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$$$$ G_THETA1 NOTICE  CHAT      11/09/12    21:16:25     7124           
                                             DATE     11/09/12
                                             
    Procedure G_THETA1                       Voir aussi : CH_THETA
    ------------------                           
    G_THETA1 TAB1 MAT1 TAB2 ;

                                TAB2.'CHTHETA'     .'DEPLACEMENT' 
                                    .'CONTRAINTE'  .'VARINTERNE'
                                    .'TEMPERATURE' .'TREFERENCE'
                                    .'TALPHAREFE'
                                    .'CHARGEMENT'  .'TEMPS'
                                    .'GRANDS_DEPLACEMENTS'
                                    .'PRESSION'    .'REPRIS'   
                                    .'PARALLELE'   .'INTERFACE'
                                    .'LOI'         .'DEFINELA'
                                    .'DEFI_INI'    .'DEPL_INI'
                                    .'CONT_INI'    .'MODMIXTE'
                                    .'TEMP_INI'    .'TEMP0'
                                    .'AVANCE'      .'LEVRESUP'
                                    .'LEVREINF'    .'FONDFISS'
                                    .'TDYN'        .'VITESSE'           

    Description :
    ____________

    This procedure calculates 
    1) the energy release rate, G, in elasticity or elasto-plasticity 
       or the C* integral in visco-plasticity by means of the G_THETA 
       method. It can deal with problems in :
          - two-dimensions
          - three-dimensions
          - axisymmetry
       used materials can be :
          - homogeneous
          - non-homogeneous
          - composite
       and applied loadings may include :  
          - mechanic loads
          - thermic loads
          - volumic forces (or pressures on the crack bottom)
       In elasto-plasticity or visco-plasticity, the calculation is
       performed in relation to the evolution parameter values (pseudo 
       time or real time) defined by users.
    2) Seperation of the stress intensity factors for elastic problems
       in 2D, 3D (massif elements only) or axisymetrical configuration.
       For fractures in mixed mode, only homogeneous materials under
       mechanical loadings are acceptable. 

    Contents :
    __________

    Input data, in order :

            
    TAB1 :  TABLE type object in which all the model objects of the mesh 
            GEO1 are stored and whose index is 1, 2, 3,..., n
            (n : number of model objects of the mesh GEO1).

    MAT1  : MCHAML object of CARACTERISTIQUES subtype. In the case of 
            calculations with thin shell elements, this object includes
            material's properties (Young's modulus, Poisson's   
            coefficient ...) and geometrical parameters like shell's
            thincknees, generated by operator MATER or CARA. 

    TAB2  : object (TABLE type) used for defining the calculation options
            and parameters. The indices of the TAB1 object are words 
            (written in words). Here is their list :


      Arguments compulsory for all types of calculations :
      ___________________________________________________

        index       pointed object     comments
                         type

      DEPLACEMENT   TABLE/CHPOINT  For calculations realized step by
                                   step (ex : nonlinear problems),
                                   TAB2.DEPLACEMENT is a table containing 
                                   all the displacement chpoints in index
                                   of the definition of the evolution 
                                   parameter values (ex : table RESUDEPL 
                                   of NONLIN). For calculations realized
                                   in one step only (ex : linear problem),
                                   it is the displacement chpoint of
                                   the treated problem.

      CONTRAINTE    TABLE/MCHAML   For calculations realized step by
                                   step (ex : nonlinear problems),
                                   TAB2.CONTRAINTE is a table containing 
                                   the stress field/elements in the 
                                   same index as the table TAB2.DEPLACEMENT.
                                   (ex : RESUCONT of NONLIN). The results  
                                   stored in the tables TAB2.CONTRAINTE  
                                   and TAB2.DEPLACEMENT must be bijective.
                                   For calculations realized in one step
                                   only (ex : linear problem), CONTRAINTE
                                   is the stress cham/element of the
                                   treated problem.

      CHTHETA      CHPOINT/TABLE   THETA field created by the CH_THETA 
                                   procedure for a crack tip.
                                   For a 3D crack bottom, TAB1.CH_THETA
                                   is a table indexed by the points of the
                                   front, containing each of the fields
                                   created by CH_THETA at this very point.

.
      Optional arguments
      __________________

      A)  In nonlinear calculations

        index       pointed object       comments
                         type 

     VARINTERNE       TABLE        In the case of nonlinear calculations
                                   realized step by step, this object gives
                                   the internal variables in the same
                                   index as the table TAB2.DEPLACEMENT or
                                   TAB2.CONTRAINTE (ex : table RESUVARI of
                                   NONLIN). The present table is given only 
                                   if the inelastic defomations are not nul.
                                   If this table is not given or its 
                                   contents are zero, the problem will be
                                   considered to be linear.

