Finite element analyses andsimulations of sheet metal

forming processesJaroslav Mackerle

Department of Mechanical Engineering, Linkoping Institute of Technology,Linkoping, Sweden

Keywords Finite element analysis, Metallurgy, Bibliographies

Abstract Sheet metal forming is a process of shaping thin sheets of metal by applying pressurethrough male or female dies or both. In most of used sheet-formating processes the metal issubjected to primarily tensile or compressive stresses or both. During the last three decadesconsiderable advances have been made in the applications of numerical techniques, especially thefinite element methods, to analyze physical phenomena in the field of structural, solid and fluidmechanics as well as to simulate various processes in engineering. These methods are usefulbecause one can use them to find out facts or study the processes in a way that no other tool canaccomplish. Finite element methods applied to sheet metal forming are the subjects of this paper.The reason for writing this bibliography is to save time for readers looking for information dealingwith sheet metal forming, not having an access to large databases or willingness to spend own timewith uncertain information retrieval. This paper is organized into two parts. In the first one, eachtopic is handled and current trends in the application of finite element techniques are brieflymentioned. The second part, an Appendix, lists papers published in the open literature. More than900 references to papers, conference proceedings and theses/dissertations dealing with subjectsthat were published in 1995-2003 are listed.

IntroductionThe output of scientific papers in general is fast growing and professionals are nolonger able to be fully up-to-date with all the relevant information. The increasingspecialization in various engineering fields has resulted in the proliferation ofsubject-oriented journals and conference proceedings directed to specialist audiences.The researchers have more channels for communicating the results of their researchat their disposal, but on the other hand finding the necessary information may bea time-consuming and uneasy process. Another question is whether researchers/scientists are willing to spend time looking for information. It has been pointed out thatin engineering, informal knowledge channels are the most frequently used means ofobtaining information.

During the last three decades considerable advances have been made in theapplications of numerical techniques to analyze physical phenomena in the field ofstructural, solid and fluid mechanics as well as to simulate various processes inengineering. Among these numerical procedures, the finite element methods are the

The Emerald Research Register for this journal is available at The current issue and full text archive of this journal is available at

www.emeraldinsight.com/researchregister www.emeraldinsight.com/0264-4401.htm

The bibliography presented in the Appendix is by no means complete but it gives acomprehensive representation of different finite element applications on the subjects. The authorwishes to apologize for the unintentional exclusions of missing references and would appreciatereceiving comments and pointers to other relevant literature for a future update.

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Received March 2004Accepted April 2003

Engineering ComputationsVol. 21 No. 8, 2004

pp. 891-940q Emerald Group Publishing Limited

0264-4401DOI 10.1108/02644400410554371

most frequently used today. These methods are useful because one can use them tofind out facts or study the processes in a way that no other tool can accomplish.

Sheet metal forming is a process of shaping thin sheets of metal by applyingpressure through male or female dies or both. In most of used sheet-forming processesthe metal is subjected to primarily tensile or compressive stresses or both.

The bibliography is divided into following parts and concerns.

1. Sheet metal forming in general:. material properties (texture, anisotropy, formability, etc.);. springback;. fracture mechanics problems; and. computational strategies, modelling and other phenomena.

2. Specific sheet metal/sheet metal components forming processes:. bending sheet metal forming;. stretch forming;. deep drawing;. pressing and stamping;. hydroforming; and. other processes.

This paper is organized into two parts. In the first one each topic is handled andcurrent trends in application of finite element techniques are briefly mentioned. Thesecond part, an Appendix, lists papers published in the open literature for the period1995-2003 on the subjects presented above. References have been retrieved from theauthor’s database, MAKEBASE (Mackerle, 1993). Also the COMPENDEX databasehas been checked. Readers interested in the finite element literature in general arereferred to the author’s Internet Finite Element Book Bibliography (http://solid.ikp.liu.se/fe/index.html). Basic information about the sheet metal forming techniques as wellas basic considerations that are common to all sheet forming processes can be found inSchwartz (2002). Books dealing with numerical and finite element methods in materialprocessing are, for example, Champion (1992), Kobayashi (1989), Rowe et al. (1991),Wagoner and Chenot (1995, 2001) and Yu and Zhang (1996). References to papers onfinite element applications in metal forming processes published before 1995 can befound in Mackerle and Brannberg (1994). Two important conferences should also bementioned: NUMIFORM and NUMISHEET (NUMIFORM’95; NUMIFORM’98;NUMIFORM 2001; NUMISHEET’96; NUMISHEET’99; NUMISHEET 2002).

