the suounding ai (o insulatos). Both the FEM and the BEM ae based on discete diffeential foms (Nedelec-like elements [5]). Electomagnetic Metal Foming (EMF) is one of the main applications of this development. EMF is a high velocity foming pocess whee the foce defoming the wokpiece is a magnetic one, geneated by an electical cuent induced in the wokpiece by a coil. Much wok has shown that the fomability can be significantly inceased, winkling can be mitigated, spingback can be educed and so foth. Foming of aluminum has been the main focus of EMF, due to its potential as a means of educing automobile weight. Othe pocesses could also be simulated, whee magnetic pessue induces mechanical stess and defomations and/o the Joule effect induces a heating pocess: magnetic metal cutting, magnetic metal welding, vey high magnetic pessue geneation, ail-gun type appaatus, computation of the stesses and defomations in vaious coils, magnetic flux compession, induced heating and so foth. In the fist pat, the EM module will be pesented, the FEM pat, the BEM pat, and the coupling with extenal cicuits. In a second pat, the coupling of the EM module with the est of LS-DYNA, and in paticula with the mechanical and themal modules will be pesented. In the thid pat, some compaisons between expeimental and numeical esults ae pesented on two EMF cases: the foming of an aluminum sheet on a conical die using a spial coil, and the foming of an aluminum sheet on a v-shaped die using a double pancake coil. Pesentation of the Electomagnetism Module Scala potential and Modified vecto potential fomulation. Let Ω be a set of multiply connected conducting egions. The suounding insulato exteio egions will be called Ω e. The bounday between Ω and Ω e is called Γ, and the (atificial) bounday on Ω at the end of the meshing egion (hence whee the conductos ae steel eseach int. 8 (29) No. 5 35

2 Metal Foming connected to an extenal cicuit) is called Γ c. In the following, we will denote n as the outwad nomal to sufaces Γ o Γ c. The electical conductivity, pemeability and pemittivity ae called σ, and ε espectively. In Ω e, we have σ = and =. We stat with the Maxwell equations in the so called low fequency o eddy-cuent appoximation, which is valid fo good enough conductos with low fequency vaying fields such that the condition E ε pp σe is satisfied, t whee E is the electic field. This appoximation implies a divegence fee cuent density and no fee chage accumulation. It is vey well satisfied in EMF expeiments. B E = () t B = (2) B = (3) ε E = (4) = (5) = σ E + (6) S whee B is the magnetic flux density, the total cuent density, and S is a divegence fee souce cuent density. The divegence condition (3) allows witing B as B = A (7) whee we intoduce the magnetic vecto potential A [6]. Equation () then implies that the electic field is given by A E = φ (8) t whee φ is the electic scala potential. We use the Gauge condition σ A = (9) which allows a sepaation of the vecto potential fom the scala potential in the equations. Equations (5), (6), (8) and (9) imply: σ φ = () And equations (2), (7), (6) and (8) imply: A σ + A + σ φ = () S t Equations () and () epesent the Maxwell equations in tem of the 2 potentials. They come with the following bounday conditions: n φ = on Γ (2) φ = φ c on Γ c (3) and n A = on Γ (4) n A = A c A e on Γ c (5) Equation (3) allows the connection of the conductos to a voltage souce and equation (5) to a cuent souce, although we will show in the following that the connection with a cuent souce can also be done though the BEM pat of the system, allowing moe flexibility when using conductos with non tivial topologies. Once the potentials ae computed, the electomagnetic fields ae given by Equations (8), (7) and (6). Finite element method. Equations () and () ae solved in the conductos with a Finite Element Method using a libay called FEMSTER developed at the Lawence Livemoe National Laboatoies [7]. FEMSTER povides discete numeical implementations of the concepts fom diffeential foms (often efeed as Nedelec elements) [8-9]. These include in paticula the exteio deivatives of gadient, cul and divegence, and also the div-gad, cul-cul and gad-div opeatos. FEMSTER povides fou foms of basis functions, called -foms, -foms, 2-foms and 3-foms, defined on hexaheda, tetaheda and pisms. At this time, only hexahedal elements ae