     CHARGEMENT       CHARGEMENT   In the case of nonlinear calculations
                                   realized step by step, this object must
                                   be reminded. It is necessary after the 
                                   PASAPAS procedur use. 

     TEMPS            TABLE        In the case of nonlinear calculations
                                   realized step by step, this table 
                                   describe the association of calculation 
                                   index (same as those which are contained
                                   in TAB2.DEPLACEMENT and TAB2.CONTRAINTE)
                                   with the time parameter.It is necessary
                                   after the PASAPAS procedur use.

     GRANDS_DEPLACEMENTS LOGIQUE   LOGIQUE object, egal to VRAI for large
                                   displacement calculations. In this case 
                                   the CH_THETA procedure is automatically
                                   recalled for each step so that the
                                   THETA vector is calculated with 
                                   corresponding deformed geometry. All 
                                   arguments used for calculating the
                                   initial THETA vector with non deformed 
                                   geometry should be given under the 
                                   following format : tab2.'TABLE_CH_THETA'
                                   TABLE object used for the initial THETA
                                   vector calculation.   
 
      B)  In thermo-mechanical calculations

        index       pointed object       comments
                         type 

      TEMPERATURE   TABLE/CHPOINT  For calculations realized step by
                                   step (ex : nonlinear problems),
                                   TAB2.TEMPERATURE is a table containing 
                                   all the absolute temperatures in 
                                   relation to the time evolution 
                                   parameter (ex : CHPOTHETA for NONLIN).
                                   The index of the TAB2.TEMPERATURE 
                                   and that of the table TAB2.DEPLACEMENT 
                                   (therefore, that of TAB2.CONTRAINTE or) 
                                   TAB2.VARINTERNE) may be different.
                                   Between two close instants, the tempe-
                                   rature variation is considered to be
                                   linear in this procedure. For 
                                   calculations realized in one step only
                                   (ex : linear problem), TAB1.TEMPERATURE
                                   is the absolute temperature chpoint
                                   of the problem (temperature used in 
                                   the elastic resolution).
                                   (not necessary if PASAPAS procedur has 
                                   been used).

      TREFERENCE      CHPOINT      gives the reference temperature field,
                                   i.e. the temperature field that does not
                                   create stresses. By default, this
                                   temperature chart equals that of the
                                   initial time. If the reference temperature 
                                   chart (Tref) and that of the initial
                                   time (T0) are different, the strains will
                                   be null at the initial time but there will
                                   be initial thermal stresses equalling :
                                   YOUNG*ALPH*( T0 - Tref)
                                   (chpoint TREFERENCE for NONLIN).
                                   (not necessary if PASAPAS procedur has 
                                   been used).

      TALPHAREFE      FLOTTANT     required if the thermal expension
                                   coefficient Alpha depends on the 
                                   temperature. TALPHAREFE here is that 
                                   one used to define the coefficient
                                   Alpha in the calculation of thermal 
                                   deformation
                                   EPSTH = ALPHA(T)*(T - TALPHAREFE) 
                                   - ALPHA(TREFERENCE)*(TREFERENCE
                                   - TALPHAREFE) so that for T=TREFERENCE
                                   one has EPSTH=0.

      For materials depending on temperature and calculations realized
      with NONLIN procedure, the following table is also needed
      TETMAT          TABLE        is used to define the
                                   variation of the material
                                   components in relation to
                                   temperature.
                                   This table whose dimension is
                                   equivalent to the number of
                                   the different materials in the
                                   structure is connected with the
                                   associated model objects.

      TETMAT.OBJMOD   MCHAML       object of CARACTERISTIQUES       
                                   sub-type created by operator
                                   MATE to provide material        
                                   properties associated with the   
                                   model OBJMOD. Its components
                                   may be the following types
                                   1) FLOTTANT if the component is  
                                   independent of the temperature   
                                   and constant through whole
                                   structure;
                                   2) MCHAML if the component is  
                                   independent of the temperature, 
                                   but depends upon the position
                                   of a point;   
                                   3) EVOLUTION if the component   
                                   varies in function of the
                                   temperature field;          
                                   4) NUAGE if the component is    
                                   described by a curve of
                                   EVOLUTION type depending upon 
                                   on the temperature field.

