******************************
Elastic Orthotropic Fail Model
******************************

.. code-block:: sierrainput

   BEGIN PARAMETERS FOR MODEL ELASTIC_ORTHOTROPIC_FAIL
     #
     # Elastic constants
     #
     YOUNGS MODULUS = <real>
     POISSONS RATIO = <real>
     SHEAR MODULUS  = <real>
     BULK MODULUS   = <real>
     LAMBDA         = <real>
     TWO MU         = <real>
     #
     # Required parameters
     #
     E11 = <real>e11
     E22 = <real>e22
     E33 = <real>e33
     NU12 = <real>nu12
     NU13 = <real>nu13
     NU23 = <real>nu23
     G12 = <real>g12
     G13 = <real>g13
     G23 = <real>g23
     #
     COORDINATE SYSTEM = <string>coordinate_system_name
     #
     # Normal thresholds
     #
     TENSILE_MATRIX_STRENGTH_11     = <real>f1mp
     COMPRESSIVE_MATRIX_STRENGTH_11 = <real>f1mn
     TENSILE_FIBER_STRENGTH_11      = <real>f1fp
     COMPRESSIVE_FIBER_STRENGTH_11  = <real>f1fn
     TENSILE_MATRIX_STRENGTH_22     = <real>f2mp
     COMPRESSIVE_MATRIX_STRENGTH_22 = <real>f2mn
     TENSILE_FIBER_STRENGTH_22      = <real>f2fp
     COMPRESSIVE_FIBER_STRENGTH_22  = <real>f2fn
     TENSILE_MATRIX_STRENGTH_33     = <real>f3mp
     COMPRESSIVE_MATRIX_STRENGTH_33 = <real>f3mn
     TENSILE_FIBER_STRENGTH_33      = <real>f3fp
     COMPRESSIVE_FIBER_STRENGTH_33  = <real>f3fn
     #
     # Shear thresholds
     #
     SHEAR_MATRIX_STRENGTH_12       = <real>s12m
     SHEAR_FIBER_STRENGTH_12        = <real>s12f
     SHEAR_MATRIX_STRENGTH_23       = <real>s23m
     SHEAR_FIBER_STRENGTH_23        = <real>s23f
     SHEAR_MATRIX_STRENGTH_13       = <real>s13m
     SHEAR_FIBER_STRENGTH_13        = <real>s13f
     #
     # Fracture parameters
     #
     TENSILE_FRACTURE_ENERGY_11     = <real>gi1p
     COMPRESSIVE_FRACTURE_ENERGY_11 = <real>gi1n
     TENSILE_FRACTURE_ENERGY_22     = <real>gi2p
     COMPRESSIVE_FRACTURE_ENERGY_22 = <real>gi2n
     TENSILE_FRACTURE_ENERGY_33     = <real>gi3p
     COMPRESSIVE_FRACTURE_ENERGY_33 = <real>gi3n
     SHEAR_FRACTURE_ENERGY_12       = <real>gii12
     SHEAR_FRACTURE_ENERGY_23       = <real>gii23
     SHEAR_FRACTURE_ENERGY_13       = <real>gii13
     CHARACTERISTIC_LENGTH          = <real>l_star
     #
     # Damage evolution parameters
     #
     MAXIMUM_COMPRESSIVE_DAMAGE_11  = <real>dmax1n
     MAXIMUM_COMPRESSIVE_DAMAGE_22  = <real>dmax2n
     MAXIMUM_COMPRESSIVE_DAMAGE_33  = <real>dmax3n
     COMPRESSION_COUPLING_FACTOR_11 = <real>a1pn
     COMPRESSION_COUPLING_FACTOR_22 = <real>a2pn
     COMPRESSION_COUPLING_FACTOR_33 = <real>a3pn
     TENSILE_DAMAGE_MODULUS_11      = <real>k1p
     COMPRESSIVE_DAMAGE_MODULUS_11  = <real>k1n
     TENSILE_DAMAGE_MODULUS_22      = <real>k2p
     COMPRESSIVE_DAMAGE_MODULUS_22  = <real>k2n
     TENSILE_DAMAGE_MODULUS_33      = <real>k3p
     COMPRESSIVE_DAMAGE_MODULUS_33  = <real>k3n
     SHEAR_DAMAGE_MODULUS_12        = <real>k12
     SHEAR_DAMAGE_MODULUS_23        = <real>k23
     SHEAR_DAMAGE_MODULUS_13        = <real>k13
     HARDENING_EXPONENT_11          = <real>n11
     HARDENING_EXPONENT_22          = <real>n22
     HARDENING_EXPONENT_33          = <real>n33
     HARDENING_EXPONENT_12          = <real>n12
     HARDENING_EXPONENT_23          = <real>n23
     HARDENING_EXPONENT_13          = <real>n13
     #
     # Optional parameters follow
     # Orientation Parameters
     #
     ANGLE_1_ABSCISSA  = <real>angle_1_abscissa
     ANGLE_2_ABSCISSA  = <real>angle_2_abscissa
     ANGLE_3_ABSCISSA  = <real>angle_3_abscissa
     ROTATION_AXIS_1   = <real>rotation_axis_1
     ROTATION_AXIS_2   = <real>rotation_axis_2
     ROTATION_AXIS_3   = <real>rotation_axis_3
     ANGLE_1_FUNCTION  = <string>angle_1_function_name
     ANGLE_2_FUNCTION  = <string>angle_2_function_name
     ANGLE_3_FUNCTION  = <string>angle_3_function_name
     #
     # Coefficient of thermal expansion functions
     #
     THERMAL_STRAIN_11_FUNCTION = <string>cte11_function_name
     THERMAL_STRAIN_22_FUNCTION = <string>cte22_function_name
     THERMAL_STRAIN_33_FUNCTION = <string>cte33_function_name
     #
     # Temperature dependent property functions
     #
     E11_FUNCTION  = <string>e11_function_name
     E22_FUNCTION  = <string>e22_function_name
     E33_FUNCTION  = <string>e33_function_name
     NU12_FUNCTION = <string>nu12_function_name
     NU23_FUNCTION = <string>nu23_function_name
     NU13_FUNCTION = <string>nu13_function_name
     G12_FUNCTION  = <string>g12_function_name
     G23_FUNCTION  = <string>g23_function_name
     G13_FUNCTION  = <string>g13_function_name
     #
     # Strain rate dependent parameters
     #
     REFERENCE_STRAIN_RATE               = <real>epsdot0
     ELASTIC_RATE_COEFFICIENT_11         = <real>ce11
     ELASTIC_RATE_COEFFICIENT_22         = <real>ce22
     ELASTIC_RATE_COEFFICIENT_33         = <real>ce33
     ELASTIC_RATE_COEFFICIENT_12         = <real>ce12
     ELASTIC_RATE_COEFFICIENT_23         = <real>ce23
     ELASTIC_RATE_COEFFICIENT_13         = <real>ce13
     FIBER_STRENGTH_RATE_COEFFICIENT_11  = <real>cf11
     FIBER_STRENGTH_RATE_COEFFICIENT_22  = <real>cf22
     FIBER_STRENGTH_RATE_COEFFICIENT_33  = <real>cf33
     FIBER_STRENGTH_RATE_COEFFICIENT_12  = <real>cf12
     FIBER_STRENGTH_RATE_COEFFICIENT_23  = <real>cf23
     FIBER_STRENGTH_RATE_COEFFICIENT_13  = <real>cf13
     MATRIX_STRENGTH_RATE_COEFFICIENT_11 = <real>cm11
     MATRIX_STRENGTH_RATE_COEFFICIENT_22 = <real>cm22
     MATRIX_STRENGTH_RATE_COEFFICIENT_33 = <real>cm33
     MATRIX_STRENGTH_RATE_COEFFICIENT_12 = <real>cm12
     MATRIX_STRENGTH_RATE_COEFFICIENT_23 = <real>cm23
     MATRIX_STRENGTH_RATE_COEFFICIENT_13 = <real>cm13
   END [PARAMETERS FOR MODEL ELASTIC_ORTHOTROPIC_FAIL]

