.. _R3.06.11:

**r3.06.11** Hexahedral element with one integration point, stabilized by the "Assumed Strain" method
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**Summary:**

The standard sub-integrated 8-node hexahedral element with 1 integration point introduces parasitic modes associated with zero energy (hourglass modes) and can lead to a singularity in the overall stiffness matrix for certain boundary conditions. The deficiency in the rank of the stiffness matrix, due to underintegration, must therefore be filled by adding to the elementary stiffness a so-called stabilization matrix. This is the purpose of the ASM (Assumed Strain Method) method developed here.

The main characteristic of this method is that the discretized gradient operator :math:`B` does not necessarily derive from the displacement field and from the classical relationships relating deformation to displacement. Indeed, this method ASM consists in projecting the discretized gradient operator onto an appropriate subspace in order to avoid the different types of blocking.

 **Table of Contents**




.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Introduction
    Formulation_de_l__l_ment_HEXA8___un_point_d_int_gration
    Stabilisation_de_type___Assumed_Strain_Method____ASM_
    Int_gration_de_l__l_ment_dans_Code_Aster

    Conclusion
    Bibliographie
    Description_des_versions_du_document__