cratepy.material.models.elastic.Elastic¶

class Elastic(strain_formulation, problem_type, material_properties)[source]¶

Bases: ConstitutiveModel

Linear elastic constitutive model.

_name¶

Constitutive model name.

Type:: str

_strain_type¶

Constitutive model strain formulation: infinitesimal strain formulation (‘infinitesimal’), finite strain formulation (‘finite’) or finite strain formulation through kinematic extension (infinitesimal constitutive formulation and purely finite strain kinematic extension - ‘finite-kinext’).

Type:: {‘infinitesimal’, ‘finite’, ‘finite-kinext’}

_source¶

Material constitutive model source.

Type:: {‘crate’,}

_ndim¶

Problem number of spatial dimensions.

Type:: int

_comp_order_sym¶

Strain/Stress components symmetric order.

Type:: list[str]

_comp_order_nsym¶

Strain/Stress components nonsymmetric order.

Type:: list[str]

get_required_properties()[source]¶: Get constitutive model material properties and constitutive options.

state_init(self)[source]¶: Get initialized material constitutive model state variables.

state_update(self, inc_strain, state_variables_old, su_max_n_iterations=20, su_conv_tol=1e-6)[source]¶: Perform constitutive model state update.

get_available_elastic_symmetries()[source]¶: Get available elastic symmetries under general anisotropy.

elastic_tangent_modulus(elastic_properties, elastic_symmetry='isotropic')[source]¶: Compute 3D elasticity tensor under general anisotropic elasticity.

get_technical_from_elastic_moduli(elastic_symmetry, elastic_properties)[source]¶: Get technical constants of elasticity from elastic moduli.

Constructor.

Parameters:

strain_formulation ({'infinitesimal', 'finite'}) – Problem strain formulation.
problem_type (int) – Problem type: 2D plane strain (1), 2D plane stress (2), 2D axisymmetric (3) and 3D (4).
material_properties (dict) – Constitutive model material properties (key, str) values (item, {int, float, bool}).

List of Public Methods

`elastic_tangent_modulus`	Compute 3D elasticity tensor under general anisotropic elasticity.
`get_available_elastic_symmetries`	Get available elastic symmetries under general anisotropy.
`get_material_properties`	Constitutive model material properties.
`get_name`	Get constitutive model name.
`get_required_properties`	Get constitutive model material properties and constitutive options.
`get_source`	Get material constitutive model source.
`get_strain_type`	Get material constitutive model strain formulation.
`get_technical_from_elastic_moduli`	Get technical constants of elasticity from elastic moduli.
`state_init`	Get initialized material constitutive model state variables.
`state_update`	Perform constitutive model state update.

Methods

__init__(strain_formulation, problem_type, material_properties)[source]¶

Constructor.

Parameters:

strain_formulation ({'infinitesimal', 'finite'}) – Problem strain formulation.
problem_type (int) – Problem type: 2D plane strain (1), 2D plane stress (2), 2D axisymmetric (3) and 3D (4).
material_properties (dict) – Constitutive model material properties (key, str) values (item, {int, float, bool}).

static elastic_tangent_modulus(elastic_properties, elastic_symmetry='isotropic')[source]¶

Compute 3D elasticity tensor under general anisotropic elasticity.

Parameters:

elastic_properties (dict) – Elastic material properties (key, str) values (item, float). Expecting independent elastic moduli (‘Eijkl’) according to elastic symmetries. Young modulus (‘E’) and Poisson’s ratio (‘v’) may alternatively provided under elastic isotropy.
elastic_symmetry ({'isotropic', 'transverse_isotropic', 'orthotropic', 'monoclinic', 'triclinic'}, default='isotropic') –
Elastic symmetries:
- ’triclinic’: assumes no elastic symmetries.
- ’monoclinic’: assumes plane of symmetry 12.
- ’orthotropic’: assumes planes of symmetry 12 and 13.
- ’transverse_isotropic’: assumes axis of symmetry 3
- ’isotropic’: assumes complete symmetry.

Returns:

elastic_tangent_mf – 3D elasticity tensor in matricial form.

Return type:

numpy.ndarray (2d)

static get_available_elastic_symmetries()[source]¶

Get available elastic symmetries under general anisotropy.

Available elastic symmetries:

Isotropic:
Input data file syntax:
elastic_symmetry isotropic 2 E1111 < value > E1122 < value >
or
elastic_symmetry isotropic 2 E < value > v < value >
where
- elastic_symmetry - Elastic symmetry and number of elastic moduli.
- Eijkl - Elastic moduli. Young’s modulus (E) and Poisson’s coefficient (v) may be alternatively provided if elastic_symmetry is set as isotropic.

