Analysis of Structures and

Thermomechanics forStudies & Research

www.code-aster.org

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Phenomena> Mechanical

• Static, quasi-static, linear or otherwise

• Dynamic, linear or otherwise, on a physical or modal basis

• Fracture, damage and fatigue• Soil-Structure, Fluid-Structure and

Soil-Fluid-Structure interactions

> Thermal• Stationary, transient, linear

or otherwise• Fixed or moving reference

coordinate system

> Associated phenomena• Acoustics• Metallurgy• Hydration and drying

Analysis Types > Standard> Decomposition into Fourier

modes> Substructuring> Model superposing, multiscale> Adaptive mesh> Sensitivity calculation> Fitting and optimization> Mechanical reliability

calculation

Multiphysical > Internal links with thermics

• Hydration, drying• Metallurgy

> Internal links with mechanics• Thermal• Metallurgy• Hydration and drying

> Internal couplings• Thermo-hydro mechanical• Fluid-Structure

> External coupling with othercodes• Soil-(Fluid)-Structure (MISS3D)

> External links with other codes• Hydraulics: Code_Saturne• Thermal: SYRTHES• Electromagnetism: Flux2D/3D• Fast dynamics: EUROPLEXUS

Loadings > Mechanical

• Nodal or distributed forces• Pressure• Inertia loading• Centrifugal acceleration• Imposed movements• Anelastic strain• Effect of wind

> Thermal• Temperature• Flows, linear or otherwise• Forced convection• Exchange between walls• Heating by Joule effect

> Specific loads (followingforces, electromagnetic forces,initial states)

Nonlinearities in static and dynamic

> Geometrics• Geometric updating, large

displacements, large rotations• Following forces• Continuation methods: in

displacement, by arc length, in strain, by criterion output

• Load discharge and non-radialityindicators

• Contact and friction: by a discretecontact method (active stresses,penalization, conjugated projected gradient or by an augmented Lagrangian method.)

• First order buckling

> Materials (95 constitutive laws)• Linear and nonlinear elasticity• Nonlinear hyperelasticity• Local elastoplasticity and

elastoplasticity with gradient formulation

• Nonlinear viscoelasticity• Local and with gradient

formulation damage• Elastoviscoplasticity• Metallurgical effects• Material data dependent on

temperature, metallurgical condition, hydration, drying and fluence

• Progressive strain• Hydration, shrinkage and creep

of concrete• Geomaterials

Dynamics > Modal analysis

• With or without damping (viscous, hysteretic, modal)

• Direct or by substructuring• Normalization, filtering,

modal parameters

> Linear transient response• Direct• On modal basis• By substructuring

> Transient response with localnonlinearities (on modal basis)• Shocks• Friction• Fluid blade

> Harmonic response• Direct• On modal basis• By substructuring

> Random response• Parametric and nonparametric

probabilistic• Stochastics

> Direct nonlinear analysis• Implicit• Explicit• Shocks• Plasticity, damage• Contact and friction

> Substructuring• Conventional or cyclic• Modal, transient or harmonic

analysis

> Seismic analysis• With shocks or multi-support• Spectral or transient direct linear

or on modal basis• Modal damping calculation

(RCC-G)

> Extrapolation of experimentalmeasurements• Temporal or frequential

Interactions > Fluid-Structure

• Structure-incompressible flow interaction; turbulent stresses

• Vibro-acoustics (free surface)

> Soil-Structure and Soil-Fluid-Structure• Absorbent boundary elements• Frequential coupling with MISS3D

Code_Aster offers a full range of

multiphysical analysisand modelling

methods that go wellbeyond the standard

functions of a thermomechanical

calculation code: fromseismic analysis toporous media via

acoustics, fatigue, stochastic dynamics,

etc. Its modelling,algorithms and solvers

are constantly underconstruction to

improve and completethem (1,200,000

lines of code, 200 operators).

Resolutely open, it is linked, coupled

and encapsulated innumerous ways.

Code_Aster’s Possibilities

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Thermal analysis > Linear and nonlinear

thermics• Phase change• Hydration and drying• Mobile coordinate system

resolution

> Metallurgical changes• Steels, Zircaloy• Phase hardness calculation

> Thermal treatments andwelding

Geotechnical CivilEngineering

> Constitutive laws for con-crete (reinforced or pre-stressed), geomaterials

> Hydration, drying and basiccreep at different time scales

> Passive reinforcement orpre-stressing effect withelastoplastic behaviour: bar, grids and membrane

> Creep-cracking coupling> Thermohydromechanics

(porous media, formulationin effective stresses, consti-tutive laws in kit form, etc.)

> Specific loads (hydric andgaseous flows)

> Excavation procedure> Fracture, damage, fatigue

and collapse of structures> Global release rate

• thermoelasticity: G• thermoelastoplasticity:

GP and GTP

> Local release rate in 3D> Stress intensity factors> Models of brittle and ductile

fracture, initiation and instability

> Specific load drive > Local and non-local damage> Crack modelling: joint

element and X-FEM> Decoupled damage

> Fatigue analysis• Loading history• Counting methods• Specific criteria applications

> Verification of RCC-M criteria

> Zarka-Casier method in cyclic loading

> Progressive wear> Limit analysis> Micro-macro approach:

polycrystalline model

Survey quality > Spatial error indicators

• Mécanique (en résidu pur, par lissage)

• Thermique (en résidu pur)

> Mesh refinement/ unrefinement via HOMARD

> More robust finite elements • Mechanics (underintegrated,

incompressible)• Thermics (lumped modelling)

> Mesh diagnosis> Thermomechanical time

step redistribution> Sensitivity calculations

• Mechanical• Thermal• Depending on materials,

loadings and domain variations

> Parameter fitting• Materials or loading• Depending on test sampling

or digital results.

> Reliability calculations: probability of exceedingthreshold using a FORMtype method

Modelling > Catalogue of material data> Connecting incompatible

meshes.> Superimposing models using

the Arlequin method.> Modelling connection

(3D-shell, beam-pipe, etc.)> Plane stress condition

adaptable to all models> Beam characteristics

calculation> Homogenization

(composites, repetitiveness,etc.)

