1. Reference problem#

1.1. Geometry#

The half-ring consists of two inner and outer parts, of the same thickness \(5\mathit{mm}\). The radius of the neutral fiber is \(95\mathit{mm}\). The block is a rectangle with dimensions \(50\mathit{mm}\) by \(250\mathit{mm}\). The initial distance between the block and the half-ring is \(20\mathit{mm}\).

_images/100000000000052B000002F21EB7CE532FC65A88.jpg

1.2. Material properties#

The law of behavior used is elastoplastic with linear isotropic work hardening (VMIS_ISOT_LINE).

The material of the inner part of the ring is characterized by:

  • \(E=100000\mathit{MPa}\)

  • \(\nu =0.3\)

  • \(\rho =2.7E-5{\mathit{kg.mm}}^{-3}\)

  • \(\text{D\_SIGM\_EPSI}=9.0E4\mathit{MPa}\)

  • \(\text{SY}=10.E100\mathit{MPa}\)

The material of the outer part of the ring is characterized by:

  • \(E=1000\mathit{MPa}\)

  • \(\nu =0.3\)

  • \(\rho =2.7E-5{\mathit{kg.mm}}^{-3}\)

  • \(\text{D\_SIGM\_EPSI}=9.0E2\mathit{MPa}\)

  • \(\text{SY}=10.E100\mathit{MPa}\)

The block material is characterized by:

  • \(E=300\mathit{MPa}\)

  • \(\nu =0.3\)

  • \(\rho =2.7E-5{\mathit{kg.mm}}^{-3}\)

  • \(\text{D\_SIGM\_EPSI}=10.\mathit{MPa}\)

  • \(\text{SY}=10.E100\mathit{MPa}\)

1.3. Boundary conditions and loads#

The bottom edge of the block is stuck such as \(\mathit{DX}=\mathit{DY}=0\).

A displacement \(\mathit{DX}=0\) and \(\mathit{DY}=-90\mathit{mm}\) is imposed at both ends, in plane \(\mathit{XZ}\), of the half-ring.

1.4. Other calculation parameters#

The calculation is done with the operator DYNA_NON_LINE. The diagram is used in time HHT (SCHEMA =” HHT “) with the parameter ALPHA to -0.3 (the default value of this parameter is -0.1 and it leads to a calculation time that is too long for modeling B).