# 15.3. Elastic Orthotropic Fail Model

    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 [[1]] for a full description of the material model theory and usage.

This model has identical input requirements to the Elastic Orthotropic Model detailed in Section 15.1, 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:

      # 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:

      # 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:

      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:

      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:

      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:

      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:

      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 Table 15.1.1 and Table 15.3.1.

Table 15.3.1 Additional State Variables for ELASTIC ORTHOTROPIC FAIL Model.
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.

[1]

S.A. English. A 3D orthotropic strain-rate dependent elastic damage material model. Technical Report SAND2014-17469, Sandia National Laboratories, Albuquerque, NM, 2014. URL: http://infoserve.sandia.gov/sand_doc/2014/17469.pdf.