Elements library(400 finiteelements)

> Mechanical• 2D, 2D axi (with or without

Fourier decomposition), 3D,under-integrated, incompressible

• Bars, beams (simple or multi-fibre), pipes, plates, shells,membranes, cables, discrete or non-distortable elements

> Thermics: 2D, 2D axi (with or without Fourier decomposition), 3D, shells

> Hydration-Drying: 2D, 2D axi, 3D

> THM Coupling: 2D, 2D axi, 3D

Solvers > Linear (LDLT, multifrontal,

PCG,MUMPS, FETI)> Nonlinear (Newton, etc.)> Integration schemes

(Runge-Kutta, Newmark,adaptatives, etc.)

> Modals (Power, Lanczos,IRAM, etc.)

> Extended parameter setting.Several strategies for re-numbering, storage, pre-conditioning, post-verification, etc.

Dedicated tools > Pipework stacks and

elbows ASPIC/ASCOUF> Steam Generator Tubes:

GEVIBUS

Softwareenvironment

> Integration in Salomé> Pre- / post processing:

I-DEASTM, GIBI, Gmsh, ENSIGHT, Xmgrace

> Data exchange in MED format

> Survey management tooland engineering applicationworkshop: ASTK

> Command File Editor andSyntax Analyser: EFICAS

> Portable nature of bases> Developed command

language: PYTHON• Loop, test, checking

structures, etc.• Method, class, etc.• Interactive calculation

and visualization (mathematic libraries, GUI,scale drawings, etc.)

Not forgetting… > Software under QA

(independent validations,reference of 2,000 test cases,13,000 pages of documentation, source management, qualificationof version, etc.).

> code-aster.org website(downloads, online documentation, forum, FAQ, examples, etc.)

> Communication and network (quarterly ASTER‘echos’ magazine; User Club,its network of correspondents and the annual day; Free Code_Asterunder GPL licence, etc.)

Code_Aster, an open source softwareNonlinear operators have greatly taken advantage of the source opening of Code_Aster,

in terms of feedback from the users as well as for the development of new functionalities.

Among them:

- The “slide” contact, worked out by the IFP (French Petroleum Institute)

- The hyperelastic behaviour (for elastomers): a Mooney-Rivlin modelintroduced by the Lyons 1 University.

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displacements, etc.) and to takeadvantage from options of theNewton-Raphson algorithm(choice of the matrices and theirupdate, line search, intelligenttemporal discretisation, etc.).

Non-linear operators use globalcriteria of convergence andcriteria based on physics referencevalues (stresses, distortions, etc.)These strong points provide abetter comfort of use and moreaccuracy, especially withheterogeneous residues (mixingof modelling, physics, etc.).

General methods to follow-up theevolution of instable structures orto calculate the maximum loadare available: continuationmethod in displacement or by arclength. Regarding materials withsoftening behaviour, drive byelastic prediction makes itpossible to monitor efficiently theloss in local stability by controllingthe most constrained points.Another technic consists inensuring the continuity of theresponse in distortion process.

In non-linear dynamics, numerousschemes for temporal integrationare available (Newmark, HHT,theta-method).

A fitting process (MACR_RECAL)identifies the optimal parametersby comparing the results of anexperiment with those of itssimulation. Lastly the finalrelevance of the results may becompared to various sensitivitycalculations (SENSIBILITE) and toerrors estimations (CALC_ELEM).

Kinematic nonlinearities

Nonlinearities resulting from largedisplacements may be modelledin various ways (keywordDEFORMATION).

SIMO_MIEHE processes largeplastic strains and large rotations,taking into account the wholeinformation resulting from thedeformation gradient. It isapplicable for various constitutivelaws: plasticity with isotropicstrain-hardening, viscoplasticity(with changes in the metallurgicphase) and ductile damage(ROUSSELIER model). This modelis incrementally objective andtherefore makes it possible toprocess the large rotationswithout limitations.

GREEN processes large rotations,large displacements and smalldistortions. This tool makes itpossible to use any elastic andincremental behaviour.

PETIT_REAC however solelyupdates geometrics at each timestep (necessarily small) and allowsonly small rotations.

Non-linearoperators…

... rich in functionalities and user-friendly: DYNA_NON_LINEand STAT_NON_LINE make itpossible to carry out an implicitstatic or dynamic survey withkinematic nonlinearities (largetransformations, largedeformations), nonlinearitiesresulting from the constitutive lawand awareness of thecontact/friction.

In thermics, THER_NON_LINEsimulates nonlinearities (materials, radiation, forced convection) and makes it possibleto calculate the change in the physical composition and dampness of concrete over time.

Power andproficiency

Code_Aster’s non-linearmechanics operators are thosewhich most take advantage fromthe innovations resulting from ourdevelopment activities in the fieldof computational mechanics.

Great efforts are done in order to meet the requirements of thespecialists in non-linearmechanical simulation, but also tomake the resolution poweraccessible in the most user-friendly way.

Numerous options thus make thecalculating engineer’s life easier.He/She has the possibility tocheck the carrying-out of the calculation, to follow-up real-time numerous interests(stresses, intern variables,

Damage: load drive

NonlinearIn an industrial survey

it is more and morenecessary to take into

account nonlinearities of:materials, geometrics

and contact.

Through the operatorsDYNA / THER /

STAT_NON_LINE Code Aster offers solutions

that suit each of these.

DISPLACEMENT

FOR

CE

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elements since the De Borstalgorithm makes it possible toapply them easily to shells andmulti-fibre beams.

If needed, it is also possible todevelop a new behaviour model.In order to make the validationprocess easier SIMU_POINT_MAT,a macro-command has beendeveloped and implemented inV8 (NEW V8).

