Elastoplastic Notched Plate

The aim of this test case is to validate the following functions:

• Plastic material behaviour
• Reduced integration element type

The simulation results of SimScale were compared to the results presented in [SSNP123]. The mesh used in (A) and (C) was created with the automatic-tetrahedralization-tool on the SimScale platform. The mesh used in (B) und (D) was created locally.

Import validation project into workspace

Geometry

	A	B	C	D	E	F
x [m]	0	0.004	0.005	0.005	0	0
y [m]	0	0	0.001	0.005	0.005	0.001

The corresponding nodes marked with a dash (‘) are translated 0.0001 m along the negative z-direction.

Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Static Anaylsis

Mesh and Element types :

Case	Mesh type	Number of nodes	Element type
(A)	quadratic tetrahedral	35503	3D isoparametric
(B)	quadratic hexahedral	5508	3D isoparametric
(C)	quadratic tetrahedral	35503	3D under integrated
(D)	quadratic hexahedral	5508	3D under integrated

Simulation Setup

Material:

• isotropic: E = 200 GPa, ν
  $\nu$

   

  = 0.3, σy

  ${\sigma }_y$

   

  = 200 MPa, E_T = 1000 MPa

Constraints:

• Face AA’EE’: zero x-displacement
• Face AA’BB’: zero y-displacement
• z-displacement is fixed for all nodes
• Face DD’EE’: displacement of 0.0001 m in y-direction

Results

Comparison of the cauchy stress σyy

${\sigma }_{yy}$

 along path FC. The values of the reference [SSNP123] in all figures were extracted with WebPlotDigitizer.

References

[SSNP123]

(1, 2) SSNP123 – Plaque entaillée en élastoplasticité : test des éléments QUAD4 sous intégrés