Reference problem
=====================


Geometry
---------

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


.. image:: images/100000000000052B000002F21EB7CE532FC65A88.jpg
    :width: 6.3374in
    :height: 3.6118in


.. _RefImage_100000000000052B000002F21EB7CE532FC65A88.jpg:


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:


* :math:`E=100000\mathit{MPa}`


* :math:`\nu =0.3`


* :math:`\rho =2.7E-5{\mathit{kg.mm}}^{-3}`


* :math:`\text{D\_SIGM\_EPSI}=9.0E4\mathit{MPa}`


* :math:`\text{SY}=10.E100\mathit{MPa}`

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


* :math:`E=1000\mathit{MPa}`


* :math:`\nu =0.3`


* :math:`\rho =2.7E-5{\mathit{kg.mm}}^{-3}`


* :math:`\text{D\_SIGM\_EPSI}=9.0E2\mathit{MPa}`


* :math:`\text{SY}=10.E100\mathit{MPa}`

 The block material is characterized by:


* :math:`E=300\mathit{MPa}`


* :math:`\nu =0.3`


* :math:`\rho =2.7E-5{\mathit{kg.mm}}^{-3}`


* :math:`\text{D\_SIGM\_EPSI}=10.\mathit{MPa}`


* :math:`\text{SY}=10.E100\mathit{MPa}`


Boundary conditions and loads
-------------------------------------

The bottom edge of the block is stuck such as :math:`\mathit{DX}=\mathit{DY}=0`.

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


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).