Nonlinearities incontact-friction…

Code_Aster deals withcontact/friction in different ways.Its scope of use includes thewhole range of modellings(2D/3D, beams and shells), eventually based on incompatiblemesh or with updated geometries(large slidings linked to large surfaces).

Traditional discrete formulations(with processing by penalizationor dualisation) are available. In thelast few years an important workhas been made on the algorithmsperformances. A new iterativealgorithm (projected conjugategradient) has been implementedin the field of frictionless contact. It is now possible to solve problemsinvolving thousands of meshes incontact with brilliantperformances (in terms ofcalculation as well as storage footprint).

Code_Aster is also fitted with a“continuous” method of contactbased on a weak formulation

of the contact/friction problemwith three unknown fields (displacement, contact pressure,friction pressure) and using

Regarding structure elements,GREEN_GR processes largedisplacements and large rotationsof beams and shells.REAC_GEOM is used for multi-fibre beams.

Finally the COROTATIONNELoption is used with the externalmodule for the ZMAT constitutivelaw integration.

Nonlinearities in behaviour

isotropic and anisotropic elasticity,hyperelasticity (Signorini’s model,applicable under Mooney Rivlin),plasticity with isotropic/kinematicstrain-hardening,elastoviscoplasticity (Chaboche’sand Lemaître’s models).

A wide range of behaviour models simulating damage arealso available: models forprogressive distortion (Taheri’smodel, polycrystalline model),brittle and ductile damage(Rousselier’s model).

Code_Aster also includes modelsresulting from specific issues:plasticity and damage ofconcrete, steels and joints,cohesive elements, models for soiland rock mechanics (Cam-Clay,Barcelona and Hujeux models),models for micro-macrohomogenization and coupledthermohydromechanics in kitform.

These behaviours are available fornumerous modellings and finite

Nonlinear thermomechanical calculation of a combustion turbinecompressor: bladed rotor and quartercompressor.

an augmented Lagrangian formulation. This option is particularly precise in terms ofcontact physics and also makes itpossible to use a model dedicated to micro-asperities(compliance model), which isespecially efficient in the processing of shocks in dynamics. This is also a very general option,which may be applicable in simple Lagrangian formulation aswell as in penalized formulationthrough a wise choice of coefficients, while dealing efficiently with the redundancybetween boundary conditionsand contact conditions.

The creation of fields that storethe gaps and reactions values inevery potential contact point andwhich can be displayed in form ofisoValue or curves, makes thedata processing easier. Finally theuse of contact is simplified thanksto a unique access point:AFFE_CHAR_MECA, keywordCONTACT.

Implicit nonlinear dynamic: plasticity + largestrains + contact + friction.

GeomaterialsWhy is EDF interested inmodelling the behaviourof concretes, silts, sands,

clays and rocks ?Because, beyond the

behaviour of dams, thereis also the appraisal of

solutions envisaged forstoring radioactive waste.

Code_Aster’sthermohydromechanical

models are one of thecontributions of EDF

to the thorny problem of the downstream

of the cycle.

Nonlinear geomaterials undernominal load are often subject tocreep deformation: predicting thestate of structures in the shortand long term therefore requiresthe simulation of theirconstruction phases. This isparticularly true since thebehaviour of soaking waterthrough these materials hasmechanical consequences,especially on long-term changesto the ground and rocks. It istherefore essential to calculateflows as such, since the capillaryeffects linked to partiallysaturated states significantlyinfluence the stress state. This isparticularly true for poorlypermeable materials, wherestrong suctions appear.

Special constitutive laws

The phenomenologies describedhere can, of course, only besimulated by specific models inCode_Aster. Beyond theirdiversity, they all share theproperty of representing thedeterioration of materials undershear according to confinementand accompanied by perceptiblevolume variations. Theformulation framework will varydepending on whether it is a caseof a concrete, silt, sand, clay orrock. The formalism of damage ispreferred for concretes, themicro-crack formation of whichdamages rigidity, whereas in thecase of ground, plasticity makes itpossible to take better account ofirreversible strains. The hardeningis rendered dependent onvolumetric plastic strain for claysand on shear plastic strain forrocks. In all cases, a softeningbehaviour appears beyond acertain threshold. For groundsand rocks, the functionalities inCode_Aster model theconcomitant dilatancyphenomena quite closely. Theyalso model hydraulic and thermalchanges – these lead directly to

damage such as cracking due todrying, collapse due toremoistening, plasticizing due toclay swelling and groundbreakdown due to the thermaldilation of water.

An offering adaptedto geomaterials

For sands and silts, the first levelof CJS (Cambou, Jeffari, Sidoroff)laws, which is very close to theMohr-Coulomb criterion, allowsan approach of the “load limit”type. The second and third levelsintroduce a coupling betweenisotropic and deviatoric plasticmechanisms with isotropic orkinematic hardening includingdilatancy and strain-softening forthe third level. In the case ofsaturated clays, Cam Clay(RELATION_KIT='CAM_CLAY'),the star of the models, associatesa nonlinear elasticity with aplasticity limiting stresses to adomain, which size depends onthe consolidation pressure. Itsextension to non-saturatedgrounds, known as the Barcelonamodel, makes this domain alsodependent on capillary pressure.For rocks, EDF took advantage ofthe experience of the HydraulicEngineering Centre of Chambéry(Centre d'Ingénierie Hydraulique),which has demonstrated the needto retain the ‘post-peak’ (i.e.cracked) behaviour of rocks andoffered a generalization of theHoek and Brown model('LAIGLE'). The Hoek and Brownmodel, much simpler butapproved by the geophysicians, isalso available, as well as theDrucker-Prager elastoplasticmodel for concrete and somekinds of grounds. Code_Astermeets the variety of hydraulicphenomena in porous media withsimple models for drying andhydrating concrete, or morecomplex ones based on coupledintegration of two nonlinear flowlaws and the integration of theenergy conservation law.