      C)  If a pressure (or a volumic force)
          is applied on the crack edges

        index       pointed object         comments
                         type

      PRESSION    CHPOINT/CHARGEMEN   This chart is provided when 
                                      a pressure or a volumic force
                                      is applied on the crack
                                      bottom. If this force varies
                                      with the time (pseudo time or 
                                      real time), one gives an 
                                      object of CHARGEMEN type. If
                                      this force keeps constant, 
                                      one gives an object of CHPOINT
                                      type.
                                      (the logical object VRAI is enough
                                      if PASAPAS procedur has been used)

      D)  In case of restarts of a calculation

        index       pointed object         comments
                         type

       REPRIS         LOGIQUE      LOGIQUE objet, egal to VRAI (ture) if
                                   you want to complete the calculations of
                                   fracture parameters with a set of new
                                   mechanical solutions. More exactely, 
                                   Once you have left G_THETA, you may 
                                   re-enter it with a set of mechanical 
                                   solutions compeleted by a new evolution 
                                   parameter. You re-enter in G_THETA 
                                   procedure by recalling on it with 
                                   the same operands as for the first call.

      E)  In the case of composite materials

        index       object type        comments

      INTERFACE  =      TABLE    This object stores all the interfaces
                                 (of MAILLAGE type) of the different
                                 materials.
                                 The index of this table is   
                                 1, 2, 3,..., N (N : number of
                                 materials interfaces. If the
                                 materials are composite, the
                                 tables TAB2 as well as INTERFACE must
                                 be constructed as follows :

           ____________ ____________ ____________ ___________
          |            |            |            |           | 
          |   TAB1.1   |   TAB1.2   |   TAB1.3 ..|.. TAB1.n  |
          |            |            |            |           |
          |____________|____________|____________|___________|
                  INTERFACE.1  INTERFACE.2 ... INTERFACE.N


      F) : In visco-plasticity for calculating the C integrale

         index       pointed object         comments
                         type
 
      LOI             MOT        gives the creep law used in calculations.
                                 the following laws are acceptable :
                                 NORTON, BLACKBURN, RCCMR_316, 
                                 RCCMR_304, LEMAITRE ou POLYNOMIAL.
      DEFINELA        TABLE      gives the unelastic deformation in the 
                                 same index as the table TAB2.DEPLACEMENT 
                                 or TAB2.CONTRAINTE (ex : table RESUDEFI
                                 of NONLIN). 
      DEPL_INI        CHPOINT    gives the displacement chpoint
                                 just at the beginning of the creep.
      CONT_INI        MCHAML     gives the stress field/elements
                                 just at the beginning of the creep.
      DEFI_INI        MCHAML     gives the unelastic deformation
                                 field/elements just at the beginning   
                                 of the creep.        
      TEMP_INI        CHPOINT    gives absolute temperature chpoint   
                                 just at the beginning of the creep.
      TEMP0                      gives the time (FLOTTANT type) from 
                                 which begins the creep. By default,
                                 this time is taken to be zero.
                           
      G) For a 3D crack front

        index         object type         comments

        AVANCE        MAILLAGE    Points of the front for which the
                                  G calculation will be performed.

      H) En cas de decouplage des modes mixtes 

        index        object type          comments                      
                                   
       MODMIXTE      LOGIQUE           VRAI (true) in the case of 
                                       seperation of the stresse 
                                       intensity factors; FAUT (by 
                                       defaut) in the case of
                                       calculations of others
                                       fracture parameters.                     
       LEVRESUP      MAILLAGE          MAILLAGE object representing the 
                                       crack's upper lip. 
       LEVREINF      MAILLAGE          MAILLAGE object representing the 
                                       crack's lower lip.
       FONDFISS    POINT/MAILLAGE      POINT (2D) or MAILLAGE object (3D)
                                       representing the crack tip.

   I) In elasto-dynamic calculations                                            
                                                                        
        index      object type           comments

        VITESSE     TABLE              TABLE object containing all the
                                       SPEEDS (obtained by using DYNAMIC 
                                       procedur).   

        TDYN        TABLE              TABLE object containing all the
                                       output INSTANTS (obtained by using 
                                       DYNAMIC procedur).                       


      Output data
      ___________


     a)  In all calculation case                                      
         -----------------------                                      
                                                                     