available in the EM module of LS-DYNA. The two othe types will soon be available. -foms ae continuous scala basis functions that have a well defined gadient, the gadient of a -fom being a - fom. At fist ode, the degees of feedom associated with a -fom ae the values of the scala field at the nodes of the mesh. In ou paticula case, the -foms ae used fo the discetization of the scala potential φ. -foms ae vecto basis functions with continuous tangential components but discontinuous nomal components. They have a well defined cul, the cul of a - fom being a 2-fom. At fist ode, the degees of feedom of a -fom ae its line integals along the edges of the mesh. They ae used fo the discetization of the electic field E, the magnetic field H and the vecto potential A. 2-foms ae vecto basis functions with continuous nomal components acoss elements but discontinous tangential components. They have a well defined divegence, the divegence of a 2-fom being a 3-fom. At fist ode, the degees of feedom of a 2-fom ae its fluxes acoss all the facets of the mesh. They ae used fo the discetization of the magnetic flux density B, and the cuent density. 352 steel eseach int. 8 (29) No. 5

3 Metal Foming Finally, the 3-foms ae discontinuous scala basis functions which cannot be diffeentiated. Thei degees of feedom at fist ode ae thei integals ove the elements of the mesh. These basis functions define spaces with an exact epesentation in the De-Rham sequence [7]. They also exactly satisfy numeical elations such as cul(gad)= o div(cul)=, which ae vey impotant fo consevation laws when solving the systems []. At fist ode, they allow one to solve patial diffeential equation at an integated Stokes theoem level which poves to be vey efficient and accuate, even on low density meshes, compaed to using vecto basis functions []. We will denote W, W 2, W 3, and W as the basis functions associated espectively with the,, 2, and 3- foms. Equation () is poected against -foms basis functions and Equation () against -foms to give, afte using the appopiate Geens vecto identities and the bounday conditions (2) - (5) []. Ω Ω σ φ W dω = A σ W dω + t Ω Ω A W dω = σ φ W dω + [ n ( A)] W dγ Γ (6) (7) o equivalently afte decomposing A and φ espectively on the -fom and -fom basis functions: S ( σ ) ϕ = (8) da M ( σ ) + S ( ) a = D ( σ ) ϕ + Sa (9) dt whee we intoduce the -fom stiffness matix S, the - fom mass matix M, the -fom stiffness matix S and the - fom deivative matix D []. The last tem of Equation (9) which involves the outside matix stiffness S is computed using a Bounday Element Method. Bounday Element Method. In ode to compute Sa, an intemediate vaiable suface cuent k is intoduced. This suface cuent, defined on the bounday Γ is such that it poduces the same vecto potential (and thus B field) in the exteio egions Ω e as the actual volume cuent flowing though the conductos []: A ( x) = k ( y) dy (2) 4π x y Γ fo all x Ω (and in paticula fo all x Γ ). One then has: e [ n ( A)]( x) = k ( x) 2 n [( x y) k ( y)] dy 3 4π x y Γ fo x x Γ (2) When poecting these equations on the -foms basis functions fo A and the twisted -foms V ( x) = n W ( x) fo k one gets the following matix equations: Pk = Da (22) Sa = Qk Q k Q k (23) S + whee we intoduce the BEM matices D P i = Vi ( x) V ( y dγxdγy 4 x y ),, π ΓxΓy D = V ( x) W ( x) dγ i, S i, i Γx Wi ( x) V 2 Γx x x (24) Q = ( x) dγ, (25a) Q 4π = Di, ΓxΓy Wi ( x) { nx [( x y) V ( y)]} dγx dγ 3 y x y (25b) The BEM method is vey appealing since it does not need a mesh in the ai suounding the conductos. It thus avoids the meshing poblems associated with the ai, which can be significant fo complicated conducto geometies. Also, fo vey small gaps between conductos, an ai mesh could include a lage numbe of vey small and distoted elements. Even moe impotantly, the BEM avoids emeshing poblems which aise when using an ai mesh aound moving conductos. Anothe advantage of the BEM is that it does not need the intoduction of somewhat atificial infinite bounday conditions. The main disadvantage of the BEM is that it geneates fully dense matices like P and Q D (24,25) in place of the spase FEM matices. This causes a-pioi high memoy equiements as well as longe CPU time to assemble the matices and solve the linea systems. In ode to limit the memoy equiement, a domain decomposition is done on the BEM mesh, which splits the BEM matices into subblocks. On the non-diagonal sub-blocks, a low ank appoximation based on a ank evealing QR decomposition is pefomed. Fo sub-blocks coesponding to fa away domains, the ank can be significantly smalle than the size of the sub-block, thus educing the stoage of the sub-block. We typically see eductions of by factos aound 2 between the fully dense matix and the block matix with low ank appoximations. This low ank appoximation also speeds up the matix * vecto opeation used intensively in the iteative method to solve the BEM system (22). This method still needs the steel eseach int. 8 (29) No