In the sophisticated version ofthese models without gaspressure hypothesis, theexchanges between phases aregoverned by very generalthermodynamics equilibrium laws.The flows are Darcean, withpermeabilities and saturationlinked by any laws supplied by theuser. The same applies to therelationship between saturationand capillary pressure. Thedistribution mechanisms withingaseous (“dry” gas and vapour)and liquid (dissolved gases andliquid water) mixtures aregoverned by the Fick laws.

Significantexperienceand feedback

Significant experience andfeedback The age of some ofthese models and the length oftime they have been used havecontributed to increasing theirrobustness. Coupled THMmodelling is well suited to theEDF requirements: tightness ofthe containment vessels ofnuclear power stations, problemsconnected with the deep storageof waste, re-saturation and thethermo-mechanics of swellingclays, damage during excavationand the consolidation of galeries,etc

Optimizedarchitecture in THMOptimized architecture in THMMajor breakthroughs have beenachieved lately in the field of THMmodelling, especially in optimizingthe degrees of freedom of thearchitecture with a second-orderinterpolation for mechanics andfirst-order interpolation for ther-mo-hydraulics. The numerical inte-gration methodology has alsobeen improved, resulting in theseparation of the integrationpoints for the terms of the diffu-sive kind (Gaussian quadrature)

or of the capacitive kind (topof the element). To do this,

you have to use theselective modelling,adding an S at theend of its name (i.e.D_PLAN_HMS).

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Water saturationmap in a medium-level waste slot

Close-up on a storage gallery – Andraarchitecture

Note The latest developments of the CORR_ACIER constitutive law for reinforcements(BARRE elements) describing a damageable elasto-plastic behaviour in whichthe fracture plastic strain depends on the corrosion index.

In forecasting andcontrolling the mechanical

behaviour of civilengineering structures forpower production such as

the containment vessels,the nuclear power station

cooling towers or thedams, EDF’s concerns for

the safety of theinstallations are dominant.The resolute positioning of

Code_Aster on thenonlinear modelling of pre-stressed reinforced concretemakes it possible to calmlyconsider digital monitoring

of such structures overtime.

Evaluating the service life of aconcrete structure as well asanticipating and correcting itsdefects require knowledge of itscondition at early age or at agiven time. This creates interest inthe diversity of concretemodellings, the methodology ofworkable surveys and theexperimental validation of these:thermohydration, drying,shrinkage, cracking, damage,creep and the effect of active andpassive reinforcements. Beyondphysical behaviour, the range ofproblems to be covered is vast;for example, the tightness ofconcrete containment vessels fornuclear power stations and theirdistortion over time, as well as theeffects of accidental loads such asearthquakes, loss of primarycoolants or shock of projectiles.

Physico-MechanicalBehaviour ofConcrete

Changes in the properties ofconcrete are processed byassociated thermo-hydration anddrying models (Granger, Bazant,Mensi, etc.). The Aster operatorscalculate concrete shrinkage at anearly age from variations inhydration and desiccationshrinkage using a dryingcalculation. For specific creep,two models are available:GRANGER and BETON_UMLV_FP.Desiccation creep can bemodelled using the Bazant’sapproach which is available eitheralone (BAZANT_FD) or coupledwith the specific creep of theBETON_UMLV_FP law.

Nonlinearmechanical models

The mechanical nonlinearbehaviour of concrete isprocessed by various models thathave to be chosen depending onthe issue that is dealt with. A newmodel depicting the “parabolicrectangle” statutory law in 2D(BETON_REGLE_PR) is available.

It is well suited to models basedon elements such as shells, undermonotone load, and completesthe already existing models:Laborderie (LABORD_1D), DoubleDrucker Prager(BETON_DOUBLE_DP), Mazars(MAZARS), Badel(ENDO_ISOT_BETON), Godard(ENDO_ORTH_BETON). Thedamage models may be regulated(GRAD_EPSI) in order to get rid ofthe numerical dependence to themesh size. Lastly continuationmethods make it possible toovercome potential snap-backs.

Pre-stressed concrete

Code_Aster offers variousfunctionalities to analyse thebehaviour of pre-stressedstructures. The pre-stressedconcrete and cables meshes canbe meshed separately in order tomake this task easier. Thanks tothe DEFI_CABLE_BP command, itis possible to link the cables to theconcrete, as well as calculate themandatory tension profile andintegrate it into the model.Depending on the kind of study,using the STAT_NON-LINE orCALC_PRECONT commandsmakes it possible to apply tensionto the cables and to phase them.

Concrete reinforcements can bemodelled by finite elements ofbars or mesh reinforcements.When combined with elements ofshells in order to depict tied rebar cage, they may betransformed from the neutrallayer surface. A non-linear lawcan be applied to mesh reinforcements in order to simulate plasticization and non-linear strain mechanisms.

Resistance to seism of a publicbuilding. Monitoring of the seis-mic protection support devices.Nonlinear transient dynamicanalysis with discrete elementssuch as linear spring and nonlin-ear damper. Studies carried outby the NECS company(www.necs.eu).

Mechanical performance of con-crete with web plate pipes. Im-pact of corrosion on mechanicalperformance.

Non linear static study includingconcrete cracking, reinforcementsplasticizing and web plate corro-sion.

Studies carried out by the NECScompany (www.necs.eu) forEDF/MMC.

Behaviour curve of the pipe.Test/Aster simulation comparison.

Mesh of pre-stressed cables of a containment building.

Modelling of the shear stresses on concrete: EDF SEPTEN study.

Force of the dampers during theseism.

Displacement of the #2 flooringduring the seism

Civil engineering, concrete

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Analyse a crack withoutmesh…..is now possible thanks to the implemen-tation of the X-FEM method in Code_Aster.The crack is defined in a geometrical way(DEFI_FISS_XFEM operator) and is intro-duced into the sane mesh by enriching thestandard finite elements. In the post-pro-

cessing of the mechanical calculation,the stress intensity factors may be

calculated with the CALC_Goperator. It is possible to takeinto account the contact onthe crack lips.