Sheet metal forming in generalSheet metal forming is process where the pressure is applied through male/femaledies or both. The metal is subjected to tensile/compressive stresses or both.Some phenomena are common to all sheet forming processes and are handled inthis section. They are divided into following subcategories: material properties

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(texture, anisotropy, formability, etc.), springback, fracture mechanics problems, andcomputational strategies, modelling and other phenomena.

Material properties. Texture/grain size of the metal is important for the formingprocess – too large grains produce a rough appearance when formed. Anisotropy ofsheet metal is in two directions – in the direction of the sheet plane, and in thethickness direction. The behavior of the material depends on the direction ofdeformation.

The models for metal plasticity at low temperatures consist either ofphenomenological yield criteria applied to standard materials and with theassumption of isotropic hardening, or of polycrystalline models where, at least,crystallographic texture is taken into account. Another approach combines some of theadvantages of both methods and involves fitting the constants of a simple analyticalfunction to data produced by plasticity calculations, rather than by experiments.

The plastic anisotropy of sheet metals is usually caused by preferred orientation ofgrains, developed by mechanical deformation and heat treatment. The influence of thismechanical deformation on the development of preferred orientation and resultinganisotropy has been simulated by both the finite elements and experiments.

The polycrystalline materials exhibit significant plastic anisotropy attributed to thepresence of crystallographic texture. This plastic anisotropy affects the subsequentforming process. Many papers have been published where constitutive relationsdescribing the initial and induced anisotropy of the material are presented.

The definition of formability is not easy because a large number of variables areinvolved. The effect of process parameters such as tool type and size, friction at theinterface tool/sheet, plane anisotropy, feed rate, etc. on the formability can be studiedby tests and finite element analyses.

The effect of crystallographic textures on the formability of metal sheets was, forexample, studied by using the crystalline plastic theory, based on the hardening andsoftening evolution equations defined on the slip systems of a crystal lattice cell.

Topics included: constitutive modelling; microstructure-based constitutivemodelling; microstructure; crystallographic texture; texture-related properties;grain-oriented modelling; texture evolution; evolution of through-thickness texturegradient; sheet metal formability; drawability; bendability; press formability; forminglimit; yielding descriptions; orthotropic plasticity; crystalline plasticity; polycrystalplasticity; anisotropy in sheet forming; large deformation anisotropy; plasticanisotropy; anisotropic elastoplastic behavior; modified anisotropic Gurson yieldcriterion; generalized mixed kinematic-isotropic hardening; exponential hardening;workhardening; Bauschinger effect; influences of geometrical parameters; three-pointbending test; sheet forming test; tensile test; plane strain test; dome test; and OSUformability test.

Materials: steel; high-strength steel; silicon steel; ferritic stainless steel; austeniticstainless steel; BCC steel; aluminum; aluminum alloys; magnesium alloys; brass;zirconium; and polycrystalline alloys.

Springback. Springback in sheet metal forming is due to the elastic recovery of themetal after it is deformed. Compensation for it in practice is usually accomplished bythe part overbending.

In sheet metal forming, tool and process parameters have to be appropriatelychosen. The dimension precision is a major concern in sheet metal bending where

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the considerable elastic recovery during unloading leads to springback and sidewallcurl. Therefore, the tool design should be based on the accurate prediction of elasticrecovery amount. This prediction is possible by using finite element methods even if itis not easy.

The out-of-plane forming is characterized by small strains, large deformations,frictional contact boundary changes, and that the elastoplastic deformation is coupledwith thermal field problems.