The elastic orthotropic fail model is an empirically based constitutive relation that is useful for modeling polymer matrix composite structures. Refer to the SAND report by English [:footcite:`mat:ref:english`] for a full description of the material model theory and usage.

This model has identical input requirements to the Elastic Orthotropic Model detailed in :numref:`material-elastic-orthotropic`, supplemented with additional parameters for failure modeling.  The following is a brief description of additional inputs required for the Elastic Orthotropic Fail Model.

- The strengths for each component of damage are given by the commands:

  .. code-block:: sierrainput

     # Normal thresholds
     TENSILE_MATRIX_STRENGTH_11     = <real>f1mp
     COMPRESSIVE_MATRIX_STRENGTH_11 = <real>f1mn
     TENSILE_FIBER_STRENGTH_11      = <real>f1fp
     COMPRESSIVE_FIBER_STRENGTH_11  = <real>f1fn
     TENSILE_MATRIX_STRENGTH_22     = <real>f2mp
     COMPRESSIVE_MATRIX_STRENGTH_22 = <real>f2mn
     TENSILE_FIBER_STRENGTH_22      = <real>f2fp
     COMPRESSIVE_FIBER_STRENGTH_22  = <real>f2fn
     TENSILE_MATRIX_STRENGTH_33     = <real>f3mp
     COMPRESSIVE_MATRIX_STRENGTH_33 = <real>f3mn
     TENSILE_FIBER_STRENGTH_33      = <real>f3fp
     COMPRESSIVE_FIBER_STRENGTH_33  = <real>f3fn
     # Shear thresholds
     SHEAR_MATRIX_STRENGTH_12       = <real>s12m
     SHEAR_FIBER_STRENGTH_12        = <real>s12f
     SHEAR_MATRIX_STRENGTH_23       = <real>s23m
     SHEAR_FIBER_STRENGTH_23        = <real>s23f
     SHEAR_MATRIX_STRENGTH_13       = <real>s13m
     SHEAR_FIBER_STRENGTH_13        = <real>s13f