Damage of reinforcedconcreteTwo new models of damage through bend-ing (GLRC_DAMAGE and GLRC_DM) havebeen developed for the static or seismicstudy of the behaviour of reinforced con-crete plates..

Fracture mechanic in modaldynamicThe POST_K-TRANS operator makes it pos-sible to identify quickly and accurately thedevelopment of the stresses intensity factorsover time, in post-processing of a transientdynamic calculation on a modal basis.

Fracture, Damage and Fatigue

The analysis of the causesof destruction of a

structure or a mechanicalcomponent must take

into account the actualnature of the

deterioration recordedand the degree of

fineness being sought. Byoffering a wide range of

models and analysis toolsfrom the most widely

tested to the mostexploratory, Code_Aster

covers the range ofproblems of damage,

fracture, fatigue and limit loads.

For mechanical deteriorationunder repeated loadings, wespeak of “fatigue”. Otherwise it isa case of “fracture” or“damage”. The mechanics offracture relies on global criteriafor deciding whether an existingcrack will propagate, whereas thedamage mechanics is directlylinked to the materials for thedetection of initiation anddevelopment of the damagedareas.

Cracks developmentTwo key parameters make itpossible to analyse the stabilityand the propagation of a crack:the energy release rate G and thestress intensity factors K. InCode_Aster these parameters canbe calculated in linear elasticitythanks to the operators CALC_G(energetic method) andPOST_K1_K2_K3 (displacementjumps interpolation), in varioussituations: 2D and 3D, surface or volume force, pressure on thelips, etc.

In elasto-plasticity it is still possibleto use CALC_G to calculate Gprovided that the load remainsmonotonous and radial. Two newparameters have beenimplemented in order to gobeyond these limits: GTP (full-plastic G, calculated withCALC_G on breach in ductilefracture) and GP (plastic G). Thelatter, only used for brittlefracture, is an extension of theplasticity in the Francfort-Marigoformulation. The POST_GPoperator makes it possible toidentify the critical values of GPand predict the moment offracture for a given thermo-mechanic transient.

An approach based on elementsof joint (PLAN_JOINT model) ordiscontinuity elements(PLAN_ELDI model) makes itpossible to model thedevelopment of two-dimensionalcracks in a given direction, instatic as well as in dynamics, withan interface model of thecohesive zone kind (taking intoaccount residual interactionbetween the crack lips, CZM_EXPor CZM_EXP_REG behaviour).

Damage ofstructures

Cracking according to aninterface law is just a mode of deterioration, the damagemechanics makefiner modellingpossible because it uses thematerial point scale.

If we limit ourselves to the studyof initiation in the strictest senseof the word, the operatorPOST_ELEM supplies a probabilitythanks to the WEIBULL model.

However if we want to model theentire response of the structure,from initiation to destruction, it isessential to resort either toconstitutive laws coupling thedevelopment of the damage andstresses on the material pointscale (ENDO_ISOT_BETON,ENDO_ORTH_BETON or MAZARScriteria for concrete, ROUSSELIERfor steel) or to softening plasticitymodels (BETON_DOUBLE_DP forconcrete, DRUCKER_PRAGER forsoils and VENDO_CHAB formetals).

However, if they authorize finermodelling, these laws come upagainst two difficulties: theinstability of the overall responseof the structure and thelocalization of strains. In order toovercome these, Code_Asterprovides two innovativeresponses: Specific continuationmethods make it possible tomonitor instabilities (snap-back/through phenomena) andnon-local formulation behavioursavoid pathological dependenceon the discretization.

Fatigue damageMost failures of industrialcomponents in normal operationare due to fatigue. Its latentnature is only equalled by itsnoxiousness, which is why theevaluation of this type ofphenomenon is important fromthe design stage.

Depending on the type of fatigue(low cycle fatigue , high cyclefatigue, etc.) the type of stresses(deterministic, random, periodic,multiaxial, distortions, etc.),available input data (componentor stress tensor, etc.) and desired

results (field in one point or onthe structure, criterion).

X-FEM method: multi-cracked pipe. Post-processing mesh.

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RRA circuit elbow: damage calculation by the Dang Van criterion and thermal cracking.

Dynamics

They solve the Helmholtzequation to deduct the noise leveland acoustic intensity fields fromit.

Modelling an arch dam in case of aseism: soil-structure coupling betweenthe civil engineering and the tank.

Modal stresses on an alternatormodel

The dynamic behaviour ofstructures may lead tosurprises that are not

always pleasant. A simpleresonance may have the

stress levels of a pumprising! During an

earthquake, watersurface movements may

cause a reservoir tovacillate! Luckily,

Code_Aster can help tomodel the inertia of

structures and itsunexpected effects during

transient or stationaryphenomena.

Introducing inertia terms intomechanical equations makes itpossible to model the complexityof dynamic phenomena andvibratory or transient aspects.Whether they are determinist orrandom, whether the constitutivelaws are linear or not, whether ornot the distortion of structures arecoupled to acoustic or fluidmovements, whethercomponents come into contact orchafe, Code_Aster makes itpossible to model them on amodal basis or in physical space,on the entire structure or bysubstructuring.

Modal analysisCalculating the eigen frequenciesand eigen mode of a structurealready provides preciousinformation about its vibratorybehaviour. The operatorsMODE_ITER_XX calculate modaldeformations and their specificpulses, with or without structuraldamping. The modes can also bethe basis for reducing the modeland its main degrees of freedom,thus simplifying the study oftransients. It is, of course, possibleto normalize modes(NORM_MODE) or to filter them(EXTR_MODE) according tovarious conventions.

Transient orfrequential analysis

Knowing the response of thestructure to a stimulus is essentialfor closely analyzing strains andstresses over time. Dedicatedoperators handle the variousprocess: harmonic linearmechanics (periodical stresses),transient dynamics on a reducedmodal basis or physical basis(linear or non-linear, along withnumerous integration schemes),spectral analysis and combinationof seismic loads or random lineardynamics (interspectral densities).