Springback is also sensitive to many physical parameters such as materialproperties, hardening laws, coefficient of friction, elastic and plastic anisotropy or thepresence of a Bauschinger effect. Even numerical factors such as integration scheme,element type and unloading scheme are of main interest in the finite element modelling.

The springback is more severe for materials with higher strength-to-modulus ratios,i.e. high strength steels or aluminum.

An effective approach for springback determination is to couple the implicit andexplicit finite element techniques. Here, the robustness of the explicit code for handlingthe sheet forming process is combined with the CPU efficiency of the implicit code forhandling springback.

Topics in this subsection: springback simulation in 2D and 3D; plastic anisotropyand springback; finite elements for springback simulations; compensating springbackerror; springback prediction for: bending; side bending; V-free bending; L-shapedbending; U-shaped bending; hat-bending; pipe bending; sheet metal stamping;flanging; stretch/draw sheet forming; draw/bend forming; and multiplebending-unbending process.

Fracture mechanics problems. Fracture mechanics problems usually deal withlocalized necking or buckling or both (wrinkling, folding). Microdefects are theprincipal source of strain localization and final failure. What we need for the finiteelement analysis is to develop the damage-coupled plasticity material model and toestablish the damage criteria.

Necking in sheet metal forming arises due to loading and boundary conditions, andmaterial nonhomogeneities that develop when plastic deformation increases. Thelocalized necking is considered as an instability problem of the local mechanicalequilibrium. It means that the mechanical properties of the sheet where necking occursare suddenly modified and in an irreversible manner.

Wrinkling is undesired for functional or aesthetic reasons. Its prediction andprevention are important in the design of tools and process parameters. Wrinklinglimits the depth and complexity of sheet metal components.

Predicting the buckling behavior (wrinkling) for the sheet metal processes ispossible by applying an implicit or explicit finite element method. Using an implicitmethod is an eigenvalue approach but it is not easy to initiate wrinkles without initialimperfections. The explicit finite element method can generate deformed shapes withwrinkles due to the accumulation of numerical error but the onset/growth of thebuckling is sensitive to the input data (element type, mesh quality, etc.).

Fracture mechanics problems of this subsection: prediction of necking; localizednecking; post-necking behavior; prediction of wrinkling; wrinkling initiation andgrowth; plastic wrinkling; side-wall wrinkling; earing prediction; tearing failure;ductile damage modelling; damage-based formability; damage and fracture prediction;void damage; crack growth modelling; fatigue crack propagation; determination of

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buckling limit; tracing local buckling; texture effect on sheet failure; and developmentof special finite elements.

Computational strategies, modelling and other phenomena. To avoid trial and errortryout procedures, the use of finite element sheet metal forming simulations is in rapidprogress. Many research groups and professionals are developing or improving existingfinite element codes. These currently available codes are based on: rigid/visco/plastic orelasto/visco/plastic approaches. The last named group can be classified intostatic-implicit, static-explicit or dynamic-explicit codes. There are also otherformulations developed such as: quasistatic rigid-plastic/viscoplastic flow formulation,quasistatic elasto-plastic solid modelling, etc. What is desirable is to seek a trade-offbetween severe accuracy and economy. The problems that concern designers are whetherthe different finite element codes produce the same results and, if not, which one accordswith the facts. Papers describing specific finite element software for sheet forming areincluded in this subsection as well as papers dealing with benchmark problems.

The validity of finite element simulations of sheet metal forming processes dependson the accuracy of various parts involved in the calculation, i.e. the constitutiveequations, element-type used, computational methods and algorithms utilized.

Topics under consideration: 2D and 3D finite element simulations of sheet metalforming problems in general; formulations used for sheet metal forming; developmentof finite elements; friction modelling; plasticity model for interface friction; contactsearching algorithms; mesh generation; adaptive meshing; solvers for formingsimulations; thermal effect in sheet metal forming; mathematical aspects of differentanalysis strategies; inverse approach; incremental sheet metal forming; optimumprocess design for sheet metal forming; reliability assessment; parallel processing insheet metal forming; and concurrent engineering.