- The fracture energies (energy per unit area) for each plane of damage are given by the commands:

  .. code-block:: sierrainput

     # Fracture parameters
     TENSILE_FRACTURE_ENERGY_11     = <real>gi1p
     COMPRESSIVE_FRACTURE_ENERGY_11 = <real>gi1n
     TENSILE_FRACTURE_ENERGY_22     = <real>gi2p
     COMPRESSIVE_FRACTURE_ENERGY_22 = <real>gi2n
     TENSILE_FRACTURE_ENERGY_33     = <real>gi3p
     COMPRESSIVE_FRACTURE_ENERGY_33 = <real>gi3n
     SHEAR_FRACTURE_ENERGY_12       = <real>gii12
     SHEAR_FRACTURE_ENERGY_23       = <real>gii23
     SHEAR_FRACTURE_ENERGY_13       = <real>gii13
     CHARACTERISTIC_LENGTH          = <real>l_star

  The total energy density dissipated (the area under the stress-strain curve) is given by the fracture energy divided by the characteristic length ``l_star``.

- The maximum allowable damage values under compression on each plane are given by the commands:

  .. code-block:: sierrainput

     MAXIMUM_COMPRESSIVE_DAMAGE_11  = <real>dmax1n
     MAXIMUM_COMPRESSIVE_DAMAGE_22  = <real>dmax2n
     MAXIMUM_COMPRESSIVE_DAMAGE_33  = <real>dmax3n

- The proportion of tensile damage translating to compressive damage for  each of the orthotropic planes are given by the commands:

  .. code-block:: sierrainput

     COMPRESSION_COUPLING_FACTOR_11 = <real>a1pn
     COMPRESSION_COUPLING_FACTOR_22 = <real>a2pn
     COMPRESSION_COUPLING_FACTOR_33 = <real>a3pn

- The slopes of the matrix mode damage portion of the stress-strain curve, or damage moduli terms, are given by the commands:

  .. code-block:: sierrainput

     TENSILE_DAMAGE_MODULUS_11      = <real>k1p
     COMPRESSIVE_DAMAGE_MODULUS_11  = <real>k1n
     TENSILE_DAMAGE_MODULUS_22      = <real>k2p
     COMPRESSIVE_DAMAGE_MODULUS_22  = <real>k2n
     TENSILE_DAMAGE_MODULUS_33      = <real>k3p
     COMPRESSIVE_DAMAGE_MODULUS_33  = <real>k3n
     SHEAR_DAMAGE_MODULUS_12        = <real>k12
     SHEAR_DAMAGE_MODULUS_23        = <real>k23
     SHEAR_DAMAGE_MODULUS_13        = <real>k13

- Small nonlinearity in the matrix mode damage evolution can be added using the hardening exponents for each of the orthotropic planes via the commands:

  .. code-block:: sierrainput

     HARDENING_EXPONENT_11          = <real>n11
     HARDENING_EXPONENT_22          = <real>n22
     HARDENING_EXPONENT_33          = <real>n33
     HARDENING_EXPONENT_12          = <real>n12
     HARDENING_EXPONENT_23          = <real>n23
     HARDENING_EXPONENT_13          = <real>n13

- Strain rate dependence is defined by the commands:

