***************
Honeycomb Model
***************

.. code-block:: sierrainput

   BEGIN PARAMETERS FOR MODEL HONEYCOMB
     #
     # Elastic constants
     #
     YOUNGS MODULUS = <real>
     POISSONS RATIO = <real>
     SHEAR MODULUS  = <real>
     BULK MODULUS   = <real>
     LAMBDA         = <real>
     TWO MU         = <real>
     #
     # Orthotropic response
     #
     MODULUS_TTTT = <real>
     MODULUS_LLLL = <real>
     MODULUS_WWWW = <real>
     MODULUS_TTLL = <real>
     MODULUS_TTWW = <real>
     MODULUS_LLWW = <real>
     MODULUS_TLTL = <real>
     MODULUS_LWLW = <real>
     MODULUS_WTWT = <real>
     #
     # Material orientation
     #
     TX = <real>
     TY = <real>
     TZ = <real>
     LX = <real>
     LY = <real>
     LZ = <real>
     #
     # Yield behavior
     #
     YIELD_STRESS = <real>
     A1           = <real>
     B1           = <real>
     C1           = <real>
     A2           = <real>
     B2           = <real>
     C2           = <real>
     A3           = <real>
     B3           = <real>
     C3           = <real>

     TS  = <real>
     LS  = <real>
     WS  = <real>
     TLS = <real>
     LWS = <real>
     WTS = <real>

     ESTL = <real>
     ESTW = <real>
     ESLW = <real>
     ESLT = <real>
     ESWT = <real>
     ESWL = <real>

     MODULUS_FUNCTION = <string>
     RATE_FUNCTION    = <string>
     T_FUNCTION       = <string>
     L_FUNCTION       = <string>
     W_FUNCTION       = <string>
     TL_FUNCTION      = <string>
     LW_FUNCTION      = <string>
     WT_FUNCTION      = <string>
     TTP_FUNCTION     = <string>
     LLP_FUNCTION     = <string>
     WWP_FUNCTION     = <string>
     TLTLP_FUNCTION   = <string>
     LWLWP_FUNCTION   = <string>
     WTWTP_FUNCTION   = <string>
     TTLP_FUNCTION    = <string>
     TTWP_FUNCTION    = <string>
   END [PARAMETERS FOR MODEL HONEYCOMB]

The honeycomb constitutive model is used to model the energy absorbing capabilities of aluminum honeycomb. There are three orthogonal material directions for the model: :math:`T`, :math:`L`, and :math:`W`. The :math:`t`-direction is generally considered as the "strong" direction, the :math:`W`-direction is the "weak" direction, and the :math:`L`-direction has an intermediate strength. This convention, however, does not necessarily need to be followed when defining material inputs.

.. math::

   \begin{Bmatrix}
     \dot{\sigma}_{TT} \\
     \dot{\sigma}_{LL} \\
     \dot{\sigma}_{WW} \\
     \dot{\sigma}_{TL} \\
     \dot{\sigma}_{LW} \\
     \dot{\sigma}_{WT} \\
   \end{Bmatrix}
   =
   \begin{bmatrix}
     E_{TTTT} & E_{TTLL} & E_{TTWW} & 0 & 0 & 0 \\
     E_{TTLL} & E_{LLLL} & E_{LLWW} & 0 & 0 & 0 \\
     E_{TTWW} & E_{LLWW} & E_{WWWW} & 0 & 0 & 0 \\
     0 & 0 & 0 & E_{TLTL} & 0 & 0 \\
     0 & 0 & 0 & 0 & E_{LWLW} & 0 \\
     0 & 0 & 0 & 0 & 0 & E_{WTWT} 
   \end{bmatrix}
   \begin{Bmatrix}
     \dot{d}_{TT} \\
     \dot{d}_{LL} \\
     \dot{d}_{WW} \\
     \dot{d}_{TL} \\
     \dot{d}_{LW} \\
     \dot{d}_{WT}
   \end{Bmatrix}

Output variables available for this model are listed in :numref:`honeycombstvar`.

.. _honeycombstvar:

.. csv-table:: State Variables for HONEYCOMB Model
   :align: center
   :delim: &
   :header: Index, Name, Description

   1 & ``CRUSH`` & minimum volume ratio
   2 & ``EQDOT`` & effective strain rate
   3 & ``RMULT`` & rate multiplier
   5 & ``ITER``  & iterations
   6 & ``EVOL``  & volumetric strain