Some finite element codes developed, commercial and in-house, which are used forthe simulation of sheet metal forming are represented with papers in Appendix:LS-DYNA; FAST-3D; OPTRIS; LAGAMINE; ITA3D; AUTOFORM; DYNAFORM;MSC/DYTRAN, STAMPAR, STAMPACK, FAST_FORM3D. There are, of course, alsoother well-known codes which have been used in sheet metal forming simulations, i.e.ABAQUS (implicit and explicit version), PAM-STAMP, DEFORM, HYDROFORM,MARC, LS-NIKE, RADIOSS, ANSYS, ADINA, etc.

Specific sheet metal/sheet metal components forming processesSheet metal forming processes are accomplished by other processes such as bending,stretching, deep drawing, roll forming, spinning, etc. In most of these operations thereare no major changes in the thickness of the sheet metal but in the shape. In thissection, specific forming processes are presented for manufacturing various metalcomponents. These processes are classified into: bending sheet metal forming, stretchforming, deep drawing, pressing and stamping, hydroforming, and other processes.References are listed in the Appendix into the same categories.

Bending sheet metal forming. Sheet metal bending is a standard operation in manymanufacturing processes. Bending can be provided along a straight line or a curvedpath. In addition tomale and female dies, the female die can be replaced by a rubber pad.

Finite element method makes possible that the deformed geometrical and punchload distribution of sheets are computed through the whole process until to theunloading state after forming. The effects of various parameters can be studied.

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An accurate finite element analysis of the elastic phenomena in bending isnecessary to determine the overbending angle required to compensate for thespringback effect. It is important to mention that even if the responses of variousmaterials are known, bending still can be a nonreproducible process due to thebatch-to-batch variability of mechanical properties of nominally identical material.

Topics of this subsection: 2D and 3D simulation of sheet bending process;U-bending; UO-bending; V-bending; bending/reverse bending of sheet metals; effect ofmodelling parameters; contact problems for sheet metal bending; strain gradienteffects in bending; residual stresses in sheet metal bending; springback effect;springback in side bending; and design of sheet metal punches.

Materials: metals; steel; stainless steel; aluminum; aluminum alloys; andaluminum-rubber.

Some final products: irregular shapes; multiple parts; profiles; automobile parts; andbumpers.

Stretch forming. In stretch forming the sheet is clamped between jaws and stretchedover a form block. The advantage is low cost, small residual stresses, and eliminationof wrinkles.

A common feature for all stretching-bending operations is that most of thecross-section is in tension. This means that the local buckling phenomena, oftencausing problems in bending of thin-walled structures, are avoided. The tensile forcealso provides a rather homogeneous stress state in the cross-section leading todecreased springback after unloading.

Topics include: stretch bending simulation; axisymmetric sheet stretching; biaxialstretching; influences of geometrical parameters; evaluation of various materialmodels; tribological influence on strain path; CNC-controlled stretch forming; andstretch flange forming.

Materials: metals; steel; aluminum; and aluminum alloys.Some final products: automotive components; and bumpers.Deep drawing. Deep drawing of sheet metal requires a control of many factors such

as blank-holder pressure, material properties, die geometry, lubrication, etc. Without aknowledge of the deep drawing process and material characteristics of sheet metals, itwould be difficult to optimize the process and prevent the defects.

In drawing, metal sheet is either formed in a single operation, or progressivedrawing steps are applied to reach the final form. Deep drawing of anisotropic sheets isa complicated process including strong nonlinear characteristics, complicatedloading/unloading history and even strain localization phenomenon.

There are many parameters influencing the deep drawing process: the punch anddisc radii, the punch velocity, clamping force, friction and draw depth. It is not easy toshow which of these variables is the most influential in a specific situation.

In the deep drawing, flange earing is an unwanted forming defect, which is due tothe anisotropy produced by the plasticity deformation of the sheet metal making itsplastic flowing change in the deep-drawing.

