3. B modeling#

3.1. Characteristics of modeling#

The modeling is of the « material point » type with linear relationships on the components of the strain tensor simulating incompressibility, in non-linear quasistatics.

We consider here phase 2 of loading, with an initial hydrostatic stress state \({\sigma }_{\mathit{xx}}^{0}\mathrm{=}{\sigma }_{\mathit{yy}}^{0}\mathrm{=}{\sigma }_{\mathit{zz}}^{0}\mathrm{=}{\sigma }^{0}\mathrm{=}\mathrm{-}30\mathit{kPa}\)

The data is the same as modeling A.

3.2. Characteristics of the mesh#

No finite element

3.3. Tested sizes and results#

The solutions are calculated at point \(C\) and compared to the results obtained with GEFDYN (same tests as modeling A). They are given in terms of isotropic pressure, plastic volume deformation \({\varepsilon }_{v}^{p}\) and mobilization factors, and summarized in the following tables:

\(3\mathrm{\cdot }P\text{'}\mathrm{=}{\sigma }_{\mathit{ij}}\mathrm{\cdot }{\delta }_{\mathit{ij}}\) \((\mathrm{kPa})\)

(\(\mathit{kPa}\))	Code_Aster (\(\mathit{kPa}\))	GEFDYN (\(\mathit{kPa}\))	Relative error



-15	-80.223	-80.194	0.038%
15	-73.988	-74.078	-0.122%
-15	-66.055	-66.250	-0.295%
15	-52.625	-52.999	-0.707%
-15	-45,539	-45.672	-0.292%

\({\varepsilon }_{v}^{p}\mathrm{=}\mathit{trace}({\varepsilon }^{p})\)

(\(\mathit{kPa}\))	Code_Aster	GEFDYN	Relative error



-15	-2.62e-5	-2.63e-5	-0.225%
	-2.80e-5	-2.78e-5	0.854%



	-4.48e-5	-4.43e-5	1.076%



	-7.11e-5	-7.05e-5	0.842%



	-1.13e-4	-1.11e-4	1.412%



	-1.85e-4	-1.85e-4	0.261%