6. D modeling

6.1. Characteristics of modeling

Same as B modeling with quadratic elements.

6.2. Characteristics of the mesh

Same as C modeling.

6.3. Tested sizes and results

For method \(G-\mathit{thêta}\) (command CALC_G), the following crowns of the theta field are chosen:

	Crown 1	Crown 2	Crown 3	Crown 3	Crown 4	Crown 5	Crown 6
Rinf	0.1	0.2	0.2	0.3	0.3	0.1	0.2
Rsup	0.2	0.3	0.3	0.3	0.4	0.4	0.4

Identification	Reference type	Reference value	Precision
CALC_G /K1	“ANALYTIQUE”	0.9648	1.0%
CALC_G /K2	“ANALYTIQUE”	0.00	0.01
CALC_G /G	“ANALYTIQUE”	9.3084E-7	2.0%

6.4. Comments

With quadratic elements, no gain is noted by activating the contact algorithm with respect to linear elements (modeling B). The singularity at the point of detachment could cause poor convergence of the contact algorithm (the space of the multipliers hardly captures the singularity of the stress field at the point of detachment, cf.), which would create a difficulty in capturing the expected solution for this physical problem.

However, the results are very satisfactory given the low refinement of the mesh (less than 1500 elements).