Topics of this subsection: 2D and 3D finite element simulations of deep drawing;micro-macro analysis; axisymmetric deep drawing; multi-step deep drawing; warmdeep drawing; deep drawing with elastomer membranes; redrawing process; frictioncontact problem studies; prediction of forming limit; prediction of necking; predictionof wrinkling; prediction of springback; texture evolution during deep drawing; residual

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stresses in deep drawing; earing problems; influence of punch shape; design of dies;optimum blank shape determination; control of blank holder force; pliable blankholder; modelling of drawbeads; forming load in deep drawing; influence of blankholder pressure; tool wear in deep drawing; monitoring of deep drawing process;prediction of process conditions; sensitivity and stability evaluation.

Materials: metals; steel; stainless steel; austenitic stainless steel; high strength steel;coated steel; aluminum; aluminum alloys; aluminum-stainless steel laminates;titanium; magnesium alloys; copper.

Some final products: square cups, cylindrical cups, elliptical cups; nonsymmetriccups, concave components; square boxes; rectangular parts; automotive components;can forming.

Pressing and stamping. The steps common for pressing and stamping are thepreparation of a flat blank and shearing or stretching the metal into a die to formthe desired shape. In stamping the flat stock is placed into a die and then formedwith movable die or punch. The die can also perform perforating, blanking,shearing, etc.

The real stamping process of metal sheets consists of four modes of deformation ina mixed form, namely: bending, stretching, stretch flanging, and deep drawing. Toobtain the desired final product, forming failures such as local necking and shapeinaccuracy (wrinkling and springback) have to be avoided.

Simulating sheet stamping processes with finite elements is a complicatedprocedure due to material and geometrical nonlinearities, time changing boundaryconditions, and contact problems with friction.

Flanging is a forming process in autobody panel stamping, that can affect theassembly quality of autobody. This process can be classified into the stretch-type orshrink-type flanging.

Topics include: 2D and 3D finite element analysis of pressing and stamping;multi-stage stamping; application of viscous pressure forming to low volumestamping; laser-aided stamping; magnetic pulsed stamping; inverse approach forstamping process; tailored blanks stamping process; effect of material and processvariables; contact problems; die design; blank design; drawbead modelling; drawbeadrestraining force; reliability assessment; design and optimization of stamping process.

Materials: metals; steel; coated steel; aluminum; aluminum alloys; and galvanizedsheets.

Some final products: autobody parts; automobile fuel tank; car roof; automobile rearfloor panel; motorcycle oil tank; and bathtub.

Hydroforming. The hydroforming process produces first of all hollow, lightweightcomponents with complex shapes and variable cross sections by means of hydraulicpressure, in most cases using circular tubes as a source material. This process isachieving increasing acceptance in the automotive and aircraft industry.

Hydroforming offers a better structural integrity of the product, lower productioncost, material saving, fine thickness distribution, fewer secondary operations, andreliability improvement. The main failure modes are buckling, wrinkling, andbursting.

The principle of the hydroforming is that the starting tube is aligned to the internalsurface of a tool that encloses the tube, and through the combined action of mechanicalloading and hydrostatic internal pressure then formed. The implementation leads

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to complex process sequences with a large number of parameters of tube, the tool andthe process acting together to produce the final result.

Topics include: 2D and 3D finite element analysis of hydroforming; dielesshydroforming; tube hydroforming; sheet metal hydroforming; dual hydroformingprocess; hydro-bulge forming; preform design in hydroforming; contact problems withfriction; formability analysis; development of necking and bursting; prediction ofwrinkling; design of tubular blank; influence of material and process parameters; effectof loading path; coupled buckling and plastic instability; design sensitivity andoptimization of hydroforming.

Materials: metals; steel; aluminum; and aluminum alloys.Some final products: thin sheets; rectangular boxes; tubes; flanges; automotive

parts; automobile lower arms; automobile fuel tanks; automobile rear axle housing;toroidal shells; ellipsoidal shells; and spherical vessels.

Other processes. In this last subcategory “other processes”, references are listed inAppendix for sheet metal processes not mentioned earlier.

