Modeling A
==============


Characteristics of modeling
-----------------------------------

:math:`A\mathrm{=}\mathit{N01099}` (:math:`s=0.`)

:math:`B=\mathrm{N01259}` (:math:`s=26.68`)

:math:`C=\mathrm{N01179}` (:math:`s=\mathrm{18,0}`; :math:`\mathrm{\alpha }=\mathrm{0,77}\approx \mathrm{\pi }/4`)

**Loading:** Unit pressure distributed on the face of the block opposite the plane of the lip:

:math:`P=\mathrm{1.MPa}` in the :math:`Z\mathrm{=}\mathrm{1250.mm}` plan.


Characteristics of the mesh
----------------------------

Number of knots: 20567

Number of meshes and types: 160 PENTA15, 175 PYRAM13, 175, 9383 TETRA10 and 1290 HEXA20


Tested sizes and results
------------------------------

The values tested are:


* the local energy release rate :math:`g` in all the nodes at the bottom of the crack (option G of CALC_G). These values are tested for integration rings defined by variable radii (R_ INF_FO and R_ SUP_FO) or by the number of layers (NB_COUCHE_INF and NB_COUCHE_SUP).


* the local energy recovery rate :math:`g` for points A and B at the bottom of the crack with the calculation operator POST_K1_K2_K3.


* the stress intensity factor :math:`{K}_{I}`, calculated at the same nodes of the crack bottom as the energy release rate (options K and KJ of CALC_G). In the case of the KJ option, we also highlight that when the calculated G value is negative, we have :math:`{K}_{J}=0` (by convention).


* the :math:`{G}_{\mathit{IRWIN}}` energy return rate calculated from :math:`{K}_{I}` and the Irwin formula

In the case of the refund rate :math:`{G}_{\mathit{IRWIN}}`, we ensure that when the value of G calculated

The mesh includes only one of the lips of the crack, it is therefore necessary to use the keyword 'SYME' to automatically multiply by 2 in the Aster calculation the energy restoration rate calculated by virtual extension of the single lip.


.. csv-table::

    "**Identification**", "**Reference**", ":math:`\text{\%}` **tolerance**"
    "", "", ""
    ":math:`g(A)` crown :math:`{C}_{1}` **('LEGENDRE')**", "7.171 10-5", "1"
    ":math:`g(A)` crown :math:`{C}_{2}` **('LEGENDRE')**", "7.171 10-5", "1"
    ":math:`g(A)` crown :math:`{C}_{1}` **('** **LINEAIRE** **')**", "7.171 10-5", "1"
    ":math:`g(A)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "7.171 10-5", "1"
    ":math:`{G}_{\mathit{IRWIN}}(A)` crown :math:`{C}_{2}` **('** **LEGENDRE** **')**", "7.171 10-5", "1"
    ":math:`{G}_{\mathit{IRWIN}}(A)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "7.171 10-5", "1"
    ":math:`{G}_{\mathit{IRWIN}}(A)` **POST_K1_K2_K3**", "7.171 10-5", "4"
    "", "", ""
    ":math:`g(B)` crown :math:`{C}_{1}` **('LEGENDRE')**", "1.721 10-5", "10"
    ":math:`g(B)` crown :math:`{C}_{2}` **('LEGENDRE')**", "1.721 10-5", "10"
    ":math:`g(B)` crown :math:`{C}_{1}` **('** **LINEAIRE** **')**", "1.721 10-5", "1"
    ":math:`g(B)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "1.721 10-5", "1"
    ":math:`{G}_{\mathit{IRWIN}}(B)` crown :math:`{C}_{2}` **('** **LEGENDRE** **')**", "1.721 10-5", "4"
    ":math:`{G}_{\mathit{IRWIN}}(B)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "1.721 10-5", "6"
    ":math:`{G}_{\mathit{IRWIN}}(B)` **POST_K1_K2_K3**", "1.721 10-5", "3"
    "", "", ""
    ":math:`g(C)` crown :math:`{C}_{1}` **('LEGENDRE')**", "5.215 10-5", "1"
    ":math:`g(C)` crown :math:`{C}_{2}` **('LEGENDRE')**", "5.215 10-5", "1"
    ":math:`g(C)` crown :math:`{C}_{1}` **('** **LINEAIRE** **')**", "5.215 10-5", "1"
    ":math:`g(C)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "5.215 10-5", "1"
    "", "", ""



.. csv-table::

    "**Identification**", "**Reference**", ":math:`\text{\%}` **tolerance**"
    "", "", ""
    ":math:`{K}_{J}(A)` crown :math:`{C}_{1}` **('LEGENDRE')**", "4.067", "1"
    ":math:`{K}_{J}(A)` crown :math:`{C}_{2}` **('LEGENDRE')**", "4.067", "1"
    ":math:`{K}_{I}(A)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "4.067", "1"
    ":math:`{K}_{I}(A)` crown :math:`{C}_{2}` **('** **LEGENDRE** **')**", "4.067", "1"
    "", "", ""
    ":math:`{K}_{J}(B)` crown :math:`{C}_{1}` **('LEGENDRE')**", "1.992", "10"
    ":math:`{K}_{J}(B)` crown :math:`{C}_{2}` **('LEGENDRE')**", "1.992", "10"
    ":math:`{K}_{I}(B)` crown :math:`{C}_{2}` **('LEGENDRE')**", "1.992", "2"
    ":math:`{K}_{I}(B)` crown :math:`{C}_{2}` **('** **LINEAIRE** **')**", "1.992", "5"
    "", "", ""
    ":math:`{K}_{J}(C)` crown :math:`{C}_{1}` **('LEGENDRE')**", "3.469", "1"
    ":math:`{K}_{J}(C)` crown :math:`{C}_{2}` **('LEGENDRE')**", "3.469", "1"
    "", "", ""
    ":math:`{K}_{J}(A)` crown :math:`{C}_{2}` **('** **LINEAIRE** **', '** **NB_POINTS_FOND** ****) **", "0.0", ""