4 Metal Foming assembly of the full sub-blocks befoe doing the low ank appoximation, geneating a time consuming assembly pocess. We cuently ae woking on methods fo diectly geneating the low ank appoximations of the sub-blocks. The matices P and Q D (24-25b) become singula o nealy singula as x y, i.e. fo self face integals o integals ove neighbo faces with a common edge o a common node. Special methods have been included such as the ones descibed in [2] and [3]. These methods also allow moe accuate integation on inhomogeneous faces, i.e. faces with lage aspect atio. Divegence fee suface cuent, connection with extenal cicuits. The suface cuent k is an equivalent bounday cuent to the actual volume cuent though the volume of the conducto and needs to be divegence fee []. Howeve, the twisted -foms basis functions V do not satisfy this divegence fee constaint. We fist added it as an extenal constaint to the BEM system (22). Moe ecently, we intoduced the so called loop-sta solenoidal-iotational decomposition into the divegence fee loop basis functions and the othe ones [4-5]. At fist ode, a twisted -fom associated with a suface edge epesents a suface cuent flowing acoss the edge, i.e. with a unit suface flux acoss the edge and a zeo suface flux acoss all the othe suface edges. A loop basis function associated with a node can be seen as a linea combination with coefficients + o - of -foms associated with all the edges oiginating fom the node, so that it epesents a (divegence-fee) cuent flowing aound the node. One can show that when using fist ode basis functions, the loop basis function associated with all the nodes of the suface mesh (except one) fom a complete basis of the divegence fee cuents fo topologically simple conductos [4]. Fo non-simple conductos, i.e. containing holes o handles, a few exta non-local basis functions that we call global cuents need to be added. Fo example in the case of a tous, two exta global cuents need to be added, one coesponding to a cuent flowing in the tooidal diection, and one coesponding to a cuent flowing in the poloidal diection. An algoithm based on the constuction of a spanning tee on the suface mesh has been developed to automatically count the numbe of connected pats, get thei topologies by computing the Betti numbes [6], and in paticula the numbe of global cuents and then set the global cuent basis functions as linea combinations of the -fom basis functions. The degees of feedom associated with the global cuents ae used to impose cuent vs time constaints as a simple diichlet constaint in the BEM system (one diichlet constaint pe imposed cuent). This method allows imposing cuents in geometies whee moe taditional methods using diichlet conditions on the FEM system (5) would equie the intoduction of cuts and/o multi-valued degees of feedom. The above mentioned tooidal cuent in a tous is such an example. The use of loop and global cuent basis functions also gives an easy way to compute the self and mutual inductances, by solving BEM systems (22) with simple diichlet constaints. In this manne, the conductos can be connected to a cuent souce, a voltage souce, o an R,L,C cicuit. Global integation scheme. The time integation of the FEM system (9) is done using an implicit backwad eule method []: σ σ σ ϕ t + t ) t + t + [ M ( ) + dts ( )] a = M ( ) a dtd ( + dtsa (26) t+ The BEM pat of the ight hand side dtsa also is implicit which poved to substantially impove the stability, thus allowing lage time steps. It is computed by solving the BEM system (22)(23) coupled with the FEM system (9) in an iteative way: Pk Da (27) t+ = t+ n+ n t + t ) t + t + [ M ( σ ) + dts ( )] an+ = M ( σ ) a dtd ( σ ϕ + dtqkn+ (28) t + t + until convegence on both k n and a n. The FEM