Blanking is a constrained shearing that involves elastic deflection, plasticdeformation and the fracture of the sheet material. The aim of this process is not onlyto make the metal deform to specified shape/dimension but also to brake the material.The important parameters are: the punch-die clearance, the punch velocity, the toolgeometry and the mechanical properties of sheet metal. In the finite element modellingit is necessary to simulate the contact at all interfaces, material properties, crackpropagation and other parameters.

The roll forming process replaces the vertical motion of the dies by the rotarymotion of rolls with various profiles, where each successive roll bends the material alittle further than the preceding roll.

Superplasticity as a material property means that some materials, under the correctconditions of temperature and strain rate, exhibit high ductility resulting in large straindeformations. In superplastic forming thin sheets are blown into die cavities to producecomplex parts. This process is very sensitive to strain rate. At locations where theshape of the die is complicated unpredictably thin regions are formed. The thinningcontrol is necessary and this can include, for example, material treatment, lubrication,profiled gas pressure, thermoforming, etc.

In laser bending process, based on the phenomenon of heat expansion and coolingshrinkage, the repetitive irradiations of a defocused laser beam are applied over thesurface of a metal sheet. A temperature gradient through the sheet thickness isdeveloped and the thermal stress is induced. As a result, the permanent deformation isproduced. Laser processing parameters can control accurately the temperaturedistribution so that the proper magnitude and distribution of thermal stresses will beobtained. The desired deformation is completed without rigid tools or external sources.By this process, it is possible to bend also relatively brittle materials into large angles.

The electromagnetic forming process is based on the use of electromagnetic forcesto deform metallic workpiece at high speeds. A transient electric current is induced in acoil and this current induces a magnetic field that penetrates the conductive workpieceand generates eddy current. The Lorentz forces are induced and these drive thedeformation of the workpiece. This method is expected to help some formabilitybarriers. The finite element method can be used to study coupling betweenelectromagnetic and thermal response, and deformation of the workpiece.

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The spinning process forms parts with rotational symmetry over a mandrel withthe use of a tool or roller.

Topics of this subsection: roll forming; flat rolling; shape rolling; sheet metalextrusion; backward extrusion; sheet warm forming; sheet metal spinning; sheet metalblanking; net-shape blanking; hemming; hot gas-pressure forming; electromagneticforming; sheet metal camber process; superplastic forming; superplastic blow forming;laser bending; laser sheet forming; shot peening; analysis of ridging; binder forming;die-less forming; tailored sheet forming; multi-point forming; multi-stage forming; andvirtual manufacturing.

References

Champion, E.R. (1992), Finite Element Analysis in Manufacturing Engineering: A PC-basedApproach, McGraw-Hill, New York, NY.

Kobayashi, S. (1989), Metal Forming and the Finite Element Method, Oxford University Press,New York, NY.

Mackerle, J. (1993), “An information retrieval system for finite element and boundary elementliterature and software”, Eng. Anal. With Boundary Elem., Vol. 11, pp. 177-87.

Mackerle, J. and Brannberg, N. (1994), “Finite element methods and material processingtechnology”, Eng. Comput., Vol. 11 No. 5, pp. 413-55.

NUMIFORM’95, paper presented at the 5th Int. Conf. Num. Meth. Industr. Forming Processes,Ithaca, NY, June 1995.

NUMIFORM’98, paper presented at the 6th Int. Conf. Num. Meth. Industr. Forming Processes,Enschede, June 1998.

NUMIFORM 2001, paper presented at the 7th Int. Conf. Num. Meth. Industr. Forming Processes,Toyohashi, Japan, June 2001.

NUMISHEET’96, paper presented at the 3rd Int. Conf. Num. Simul. 3-D Sheet Metal FormingProcesses, Dearborn, MI, September 1996.

NUMISHEET’99, paper presented at the 4th Int. Conf. Worksh. Num. Simul. 3-D Sheet Formingprocesses, Besancon, September 1999.

NUMISHEET 2002, paper presented at the 5th Int. Conf. Worksh. Num. Simul. 3-D SheetForming processes, Jeju Island, November 2002.