DampingsDissipative phenomena (friction,viscosity, etc.) occur in structures;they have a significant influenceon the amplitude of responses.Damping is nevertheless often difficult to model. For ths reason,three types of damping areavailable: viscous, hysteretic andmodal.

From measurementto calculation

Numerical modelling makes itpossible to add to experimentalmeasurements in areas where nosensor is available and where onewants to calculate a stress. PROJ_MESU_MODAL extrapolates thedesired value using a modal basefrom the digital model.

Soil-structureinteractions...

... occurring in reactor buildingsor vault dams dynamics may besolved in two ways: by frequentialcoupling with MISS3D(XX_MISS_3D), integral codeequation by ECP, or via absorbentboundary elements modellingquasiinfinite domains (XX_ABSO).In all cases the anechoicityhypothesis is checked (eliminationof plane elastic or acoustic wavesdiffracted by the structuretowards infinity).

AcousticsThe survey of acousticpropagation in a compressiblefluid and for closed areas ismodelled (ACOUSTIQUEphenomenon) via twoformulations (conventional and mixed).

Pressure of fluid in a tank and freesurface movement.

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Substructuring for bettercalculation!Given the complexity of mechanical struc-tures, conventional numerical or experi-mental methods often prove to be costly.It is therefore preferable to break down theglobal model into several substructures andto study their vibratory behaviour separatelybefore connecting them. Different types ofinterface modes are available inDEFI_INTERF_DYNA: Craig-Bampton,MacNeal or dynamic interface methods.The surface meshes do not even need tobe coincident – Code_Aster adapts toincompatible connections. New develop-ments in this field also make it possible toanticipate the impact of a change in struc-ture based on measurements on the initialstructure.

Different types of fluidforce...... are modelled in Code_Aster. In vibrationunder flow (fuel rod), we distinguish twoof these: the forces that are independentof movement of the structure and are dueto turbulence or to the two-phase natureof the flow (DEFI_SPEC_TURB) and the“fluid-elastics” that give practical expres-sion to the actual fluid-structure coupling(CALC_FLUI_STRU). CALC_MATR_AJOUcalculates the coefficients associated withthis coupling. It is also possible to studythe vibro-acoustic coupling and the rattlingof structures filled with liquid (piping, tanks,etc.) with free surface using ad hoc ele-ments (XX_FLUI_PESA/STRU modelling...).This strong coupling is processed by a sym-metrical formulation (u, p,f). It is possibleto use it in harmonic or directly transient

analysis: the structure may show any typeof nonlinearity while the fluid remains mod-elled in a linear way.

From multiscale to multiphysics

In the power industry, aselsewhere, the

phenomena are oftencoupled. Code_Aster

offers tools for makingchainings or couplings ofphenomena internally as

well as externally withother specialized codes.

For multiscale and multiphysics, itis possible to distinguish theinternal and external approachesof the code. In the first case, themultiplicity of the physics isdirectly taken into account byCode_Aster, whereas in the othercase the interaction is done eitherby coupling or by chaining withanother calculation software.

Internal approaches

Thermomechanical chaining forsurveys with materials thatdepend on temperature oranother variable.

By strongly coupling the thermal,hydraulic and mechanicalequations(thermohydromechanical), we areinterested in porous media,whether or not these aresaturated: rocks, clays, concretes.Thermo-metallo-mechanics, usedin particular for the simulation ofmultipass welding.The fluid-structure interaction makes itpossible to calculate the vibrationsof a structure containing (orrunning in) a fluid that is restingor flowing.

A power-mechanics chainingprovides the dynamics ofstructures subjected to Laplaceforces which are induced by therelative positions of theconductors.

Thanks to the MED format, Modelling andData Exchange...... of finite elements developed by EDF-R&D and the CEA, Code_Aster exchangesmeshes, topological entities and resultswith other codes. The structure of the lat-ter is relatively rich: all types of fields byelements (constant by element, at theGauss points or at the nodes), fields thatare either defined or not defined through-out, and fields involving heterogeneousvalues components (i.e. a 3D model linkedto shells and beams).This richness, which

guarantees the opening to the use ofnon-proprietary pre- and post-pro-

cessing tools, has a single inputpoint, FORMAT=’MED’, in

L I R E _ M A I L L A G E ,L I R E _ C H A M P a n dIMPR_RESU.

Micro-macroDefining a behaviour from elementarybricks: a given flowing law, kinematicstrain or other isotrope, make it possibleto avoid defining all the combined behav-iours. Via the operator DEFI_COMPOR,these bricks are associated with amonocrystal and its sliding systems, thuscreating a behaviour model specific to agroup of meshes in STAT_NON_LINE.

Calculations of aggregates where everychained grain is made up of an orientedmonocrystal can now be carried out. Thisnew “micro-macro” functionality opensthe way to a fully modular multiscale. Allthat needs to be done is to integrate thesevarious scales into a polycrystal made upof several monocrystals and to define alocalization rule for the whole thing andthe calculation can be started!

10

The Arlequin method opens perspectives for the multiscale byconnecting various digital modelsusing a superimposition technique: cracks, welds, supportstructures, etc.

Cracks may also be analysedwithout meshing them with the X-FEM method.

3D / shell connection and crackedpatch under Arlequin

Saturne/Aster chaining

Aggregates calculation

The micro-macro makes itpossible to manipulate theconstitutive laws in a modularway on diverse scales (see box).

The HOMARD meshrefinement/unrefinement toolcombined with the error orsensitivity indicators analysis(calculation of the analyticalderivative depending on the data)is a means for the user to judge the calculation quality.

External approaches

Code_Saturne chaining (EDF,thermohydraulics for fluid) –Syrthes (EDF, thermal change forthe wall) – Code_Aster (structure)with temperature or pressure fieldinterpolation on the mechanicalmesh. Code_Aster – Europlexus

chaining (fast dynamics codefrom the EDF-CEA-CCR/Ispra-Samtech consortium).