System (28) is solved using a diect solve. The BEM system (27) is solved using a pe-conditioned gadient method. The diagonal of the matix has been used as a pe-conditione. Moe ecently, the diagonal block has been used instead [7], with significant eduction in the numbe of equied iteations (typically by a facto between.5 and 3). Coupling of the EM Module with LS-DYNA Mechanical solve. Once the EM v fields have been computed, the Loentz foce F = B is evaluated at the nodes and added to the mechanical solve. The mechanical and electomagnetic solves each have thei own time step. Fo a typical EMF simulation, the mechanical time step is about times smalle than the electomagnetic one. At this time, the explicit mechanical solve of LS-DYNA is used when coupled with electomagnetism. The mechanical module computes the defomation of the conductos and the new geomety is used to compute the EM fields in a Lagangian way. Since the EM module is fully integated in LS-DYNA, all the mateial models ae available. LS-DYNA povides moe than 3 metallic and non-metallic mateial models, many of them equipped with failue citeia, such as metals, plastics, visco-elastic, elasto-viscoplastic, glass, foam, elastomes and ubbes. Included also ae stain ate and tempeatue dependant plasticity models such as Johnson-Cook [8], Zeilli-Amstong [9] o Steinbeg [2] models, which ae paticulaly suitable fo high speed foming simulations. Numeous equations of state ae also available. These models can be used on an extensive 354 steel eseach int. 8 (29) No. 5

5 Metal Foming element libay with both unde-integated and fullyintegated element fomulations. It includes diffeent solid elements, thick shells, diffeent 3- and 4-node shells and beams. At this time, the EM module is only available on solid elements. It should soon be extended to shells with appopiate teatment of the diffusion of the EM fields. Finally, efficient contact algoithms have been developed fo the mechanical solve, and ove 25 diffeent contact options ae available. At this time, the contact puely is mechanical and themal, not electomagnetic, i.e. a cuent cannot flow fom one conducto to anothe if they come in contact duing the simulation. This will be added as well as an electomagnetic sliding contact capability, necessay fo ail-gun applications. Themal solve. The Joule heating tem 2 /σρ is added to the themal solve allowing to update the tempeatue. Seveal themal models ae available, isotopic, othotopic, isotopic with phase change and so foth. The tempeatue can be used in tun in an electomagnetic equation of state to update the electomagnetic paametes, mainly the conductivity σ. At this time, a Bugess model [2] has been intoduced. Input-output. Electomagnetic cads have been added to the standad LS-DYNA cad list used to ceate the input deck. The LS-PREPOST softwae can be used to visualize the electomagnetic fields - cuent density, electic field, magnetic flux density, Loentz foce, oule heating, conductivity, suface cuent - in the same envionment as the mechanical and themal fields. These include finge component, iso-contou, vecto plots at a given time, and also time histoies on chosen elements. Figue. Mesh of case. Only half of the sheet and die ae epesented. Figue 2. 3D shape of the sheet fo case (only half of the sheet is epesented), at 45s (top left), 7s (middle ight) and s (bottom left). Compaisons between Expeimental and Numeical Results on EMF cases We now pesent some compaisons between expeimental and numeical esults on actual metal foming expeiments. Dealing with eal life models allows us to show the code s capability to handle complicated stuctues. Moe quantitative compaisons on simple cases have aleady been pesented in [2]. Case : foming of conical samples with a spial coil Expeimental setup. The fist case deals with the electomagnetic foming of a mm thick aluminum sheet on a conical die. This foming epesents pat of the wok pefomed by some of the authos at the Depatment of Mechanical Engineeing, Univesity of Wateloo, Ontaio, Canada. It is descibed in [22-24] whee details of the expeimental pocedues can be found. Conical samples of 4 side angle wee analysed fo this study. A seven-tun bass spial coil with a nominal diamete of mm and a maximum diamete of 5 mm at the end was used. An IAP Magnepess magnetic pulse geneato with a stoage capacity of 22.5 kj at 5kV was