     TAB2.G = 1) For the calculation of the energy release rate G or the 
                 C* integral, TAB2.G is, in 2D, a TABLE object if
                 mechanical solutions have been found step by step, but a
                 FLOTTANT objet if they have been found in one step only.
                 In the first case, TAB2.G has the same index as the table
                 TAB2.DEPLACEMENT or TAB2.CONTRAINTE. In 3D, if mechanical
                 solutions have been found step by step, TAB2.G is indexed
                 by two parameters. The first one is the time evolution
                 factors, and the second the points on the crack profil. If
                 mechanical solutions in 3D have been found in one step, 
                 TAB2.G is only indexed by the points on the crack profil.
                 For example, in 2D the value of G or C* is   
                 (TAB2.'G'.T1) for step-by-step calculations at instant T1  
                 (TAB2.'G') for one-step calculations. In 3D
                 (TAB2.'G'.T1.P1) for step-by-step calculations at instant
                                  T1 and point P1 on the crack profil.
                 (TAB2.'G'.P1) for one-step calculations at point P1.
              2) In case of seperation of the stresse intensity factors
                 (K1, K2, K3), TAB2.G is always a TABLE object. In 2D 
                 and for step-by-step calculations, it is firstly indexed
                 by words 'I' and 'II', then by the time evolution factors
                 giving parameters G1 or G2 at a certain instant. In 2D 
                 and for one-step calculations, TAB2.G is only indexed
                 by words 'I' et 'II'. In 3D and for step-by-step
                 calculations, TAB2.G is firstly indexed by words 'I',
                 'II', 'III', then by the time evolution factors and
                 finally by the points on the crack profil giving
                 parameters G1, G2, G3 at a certain instant and a certain
                 point on the crack profil. In 3D and for one-step 
                 calculations, TAB2.G is only indexed by words 'I', 'II', 
                'III', then by the points on the crack profil. For exampl,
                 the value of G2 is in 2D
                 (TAB2.'G'.'II'.T1) for step-by-step calculations 
                                    at instant T1  
                 (TAB2.'G'.'II') for one-step calculations. In 3D,
                 (TAB2.'G'.'II'.T1.P1) for step-by-step calculations at 
                                       instant T1 and point P1 on the 
                                       crack profil.
                 (TAB2.'G'.'II'.P1) for one-step calculations at point P1.
                 The factor Ki (i=1,2,3) is connected to Gi by
                 Ki = (Gi/Material_Constante) ** 0.5;
                 REMARQUE : The Material_Constante value is stocked
                            in TAB1.C_MATE (FLOTTANT objet).In the
                            case of crack located in the bounded
                            region of two dissimilar bodies, it
                            depends on their material caracteristics.
                            The signs for factors K1 and K2 is
                            provided by TAB1.SIGNE_K1 and TAB1.SIGNE_K1
                            (ENTIER object), egal to 1 if ther are
                            positive, -1 if negative.              
                                                                     
     b) In case of calculations performed step by step                          
        ----------------------------------------------                          
                                                                     
     TAB2.EVOLG = 1) For the calculation of the energy release rate G 
                     or the C* integral, TAB2.EVOLG in 2D is an EVOLUTION
                     object giving evolution of G or C* with the time.
                     In 3D, it is a TABLE objet indexed by the points 
                     on the crack profil and giving evolution of G or C*
                     at a certain point with the time. For example, you 
                     may illustrate the variation of G oy C* by writting
                     DESS (TAB2.'EVOLG') in 2D and
                     DESS (TAB2.'EVOLG'.P1) in 3D point P1 on the crack
                                            profil.    
                  2) In case of seperation of the stresse intensity factors
                     (K1, K2, K3), TAB2.EVOLG is always a TABLE object.
                     In 2D, it is indexed by words 'I' and 'II' giving
                     variation of G1 or G2 with the time. In 3D, it is
                     firstely indexed by words 'I', 'II', 'III', then by 
                     the points on the crack profil giving evolution of
                     G1, G2, G3 at a certain point with the time. For 
                     example, you may illustrate the variation of G2 
                     by writting
                     DESS (TAB2.'EVOLG'.'II') in 2D and
                     DESS (TAB2.'EVOLG'.'II'.P1) in 3D point P1 on the 
                                                 crack profil.    

     TAB2.'CRITERE_DECHARGE' = In case of ELASTIQUE PLASTIQUE material, 
             ISOTROPE or CINEMATIQUE, possibly THERMIQUE, we evaluate a 
             critetion of decreasing of the stresses defined by ( if, F = tensio
             curve ): crit = F(STRAINeq)/ STRESSeq. crit = 1 if no-decreasing an
             crit > 1 if decreasing. SUPTAB.'CRITERE_DECHARGE' is a TABLE type
             object indexed by the calculation times as TAB2.CONTRAINTE. 

       c) In case of elasto-dynamic calculations
       ------------------------------------------                            
    
     TAB2.'G' = TABLE object containing G values indexed by
                calculations instants.
                           
     Remark :
     _______

      The TABLE TAB2 also contains other objects used for resuming
      calculations; this table, as well as the objects GEO1, TAB1 and
      MAT1 should be saved for resumimg a later calculation.
      Since the results are located in TAB1, this procedure does not
      create any other object.





 
 
 
 
 

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