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Elastoplastic Notched Plate

Overview

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

ElastoplasticNotchedPlate

Geometry of the plate

  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
ElastoplasticNotchedPlate-mesh-a

Mesh used for the SimScale case (A)

ElastoplasticNotchedPlate-mesh-b

Mesh used for the SimScale case (B)

Simulation Setup

Material:

  • isotropic: E = 200 GPa, \(\nu\) = 0.3, \(\sigma_y\) = 200 MPa, ET = 1000 MPa
ElastoplasticNotchedPlate-material

Dependency of the Young’s modulus

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 \(\sigma_{yy}\) along path FC. The values of the reference [SSNP123] in all figures were extracted with WebPlotDigitizer.

ElastoplasticNotchedPlate-result

Comparison of the cauchy stress along path FC