$$$$ 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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