Rowe, G.W. et al. (1991), Finite Element Plasticity and Metalforming Analysis, CambridgeUniversity Press, New York, NY.

Schwartz, M. (Ed.) (2002), Encyclopedia of Materials, Parts and Finishes, CRC Press,Boca Raton, FL.

Wagoner, R.H. and Chenot, J.L. (1995), Fundamentals of Metal Forming, Wiley & Sons,New York, NY.

Wagoner, R.H. and Chenot, J.L. (2001), Metal Forming Analysis, Cambridge University Press,Cambridge.

Yu, T.X. and Zhang, L.C. (1996), Plastic Bending: Theory and Applications, World ScientificPublication, Singapore.

Appendix. A bibliography (1995-2003)This bibliography provides a list of literature references on finite element analyses andsimulations of sheet metal forming processes, theory and applications. The listing presentedcontains papers published in scientific journals, conference proceedings, and theses/dissertations

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retrospectively to 1995. References have been retrieved from the author’s database,MAKEBASE. Entries are grouped into the same sections described in the first part of thispaper, and sorted alphabetically according to the first author’s name. In some cases, if a specificpaper is relevant to several subject categories, the same reference can be listed under therespective section headings, but the interested reader is expected to consider also areas adjacentto his/her central area of research interest.

Sheet metal forming in general

Material properties (texture, anisotropy, formability, etc.)Ahmetoglu, M. et al. (2000), “Evaluation of sheet metal formability, viscous pressure forming

(VPF) dome test”, J. Mater. Process. Technol., Vol. 98 No. 1, pp. 1-6.Bammann, D.J. et al. (1995), “Modeling large deformation anisotropy in sheet metal forming”, in

Shen, S.F. and Dawson, P. (Eds), NUMIFORM ’95, Balkema, Amsterdam, pp. 657-60.Barlat, F. et al. (1997), “Yielding description for solution strengthened aluminum alloys”, Int.

J. Plast., Vol. 13 No. 4, pp. 385-401.Barlat, F. et al. (2003), “Plane stress yield function for aluminum alloy sheets. Part 1: theory”, Int.

J. Plast., Vol. 19 No. 9, pp. 1297-319.Barlat, F. et al. (2003), “Texture, microstructure and forming of aluminum alloy sheets”, Mater.

Sci. Forum, Vols 426-432, pp. 99-106.Bate, P.S. et al. (1998), “Increasing the drawability of AA2014 Al-Cu by differential heat

treatment”, Metall. Mater. Trans. A, Vol. 29 No. 5, pp. 1405-14.Beaudoin, A.J. (1998), “Anisotropy in sheet forming – studies from the macroscale and

microscale viewpoints”, 4th World Cong. Comput. Mech., Buenos Aires, p. 1161.Beaudoin, A.J. et al. (1995), “Analysis and anisotropy in sheet forming using polycrystal

plasticity”, paper presented at the 10th Conf. Eng. Mech., Boulder, pp. 1018-21.Beaudoin, A.J. et al. (1996), “Incorporating crystallographic texture in finite element simulations

of sheet forming”, in Lee, J.K. et al. (Eds), Numisheet’96, Dearborn, pp. 17-24.Bouaifi, B. and Sommer, D. (1996), “Influence of joining techniques on the microstructure and

formability of steel sheet”, Weld. Res. Abroad, Vol. 42 No. 3, pp. 37-40.Boubakar, M.L. et al. (1995), “Anisotropic elastoplastic behaviour in 3D sheet metal forming

simulations”, in Owen, D.R.J. (Ed.), 4th Int. Conf. Comput. Plast., Pineridge Press, Swansea,pp. 1471-82.

Boubakar, M.L. et al. (1997), “Numerical implementation of orthotropic plasticity for sheet-metalforming analysis”, J. Mater. Process. Technol., Vol. 65 Nos 1/3, pp. 143-52.

Brunet, M. and Morestin, F. (2001), “Experimental and analytical necking studies of anisotropicsheet metals”, J. Mater. Process. Technol., Vol. 112 Nos 2/3, pp. 214-26.