Frequential response by MISS3D(ECP, code of integral equationsfor wave propagation) to aseismic excitation for stratifiedsoils with or without fluid domainnext to the modal analysis withCode_Aster. Importing intoCode_Aster of volume stressfields delivered by theelectromagnetism codeFlux2D/3D with a view tocalculating the thermomechanicalbehaviour of transformers orelectric motors.

Code_Aster, a flexibleand open program

With the Code_Aster’sarchitecture, advanced

users can easily work onthe code, partly thanks to

PYTHON, in order towrite professional

applications, introducefinite elements andconstitutive laws or

define new exchangeformats.

PYTHON commandslanguage

The Code_Aster user describesthe parameters and progressionof the survey in a command file.The grammar and vocabulary ofthis language, which is specific toCode_Aster and written in thePYTHON language, are describedin catalogues. This structuring ofthe information makes it possibleto enhance the language withnew commands at lesser cost orto encapsulate recurringcalculation sequences into macro-commands.

A more advanced use enablesusers to introduce programmingin their datasets: from basic ones(check structures, loop and tests)to more complex ones using allthe richness of PYTHON(methods, classes, importinggraphics or mathematicalcalculation modules, etc.)

Here is a first basic example:Optimising a pipe bend-

radius. Anycalculation result

can be uploaded in thePYTHON space. Here we use anindicator for maximal stress in theelbow in order to repeat themesh, calculation and post-processing tasks, thus optimizingthe pipe bend-radius.

Another example: with theMEIDEE macro-command, it ispossible to launch calculations forstress identification on wirestructure. Using graphics modulesprovides an intuitive interface thathelps proceeding to theidentification. By encapsulating itinto a macro-command itbecomes a professional tool thatmake the methodology reliableand durable.

Python HCI module

Graphic display modules

Code_Aster Commands

Expansion calculation➔ Wide mode basis

Criteria calculation

Relevantcorrelation ?

Resultsdisplay

Choice of input data,mode selection, etc.

IMPR_RESU

MAC_MODES...

PROJ_MESU_MODALREST_BASE_PHYS...

no

yes

Start of MACR_VISU_MEIDEE"Correlation" tab

Writing of th results,end of the macro

Example of use of Python in a macro-command: scheme presentingMACR_VISU_MEIDEE.

Finite elements andconstitutive laws

If your problem does not adapt tothe hundred constitutive lawscurrently present, programming ormodifying a constitutive law iseasy. After consequently enrichingthe catalogue defining the materialparameters, the routine integratingthis constitutive law and giving thestress tensor, updated internal

Optimization of a bend

variables, tangent matrices, etc.must be written.

If you do not find a suitableelement among the 480 thatalready exist, you may create yourown one. The documentationprovides a step-by-stepguiding to proceed to thisdevelopment, whichdoes not requireknowledge of thewhole application. 11

A new lookIn 2007 the website was rebuilt, usingwell-tried technologies in order to addnew functionalities: wiki, RSS feed, new-looking forum, etc.

Code_Aster as a freesoftware! Why?The answer is clearly recognition andenhancement through use. Defects are

identified fully and more quickly,while diverse know-how and the

creativity of professional con-tributions will finally speedup and guarantee bettervalidation/qualification ofmodels by users of the net-

work. Beyond the technical aspect, thepolitical dimension provided by EDF R&Dand its Free Code_Aster under GPL license(General Public License), resulting fromthe skill and quality requirements innuclear engineering, is resolutely posi-tioning itself within the innovation –industry transfer. This process is intendedto stimulate Aster contributions from boththe public and private sectors (see AE no.43) by offering them in return a sustain-able and reusable platform for their ownwork. Code_Aster can be downloadedbiannually and each time benefits fromthe Aster methodology of non-regressionin terms of accuracy and performance.

The www.code-aster.orgwebsite, the code’s

multimedia base, meetsthe double requirement

of being at the service ofthe users and developers

and supporting itsdistribution as a free

program. Guided tour ofthe sections and

categories of the site,taking a look at the

technical and politicalmotives of makingCode_Aster freely

available.

PresentationThe Code_Aster, Functionalitiesand Domains categories resumeand develop the chapters of thisCode_Aster V8 brochure. Theslides presented at the AnnualUser and Free Code_Aster opendays are also available. TheStudies example section isdevoted to Aster industrialsurveys. The distinction betweenthe Free, Development andOperation versions is explained inthe Versions section. The Quality control section givesdetails on the acceptance criteriafor changes and corrections.Finally, the Tools section listsprograms using or used byCode_Aster.

DocumentationThe Documentation section provides all the code’s technicaldocumentation. TheAdministration file (quality procedures), the data regardingMaterials and the documentationconcerning the EDF qualifiedversion are in restricted access inthis section. A wiki is available forthe free community to writedocuments to get to knowCode_Aster, examples or tutorialscoming in addition to the officialdocumentation.

DownloadThis section provides access todownloads of Code_Aster. The source code is provided alongwith its tools and pre-requisites ina single package called “aster-full”, thus makingthe setup much easier (it oftenconsists in a single commandline). The weekly updates of the Development version are also available online.

SupportCourse material and tutorialsfrom the trainings are availablefor users. The rules applying todeveloping and having yourdevelopment validated within thecentralized version are given in

the Presentation section. InOrganization, the successiveupdate histories of thedevelopment version areavailable together with reports (restrictedaccess) and an organizationalchart of the participants contributing to the code.

In NEW Version you can findinformation about the setup of a development version.

ServicesThis section has a restrictedaccess and addresses the EDFusers and provides all the information concerning accessto the code, hotline, trainingsand the users club.

Code_Aster, the website and the free version

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Feedback...... is a precious tool in the developmentprocess. It collects user requests, indexes anyreports and monitors their changes over time.It uses Intranet technologies in order to man-age a database of more than 10,000 records.

More and more...... calculation resources for Code_Aster users:a centralized Bull Novascale machine (120processors at 1.6 GHz, 960 GB memory), a

development cluster of 10 Opteron 64 bitprocessors and access to the massively par-allel machines of the Research andTechnology Calculation Centre (CCRT) of theCEA.

