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 and Table 15.2.

Table 15.2 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.