Bryant, J.D. et al. (1996), “Effect of crystallographic texture on formability in AA6111 autobodysheet”, Alumin. Magnes. Automot. Appl., Cleveland, pp. 85-95.

Buvat, C. and Ossart, F. (2000), “Grain oriented silicon steel modeling: finite elementimplementation of the coenergy model”, paper presented at the 2000 IEEE INTERMAGConf., Toronto, p. FD11.

Carleer, B.D. et al. (1996), “The analysis of planar anisotropic sheet metal”, in Kals, H.J.J. et al.(Eds), Shemet ’96, Vol. 2, pp. 193-204.

Chien, W.Y. et al. (2001), “Modified anisotropic Gurson yield criterion for porous ductilesheet metals”, J. Eng. Mater. Technol., ASME, Vol. 123 No. 4, pp. 409-16.

Cho, J.H. et al. (1999), “Effect of texture on uniaxial tension in AA3003 sheet withinhomogeneous texture”, ICOTOM-12, Canada, pp. 587-92.

Choi, T.H. and Huh, H. (1999), “Sheet metal forming analysis of planar anisotropic materials by amodified membrane finite element method with bending effect”, J. Mater. Process.Technol., Vols 89-90, pp. 58-64.

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Choi, S.H. et al. (2000), “Texture evolution of FCC sheet metals during deep drawing process”, Int.J. Mech. Sci., Vol. 42 No. 8, pp. 1571-92.

Chou, C.H. et al. (1996), “An anisotropic stress resultant constitutive law for sheet metalforming”, Int. J. Num. Meth. Eng., Vol. 39 No. 3, pp. 435-49.

Chow, C.L. and Yang, X.J. (2002), “A generalized mixed kinematic-isotropic hardening plasticmodel coupled with anisotropic damage for sheet metal forming”, ASME Int. Mech. Eng.Cong. Expo., AMD Vol. 252, ASME, pp. 37-44.

Chun, B.K. et al. (2002), “Modeling the Bauschinger effect for sheet metals. Part I: theory”, Int.J. Plast., Vol. 18 Nos 5/6, pp. 571-95.

Chun, B.K. et al. (2002), “Modeling the Bauschinger effect for sheet metals. Part II:applications”, Int. J. Plast., Vol. 18 Nos 5/6, pp. 597-616.

Chung, K. et al. (1996), “Finite element simulation of sheet forming based on a planaranisotropic strain-rate potential”, Int. J. Plast., Vol. 12 No. 1, pp. 93-115.

Chung, K. et al. (2000), “Ideal sheet forming with frictional constraints”, Int. J. Plast., Vol. 16 No. 6,pp. 595-610.

Chung, Y.H. et al. (2002), “Evolution of texture and microstructure in AA 3004 sheets duringcontinuous confined strip shearing deformation and subsequent annealing”, Mater. Sci.Forum, Vols 396-402, pp. 475-80.

Chung, Y.H. et al. (2002), “Effect of strain paths on the evolution of texture and work hardening inAA 5052 sheets during continuous confined strip shearing deformation”, Mater. Sci.Forum, Vols 408-412, pp. 1495-500.

Comstock, R.J. et al. (2001), “Simulation of axisymmetric sheet forming tests”, J. Mater. Process.Technol., Vol. 117 Nos 1/2, pp. 153-68.

Dawson, P.R. and Beaudoin, A. (1997), “Incorporating crystallographic texture indeformation process simulations”, JOM, Vol. 49 No. 9, pp. 34-41.

Dawson, P.R. et al. (2003), “Advances in sheet metal forming analyses: dealing with mechanicalanisotropy from crystallographic texture”, Int. Mater. Rev., Vol. 48 No. 2, pp. 86-122.

Doege, E. et al. (1997), “Application of an anisotropic extension of Gurson model to practicalengineering problems”, in Owen, D.R.J. (Ed.), 5th Int. Conf. Comput. Plast., CIMNE,pp. 1453-8.

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