u4.82.41 Operator POST_JMOD

Goal

This operator aims at calculating the modified J -integral in 3D (“3D’modeling) using The domain integral method based on the work rice [1] _ (standard or without initial state) and Lei [2] _ (with initial state). The theoretical and numerical descriptions of this method are presented in the associated reference document [R7.02.22]. It works for:

• elastic and plastic materials;

• proportional/non-proportional and mixed-mode loads;

• initial strain associated with an initial equilibrium stress.

This operator is only available now for meshed crack (not yet for un-meshed « X- FEM » cracks).

. toctree:

hidden:

Self

Syntax

table = POST_JMOD (
    ◇ FOND_FISS = crack_bottom,
    ◆ RESULTAT = evol_noli/evol_elas,
    ◇ NB_COUCHES = int (default: 4),
    ◇ OPTION =/"J",
               /"JMOD ",
    ◇ ETAT_INIT = _F (
         ◆ EPSI = cham_elem/cham_no,
      ),
    ◇ GROUP_NO = big,
    ◇ NB_POINT_FOND = int,
    ◇/INST = float,
      /NUME_ORDRE = int,
    # If: (exists (" INST "))
        ◇ PRECISION = float (default: 1e-06),
    ◇ TITRE = text (default: "POST_JMOD "),
)

◆: mandatory
◇: optional
: present by default
&: together
/: only one among
|: several possible choices

Operands

Operand FOND_FISS

This operand allows providing the concept fond_fisscreated by the command DEFI_FOND_FISS Which contains necessary information for the automatic Search of the crack front and one (symmetry problem) or two (non-symmetry problem) crack lips. The only requirement is that hexahedral elements must be used for elements which are used to perform contour integral. Also, it is recommended (not obligatory) that The planes passing through the crack tip nodes are planar within the contour integral zone.

Note

There is no other restrictions on the mesh as long as it is obtained via the command DEFI_FOND_FISS. For verification purpose, the users are commended to first launch A study with CALC_G (without initial stress) to ensure the quality of mesh and Crack definition prior to launch POST_JMOD.

Operand RESULTAT

Resu is a concept of the types evol_elas or evol_noli. It is the result of STAT_NON_LINE or MECA_STATIQUE calculations that contain the displacement field for the entire model.

Operand MODIFICATION

For MODIFICATION = “NON”, the J-integral valid under the conditions of initial strain and proportional loading is computed according to Equation (6) in the reference manual [R7.02.22].

For MODIFICATION = “OUI”, the modified J-integral valid under the conditions of initial Strain and non-proportional loading is computed. It is based on Lei’s modification in [1] _ And is calculated according to the equation (10) in the reference manual [R7.02.22].

Operand NB_COUCHES

Lcontour is the number of contours around the crack tip on which the*J-* integral Calculation using domain integral method is performed.

The macro-command POST_JMOD only works:

• if linear elements: NB_COUCHES < 20

• if quadratic elements: NB_COUCHES < 10

By default, NB_COUCHES = 4.

Note

Based on LEI’s modifications in [1] _, when calculating*J* using a FE program, The*J* values obtained on the first 2 to 3 contours are generally dropped because Of the severe stress, strain and displacement data at the vicinity of the crack tip. In order to minimize the effects of the consistently near tip computational results A on the calculation of the correction part for the modified J, a very small area Surrounding the crack tip is excluded from the integration area has been modified. That explains why the number of contours is assigned to be 4 by default.

Operand ETAT_INIT

In the presence of initial strain, the*J* formulation according to the equations (6) and (13) of [R7.02.22] will be used. The initial strain must be a deformation field. That is TYPE_CHAM = “XXXX_EPSI_R”. Here, XXXX can be ELGA or ELNO or NOEU. The initial strain must be self-equilibrium. Any type of initial strain that previously Existed in structure prior to calling POST_JMOD is accepted.

Note

If only the initial auto-equilibrium stress is available, an associated initial strain Should be first obtained via the STAT_NON_LINE operator. It is very important to ensure the auto-equilibrium of the initial state. Also, the user would need to employ the total initial strain.

Operands GROUP_NO, REDU_NODE

These operands allow reducing the number of nodes around the crack tip to compute J. By default, without this input, the calculation of*J* is performed for all nodes of The crack front. In order to save computing time, the user has the possibility to:

• select desired crack tip nodes by its names (keyword GROUP_NO);

• reduce the number of crack tip nodes of crack front to number_timestimes (keyword REDU_NODE).

  For example, if the front has 20 crack tip nodes and number_times = 4, the operator Will perform the calculation on 20/4 = 5 nodes along the crack front (including the extreme points).

Operands INST, PRECISION, NUME_ORDRE

The keyword INST allows to access only the result of*J* corresponding to a list of Times [U4.71.00]. Because the instant values are usually Real numbers, therefore, the keyword PRECISION allows to find the exact values of moments in the interval [inst-coef_precis, inst+coef_precis]. By default, PRECISION = 1.E-06 is set.

The keyword NUME_ORDRE allows to access only the result of*J* corresponding to a list of indexes [U4.34.02] and [U4.71.00].

If INST and NUME_ORDRE are not provided, J will be calculated and printed for all Times and all order numbers.

Operand TITRE

This operand provides the title for the result table [U4.03.01].

Current framework of application

The capabilities of POST_JMOD depend on the characteristics of the inputs such as modeling, mesh, element types and load. The current framework of applications of POST_JMOD is as follows..

		J calculation by POST_JMOD
Modeling	“D_ PLAN “	YES
	“C_ PLAN “
	“AXIS”
	“3D”
Mesh	MESHED CRACK	YES
	NON - MESHED CRACK	NO
Element types	2D and AXIS - ALL ELEMENT TYPES	YES
	3D HEXAHEDRAL ELEMENT	YES
	3D NON - HEXAHEDRAL ELEMENT	NON
Mechanical load	PROPORTIONAL LOAD	YES
	NON - PROPORTIONAL LOAD
	MIXED - MODE LOAD
Thermal load		NO
Mechanical Load on the Lips		NO

Example

Example can be found in the test cases for validations of Jmod3D development: form07a, sslv134a, sslv154a, sslv154a, sslv116a, jmod3d_t12, jmod3d_z1, jmod3d_cecc.

Example sslv116a: Circular crack in medium 3D with initial field.

The obtained results are shown below:

. [1] J. R. Rice, J. Appl. Mech., vol. 35, no. 2, pp. 379—386, 1968. .. [2] Y. Lei, N. P. O’dowd, and G. A. Webster, Int. J. Fract., vol. 106, no. 3, pp. 195–216, 2000.Y. Lei, « Improvement of modified J evaluation using finite element method »,Br. Energy Eng., 2006.