used to fom the samples. The cuents used to fom these samples wee Figue 3. Case : detail of the ebounding of the sheet fom the die: coss section of the sheet (thick line) and die (thin line) at 7s (left), s (middle) and 3s (ight). unfotunately not measued. The chage voltage was the ecoded input paamete and fo the samples in question it was 8 V. Numeical simulation. A hexahedal 3D mesh was built fo the coil and the wokpiece, and shell elements wee used fo the die. The mesh is composed of 2736 elements fo the coil, 3232 fo the aluminium sheet, with 4 elements though the thickness, and 722 shells fo the die. This mesh geneated 2356 BEM faces, and 2363 BEM nodes (and hence 2363 degees of feedom in the BEM system). Figue shows the mesh at initial time. Compaison between expeiment and simulation. Figue 2 shows the evolution of the shape of the plate. Figue 3 steel eseach int. 8 (29) No

6 Metal Foming Figue 4. Case : numeical (left) and expeimental (ight) final shape of the sheet. Die Sheet Coil Cuent Output Sheet Cuent Input 23 mm 97 mm Binde Figue 5. Case 2: Expeimental appaatus fo the v-channel samples. Figue 6. Case 2: Mesh used fo the v-channel model. The binde and die wee not included in the EM calculation. shows details of the ebounding of the sheet fom the die. Figue 4 shows a compaison between the numeical and expeimental final shape of the sheet. The final shape shows a good ageement. One can notice that the shape does not match the shape of the die, due to ebounding of the plate fom the die and a non-unifom magnetic pessue on the sheet, with a significantly lowe pessue at the cente. This low pessue aea is eflected in the cuent density plots, and is due to the shape of the coil. Case 2: foming of V-shaped samples with a double pancake coil Expeimental setup. Fo these expeiments, also pefomed at the Univesity of Wateloo, a flat double pancake coil encased in Gaolite and epoxy was used. The coil was designed to get a close to unifom magnetic pessue on a lage aea, in contast to the spial coil. The coil was connected to a Pulsa MPW 2 Reseach Edition magnetic pulse geneato, which consists of a capacito bank and a powe supply to delive the cuent to the capacitos at the equied specifications. The pulse geneato has a nominal maximum enegy capacity of 2 kj and chaging voltage of 9 kv. A tiangula o v shaped die with a side angle of 4 was chosen, since it was the maximum safe angle eached with the conical samples studied in [22]. The mateial used was AA 5754 in mm sheets in samples of 97 x 35 mm. The metal samples wee placed ove the coil with sheets of an insulating mateial (Kapton ) sepaating the coil fom the sample fo additional insulation. The sheet was then clamped using a hydaulic pess. Two sets of samples wee fomed, one whee the samples did not make impact with the die and the othe whee the mateial impacted the die. These samples wee fomed using 3 V and 5 V espectively. Figue 5 shows the appaatus used fo these expeiments. Numeical simulation. The coils and wokpieces wee modeled using eight node hexagonal solid elements. The sheet was modeled with an elastic-plastic piecewise linea plasticity model descibed in [22,23]. An isotopic quasistatic model was deemed acceptable since AA 5754 has shown little stain ate sensitivity [25]; howeve, the mateial has not been tested unde the conditions encounteed duing EMF. The coils wee modeled as elastic mateials with a Young s Modulus of 97 GPa. Both expeimental and numeical esults showed no noticeable defomation of the coil. The bindes and dies wee modeled as igid bodies using shell elements, and wee 356 steel eseach int. 8 (29) No. 5

7 Metal Foming Figue 7. Case 2: v-channel sample fomed with a 3 V chaging voltage. The sample did not make contact with the die. Figue 8. Case 2: numeical final shape fo a v-channel foming pocess with a 3 V chaging voltage. Contous ae of effective plastic stain, fom (black) to. (white). Mateial at the edges is fomed to a lowe height to do the foce distibution Figue 9. Case 2: v-channel sample fomed with a 5 V chaging voltage. The shaded aeas indicate whee the sample made contact with the die. The uneven foming is attibuted to coil impefections which esult in an uneven foce distibution. Rebound of walls Figue. Case 2: numeical final shape fo a v-channel foming pocess with a 5 V chaging voltage. Contous ae of effective