Aid to use service...... provides the necessary expert-ise for complex or innovativestudies. May be asked forthrough the feedback tool.

Since 1989, Code_Asterhas been recognized

within EDF as the digitalsimulation tool delivering

innovations essential tothe expert appraisal ofproblems right in time.

Code_Aster confirms itsdual mission: a qualified

and operationalcalculation tool that takes

on board developmentsoriginating in research.

Quality throughtransparency and validation

The Aster quality criteria, whichare governing the developmentand distribution of the code, arebased on a regularly audited quality frame of referencemeeting the requirements set bythe EDF Nuclear Structures SafetyAuthority. These criteria constitutethe Aster Software Quality Planand are defined in the codeAdministration Manual. Thetheoretical foundations of Astermodels are documented in theReference Manuals. Theindependent validation of theoperational versions of the code,which is carried out by externalcalculation companies, deals withthe software’s conformity withregard to its documentation, theactual cover of the declareddomains of analysis and non-regression in terms ofaccuracy/performance. TheQuality Sheet enclosed with eachoperating version is updated persubversion (errors corrected,inclusion of relevantdocumentation).

A central team ofaround twenty EDFR&D engineers...

... is devoted to verifying theconsistency and quality of theAster platform (2,000 validationor non-regression tests):architecture, tools, versioning,launching, feedbackmanagement, validation,documentation, communication,training, etc. It is also supportedby teams in EDF applied projects,industrial and university researchand survey and services suppliers.More than 70 engineers havethus contributed to the software’sdevelopment.

ProductsThe Aster architecture, comprisedof 1,200,000 lines of FORTRAN(440,000 of which are new or

modified in V8), supported by C and Python, is based on adynamic memory manager, acommand “supervisor” and an EFcalculation engine (algorithmindependent finite element formulation). Its opening relies onwide use of catalogues describingthe commands and finiteelements.

Code_Aster isavailable in threeforms...

... operation, development andfree, all originating from a uniquesource code. This source alongwith its tools and prerequisites aremaintained and validated underUnix and Linux, but the Free Astercommunity has suggested theportage under Windows. TheOperating Version meets the IPS(Important for Safety)qualityrequirements. It is subjectto corrective maintenance andadditional validations anddocumentation over a two-yearperiod. This is the version for EDFusers and their authorizedsuppliers. It will remain availablefor 2 more years for resumingsurveys. The Development Versionis enriched every week bycorrections, improvements andinnovations (50 updatesannually). It will become theOperating Version after a 2-yeardevelopment cycle andqualification.

The Linux Aster operation anddevelopment files are accessibleto EDF and its partners on thecentralized server. The biannualversion of Code_Aster is editedunder GPL license on www.code-aster.org. It originatesfrom the packaging of the currentDevelopment version. Weeklypatches make it possible to keepit updated.

DocumentationUse (generalities, commandsyntax, examples), IT Description(architecture, memorymanagement, supervisor, datastructures), Reference(formulations and algorithms) andValidation (elementary mechanicsor non-regression test examples).In V8: 14,000 pages (50% of thecorpus renewed) can be accessedon www.code-aster.org.

Training and helpwith modelling

The value of a simulationsoftware also relies on the skilland critical minds of its users.These qualities are acquiredthrough significant initial andongoing training. Aster coursesoffer training at all levels:“Initiation” to the code or its“Development”, learning tohandle “Post-Processing” or“Survey Quality” tools,“Dynamic” and “StaticNonlinear” analyses.

Products and services

13

14

Code_Aster, a user-friendly

EFICAS: intelligent graphical Aster command editor.

SALOME-MECA: a unique environmentfor the study steps in Code_Aster.

Integrated to the platform, thissoftware makes it easier to workwith mesh groups which are thesupports of the boundaries andloads requirements, by selectingthem directly on the geometry. Forusual studies, an assistant makes itpossible to generate automaticallya command file according to thefew users’ choices.

EFICASThe EFICAS Command File Editorand Syntax Analyser Is a softwarewith user-friendly GUI, whichdirectly generates files withguaranteed syntax in accordancewith the choices of the user. Byinterpreting the commandcatalogues it automaticallymanages syntax and keywords aswell as the various rules andexpected concept types.

SALOME-MECAThe Salome-Meca platform offers aunique environment for the variousphases of a study:

Creating the CAD geometryFree or structured meshConverting to physical data(EFICAS)Launching the Code_Astercalculation case (ASTK)Post-processing results (STANLEY)

High level calculation isno longer synonymouswith “difficult to use”.

Today with theintegration

of Code_Aster into the Salome-Meca

platform it is mucheasier to use the code.

Salome-Meca defines,carries out and post-processes

your calculation in afew clicks.

15

software

SALOME-MECA: results display

ASTK: the Code_Aster use and development hub.

STANLEY: the Code_Aster results explorer.

ASTKThe provision of a multi-platform,multi-version IT tool that is usedand co-developed by variousteams has to be done through a Study and DevelopmentsManager. This is ASTK’s aim:selecting the code version, defining the files comprised in a study, creating an overloaded version and accessingconfiguration management toolsfor developers. This interface usesnetwork protocols for transferringfiles between clients and server, or for starting remotecommands, including over theInternet. Users can easily distribute their data files andresults to different machines asthe interface ensures the transferof files, including compressedones, over the network.

STANLEYThe STANLEY application is aninteractive post-processing toolthat facilitates access to the listsof fields available in the resultsdata structures (displacements,stresses, etc.), calculating new

ones, extracting sub-parts fromthese and visualizing them inisovalues or curves (Salome-Meca,gmsh, Xmgrace). It adapts to any configuration: workstationunder Unix, Linux or Windows,calculation locally or on a remoteserver.

EDF R&D1, avenue du Général-de-Gaulle92141 Clamart cedex - France

www.edf.comEDF SA au capital de 911.085.545 euros - R.C.S PARIS B 552 081 317