3. Modeling A

3.1. Characteristics of modeling

The modeling used is 3D.

Loading and boundary conditions are modelled by:

• DDL_IMPO: (NOEUD: N08, DX: 0., DY:0., DZ:0.)

DDL_IMPO: (NOEUD: N02, DX: 0.)

DDL_IMPO: (NOEUD: N06, DX: 0.)

• imposed surface forces (keyword FORCE_FACE) on the faces (skin elements) \((\mathrm{1,}\mathrm{5,}\mathrm{6,}2)\), \((\mathrm{1, 5},\mathrm{7,}3)\), \((\mathrm{3,}\mathrm{4,}\mathrm{8,}7)\) and \((\mathrm{4,}\mathrm{8,}\mathrm{6,}2)\).

3.2. Characteristics of the mesh

Number of knots: 8

Number of meshes and types: 1 HEXA8 + 4 QUAD4 (faces)

3.3. Tested sizes and results

Identification	Instants	Reference Type	Reference
\({\epsilon }_{\mathrm{xx}}\)	\(A\)	NON_REGRESSION	1.48297 E—2
\({\epsilon }_{\mathrm{xy}}\)	\(A\)	NON_REGRESSION	1.36014 E—2
\({X}_{\mathrm{xx}}\) =V1	\(A\)	NON_REGRESSION	18.26
\({X}_{\mathrm{xy}}\) =V4	\(A\)	NON_REGRESSION	1.68688 E+1
\({\epsilon }_{\mathrm{xx}}\)	\(B\)	NON_REGRESSION	4.066 E—2
\({\epsilon }_{\mathrm{xy}}\)	\(B\)	NON_REGRESSION	1.978 E—2
\({\epsilon }_{\mathrm{xx}}\)	\(C\)	NON_REGRESSION	4.4103 E—2
\({\epsilon }_{\mathrm{xy}}\)	\(C\)	NON_REGRESSION	1.8913 E—2

Discharge indicators at a Gauss point (DERA_ELGA), and at the \({N}_{2}\) node (DERA_ELNO).

Identification	Reference type	Reference value
\(\text{DCHA\_V}\) at the moment 0.1	“NON_REGRESSION”	0.877871
\(\text{RADI\_V}\) at the moment 1.5	“NON_REGRESSION”	0
\(\text{ERR\_RADI}\) at the moment 1.5	“NON_REGRESSION”	0.0125766

In addition, in a second series of calculations, we test the error indicator due to the non-radiality of the load: using a rough temporal discretization (2 increments on the paths \(\mathrm{AB}\) and \(\mathrm{BC}\), and one increment on the others), we activate the subdivision of the time step if the error due to the non-radiality exceeds 2% (RESI_RADI_RELA =0.02). This test is carried out for 3 equivalent behaviors: VMIS_CINE_LINE, VMIS_ECMI_LINE, VMIS_CIN2_CHAB.

The results are:

VMIS_CINE_LINE and VMIS_ECMI_LINE

Identification	Instants	Reference Type	Reference	Tolerance
\({\epsilon }_{\mathrm{xx}}\)	\(A\)	AUTRE_ASTER		1.48297 E—2	0.10%
\({\epsilon }_{\mathrm{xy}}\)	\(A\)	AUTRE_ASTER		1.36014 E—2	0.10%
\({X}_{\mathrm{xx}}\) =V1	\(A\)	AUTRE_ASTER		18.26	0.10%
\({X}_{\mathrm{xy}}\) =V4	\(A\)	AUTRE_ASTER		1.68688 E+1	0.10%
\({\epsilon }_{\mathrm{xx}}\)	\(B\)	AUTRE_ASTER	4.066 E—2	0.10%
\({\epsilon }_{\mathrm{xy}}\)	\(B\)	AUTRE_ASTER	1.978 E—2	0.10%
\({\epsilon }_{\mathrm{xx}}\)	\(C\)	AUTRE_ASTER	4.4103 E—2	0.10%
\({\epsilon }_{\mathrm{xy}}\)	\(C\)	AUTRE_ASTER	1.8913 E—2	0.10%

VMIS_CIN1_CHAB

Identification	Instants	Reference Type	Reference	Tolerance
\({\epsilon }_{\mathrm{xx}}\)	\(A\)	AUTRE_ASTER	1.48297 E—2	1.00%
\({\epsilon }_{\mathrm{xy}}\)	\(A\)	AUTRE_ASTER	1.36014 E—2	1.00%
\({X}_{\mathrm{xx}}\) =V1	\(A\)	AUTRE_ASTER		18.26	1.00%
\({X}_{\mathrm{xy}}\) =V4	\(A\)	AUTRE_ASTER		1.68688 E+1	1.00%
\({\epsilon }_{\mathrm{xx}}\)	\(B\)	AUTRE_ASTER	4.066 E—2	1.00%
\({\epsilon }_{\mathrm{xy}}\)	\(B\)	AUTRE_ASTER	1.978 E—2	1.00%
\({\epsilon }_{\mathrm{xx}}\)	\(C\)	AUTRE_ASTER	4.4103 E—2	1.00%
\({\epsilon }_{\mathrm{xy}}\)	\(C\)	AUTRE_ASTER	1.8913 E—2	1.00%

For all three behaviors, the radiality error indicator provides the same result:

Identification	Reference type	Reference value
\(\text{ERR\_RADI}\) at the moment 1.5	“NON_REGRESSION”	0.011798
\(\text{ERR\_RADI}\) at the moment 2.5	“NON_REGRESSION”	0.01956

The use of the radiality criterion to automatically refine the time step leads to 56 time steps in total, against 64 in the first case (with 30 increments on AB and BC), for a result of equivalent quality (error of approximately 1.2% at t=1.5, and 2% at t=2.5).