plastic stain, fom (black) to.46 (white). ignoed fo the electomagnetic calculation. The mesh used fo the open channel models is shown in Figue 6. The sheet mesh fo the open channel simulations had 28 8 elements. The model was connected to an RLC cicuit with the esistance, inductance and capacitance of the system being povided as inputs and the softwae calculated the cuent. The values used fo the v-channel simulations wee; R= 5.96 x -3 Ohms, L= 48. x -6 mh and C= 2.7 x -7 F. A constant conductivity of 25 x 6 Ohm - m - was used fo the coil and sheet. This simplification esults in some inaccuacies; howeve, fo the puposes of this study it was consideed acceptable. Compaison between expeiment and simulation. A v- channel sample fomed using 3 V chaging voltage whee no impact with the die occued is shown in Figue 7. The pats ae not fomed unifomly, which is an indication that the foce distibution is uneven. Figue 8 shows the numeical final shape fo the same case and it can be seen that the mao featues of the pat ae pedicted. Howeve, the asymmetic height distibution of the samples (Figue 7-c) is not captued by the models. The samples fomed using a chage voltage of 5 V made contact with the die which esulted in a distinctive shape, as shown in Figue 9. The dake aeas on the pats ae the places whee the sheet made contact with the die. steel eseach int. 8 (29) No

8 Metal Foming It is appaent that the final pat does not coespond to the shape of the v-channel die. The numeical final shape is shown in Figue. The final shape is the esult of the numeical sheet ebounding fom the impact with the die. The model captues the geneal tends; howeve, thee ae discepancies that ae likely due, in pat, to the diffeence between the actual coil and the model of it and to the mateial model. The coil has geometic impefections, such as uneven heights, which ae not accuately epoduced in the mesh fo the numeical model. Also, the quasi-static mateial model used may not be captuing the actual behavio of the mateial in the foming conditions in question. Conclusions The newly intoduced Electomagnetism module of LS- DYNA was pesented. The electomagnetic fields ae computed by solving the Maxwell equations in the eddycuent appoximation, using a Finite Element Method fo the conductos coupled with a Bounday Element Method fo the suounding ai and insulatos. Loop basis functions ae used to epesent the BEM suface cuent, allowing to handle the divegence fee constaint as well as easy connection with extenal cicuits. A 2-dimensional axisymmetic vesion of the EM module is also available. Some compaisons between expeimental and numeical esults wee pesented. Such compaisons ae vey impotant to validate the module, and moe will be done in the futue. This module is integated in the 98 vesion of LS- DYNA, which should be eleased in 29. In the mean time, it is available as a beta vesion. The nea-tem futue developments fo the EM module include new BEM assembly methods, intoduction of tetahedal and wedge elements, development of an Massively Paallel Pocesso (MPP) vesion (the est of LS-DYNA is cuently available in MPP, but the EM module is only seial). The planned longe-tem developments include the intoduction of sliding contact capabilities fo the electomagnetism, emeshing capabilities, extension to othe solves (magnetostatics and so foth). Refeences [] LS-DYNA Theoy Manual, LSTC. [2] P. L Eplattenie, G. Cook, C. Ashcaft, M. Buge, A. Shapio, G. Daehn, M. Seith: Intoduction of an Electomagnetism Module in LS-DYNA fo Coupled Mechanical-Themal-Electomagnetic Simulations, 9th Intenational LS-DYNA Uses confeence, Deabon, Michigan, June 25. [3] J. Jin: The Finite Element Method in Electomagnetics, Wiley, 993. [4] J. Shen: Computational Electomagnetics Using Bounday Elements, Advances In Modelling Eddy Cuents, Topics in Engineeing Vol 24, Seies Eds: C.A. Bebbia and J.J. Conno, Southampton and Boston: Computational Mechanics Publications, 995. [5] J.C. Nedelec: A New Family of Mixed Finite Elements in R3, Num. Math, 5 (986), [6] O. Bio and K. Peis: On the use of the magnetic vecto potential in the finite element analysis of thee-dimentional eddy cuents, IEEE Tansaction on Magnetics, 25(989), No. 4, [7] P. Castillo, R. Rieben and D. White: FEMSTER: An obect oiented class libay of discete diffeential foms. 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