  .. code-block:: sierrainput

     REFERENCE_STRAIN_RATE               = <real>epsdot0
     ELASTIC_RATE_COEFFICIENT_11         = <real>ce11
     ELASTIC_RATE_COEFFICIENT_22         = <real>ce22
     ELASTIC_RATE_COEFFICIENT_33         = <real>ce33
     ELASTIC_RATE_COEFFICIENT_12         = <real>ce12
     ELASTIC_RATE_COEFFICIENT_23         = <real>ce23
     ELASTIC_RATE_COEFFICIENT_13         = <real>ce13
     FIBER_STRENGTH_RATE_COEFFICIENT_11  = <real>cf11
     FIBER_STRENGTH_RATE_COEFFICIENT_22  = <real>cf22
     FIBER_STRENGTH_RATE_COEFFICIENT_33  = <real>cf33
     FIBER_STRENGTH_RATE_COEFFICIENT_12  = <real>cf12
     FIBER_STRENGTH_RATE_COEFFICIENT_23  = <real>cf23
     FIBER_STRENGTH_RATE_COEFFICIENT_13  = <real>cf13
     MATRIX_STRENGTH_RATE_COEFFICIENT_11 = <real>cm11
     MATRIX_STRENGTH_RATE_COEFFICIENT_22 = <real>cm22
     MATRIX_STRENGTH_RATE_COEFFICIENT_33 = <real>cm33
     MATRIX_STRENGTH_RATE_COEFFICIENT_12 = <real>cm12
     MATRIX_STRENGTH_RATE_COEFFICIENT_23 = <real>cm23
     MATRIX_STRENGTH_RATE_COEFFICIENT_13 = <real>cm13

  The rate dependence is calculated with respect to the reference strain rate ``epsdot0``.  The rate coefficients for the purely empirical rate equation in each material direction are given for elastic moduli and failure parameters by the scalar values of the elastic rate coefficients ``ceij`` and fiber and matrix strength rate coefficients ``cfij`` and ``cmij``.

.. warning::

   The ``ELASTIC_ORTHOTROPIC_FAIL`` model has not been tested in conjunction with the control stiffness implicit solver block.

Output variables available for this model are listed in the Elastic Orthotropic Model in :numref:`out-tab-elortho` and :numref:`out-tab-elortho-fail`.

.. _out-tab-elortho-fail:

.. csv-table:: Additional State Variables for ELASTIC ORTHOTROPIC FAIL Model.
   :align: center
   :delim: &
   :header: Index, Name, Description

    43 & ``R1MP`` & Damage evolution variable 11, matrix, tension
    44 & ``R1FP`` & Damage evolution variable 11, fiber, tension
    45 & ``R1MN`` & Damage evolution variable 11, matrix, compression
    46 & ``R1FN`` & Damage evolution variable 11, fiber, compression
    47 & ``R2MP`` & Damage evolution variable 22, matrix, tension
    48 & ``R2FP`` & Damage evolution variable 22, fiber, tension
    49 & ``R2MN`` & Damage evolution variable 22, matrix, compression
    50 & ``R2FN`` & Damage evolution variable 22, fiber, compression
    51 & ``R3MP`` & Damage evolution variable 33, matrix, tension
    52 & ``R3FP`` & Damage evolution variable 33, fiber, tension
    53 & ``R3MN`` & Damage evolution variable 33, matrix, compression
    54 & ``R3FN`` & Damage evolution variable 33, fiber, compression
    55 & ``D1MP`` & Normal damage 11, matrix, tension
    56 & ``D1FP`` & Normal damage 11, fiber, tension
    57 & ``D1MN`` & Normal damage 11, matrix, compression
    58 & ``D1FN`` & Normal damage 11, fiber, compression
    59 & ``D2MP`` & Normal damage 22, matrix, tension
    60 & ``D2FP`` & Normal damage 22, fiber, tension
    61 & ``D2MN`` & Normal damage 22, matrix, compression
    62 & ``D2FN`` & Normal damage 22, fiber, compression
    63 & ``D3MP`` & Normal damage 33, matrix, tension
    64 & ``D3FP`` & Normal damage 33, fiber, tension
    65 & ``D3MN`` & Normal damage 33, matrix, compression
    66 & ``D3FN`` & Normal damage 33, fiber, compression
    67 & ``D12M`` & Shear damage 12, matrix
    68 & ``D12F`` & Shear damage 12, fiber
    69 & ``D23M`` & Shear damage 23, matrix
    70 & ``D23F`` & Shear damage 23, fiber
    71 & ``D13M`` & Shear damage 13, matrix
    72 & ``D13F`` & Shear damage 13, fiber
    73 & ``ORTHOTROPIC_DAMAGE_XX`` & Effective and active normal damage 11
    74 & ``ORTHOTROPIC_DAMAGE_YY`` & Effective and active normal damage 22
    75 & ``ORTHOTROPIC_DAMAGE_ZZ`` & Effective and active normal damage 33
    76 & ``ORTHOTROPIC_DAMAGE_XY`` & Effective and active shear damage 12
    77 & ``ORTHOTROPIC_DAMAGE_YZ`` & Effective and active shear damage 23
    78 & ``ORTHOTROPIC_DAMAGE_ZX`` & Effective and active shear damage 31

.. warning::

   Strongly rate-dependent models may fare poorly in implicit quasistatic solution. In implicit analyses the rate term used to evaluate the current load step is the rate seen by the model in the previous load step. This may cause the solution to oscillate between high- and low-rate equilibrium states from step to step.

.. raw::
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.. footbibliography::