Transverse isotropic (axis of symmetry 3):
Input data file syntax:
elastic_symmetry transverse_isotropic 6 euler_angles < value > < value > < value > Eijkl < value > ...
where
- elastic_symmetry - Elastic symmetry and number of elastic moduli.
- euler_angles - Euler angles (degrees) sorted according with Bunge convention.
- Eijkl - Elastic moduli.

Orthotropic (planes of symmetry 12 and 13):
Input data file syntax:
elastic_symmetry orthotropic 10 euler_angles < value > < value > < value > Eijkl < value > ...
where
- elastic_symmetry - Elastic symmetry and number of elastic moduli.
- euler_angles - Euler angles (degrees) sorted according with Bunge convention.
- Eijkl - Elastic moduli.

Monoclinic (plane of symmetry 12):
Input data file syntax:
elastic_symmetry monoclinic 14 euler_angles < value > < value > < value > Eijkl < value > ...
where
- elastic_symmetry - Elastic symmetry and number of elastic moduli.
- euler_angles - Euler angles (degrees) sorted according with Bunge convention.
- Eijkl - Elastic moduli.

Triclinic:
Input data file syntax:
elastic_symmetry triclinic 22 euler_angles < value > < value > < value > Eijkl < value > ...
where
- elastic_symmetry - Elastic symmetry and number of elastic moduli.
- euler_angles - Euler angles (degrees) sorted according with Bunge convention.
- Eijkl - Elastic moduli.

Returns:: elastic_symmetries – Elastic moduli (item, tuple[str]) required for each available elastic symmetry (key, str).
Return type:: dict

get_material_properties()¶

Constitutive model material properties.

Returns:: material_properties – Constitutive model material properties (key, str) values (item, {int, float, bool}).
Return type:: dict

get_name()¶

Get constitutive model name.

Returns:: name – Constitutive model name.
Return type:: str

static get_required_properties()[source]¶

Get constitutive model material properties and constitutive options.

Input data file syntax:

elastic_symmetry < option > < number_of_elastic_moduli >
    euler_angles < value > < value > < value >
    Eijkl < value >
    Eijkl < value >
    ...

where

elastic_symmetry - Elastic symmetry and number of elastic moduli.
euler_angles - Euler angles (degrees) sorted according with Bunge convention. Not required if elastic_symmetry is set as isotropic.
Eijkl - Elastic moduli. Young’s modulus (E) and Poisson’s coefficient (v) may be alternatively provided if elastic_symmetry is set as isotropic.

Returns:

material_properties (list[str]) – Constitutive model material properties names (str).
constitutive_options (dict) – Constitutive options (key, str) and available specifications (item, tuple[str]).

get_source()¶

Get material constitutive model source.

Returns:: source – Material constitutive model source.
Return type:: {‘crate’,}

get_strain_type()¶

Get material constitutive model strain formulation.

Returns:: strain_type – Constitutive model strain formulation: infinitesimal strain formulation (‘infinitesimal’), finite strain formulation (‘finite’) or finite strain formulation through kinematic extension (infinitesimal constitutive formulation and purely finite strain kinematic extension - ‘finite-kinext’).
Return type:: {‘infinitesimal’, ‘finite’, ‘finite-kinext’}

get_technical_from_elastic_moduli(elastic_properties)[source]¶

Get technical constants of elasticity from elastic moduli.

Parameters:

elastic_symmetry ({'isotropic', 'transverse_isotropic', 'orthotropic', 'monoclinic', 'triclinic'}, default='isotropic') –
Elastic symmetries:
- ’triclinic’: assumes no elastic symmetries.
- ’monoclinic’: assumes plane of symmetry 12.
- ’orthotropic’: assumes planes of symmetry 12 and 13.
- ’transverse_isotropic’: assumes axis of symmetry 3
- ’isotropic’: assumes complete symmetry.
elastic_properties (dict) – Elastic material properties (key, str) values (item, float). Expecting independent elastic moduli (‘Eijkl’) according to elastic symmetries.

Returns:

technical_constants – Technical constants of elasticity according with elastic symmetries.

Return type:

dict

state_init()[source]¶

Get initialized material constitutive model state variables.

Constitutive model state variables:

e_strain_mf
- Infinitesimal strains: Elastic infinitesimal strain tensor (matricial form).
- Finite strains: Elastic spatial logarithmic strain tensor (matricial form).
- Symbol: \(\boldsymbol{\varepsilon^{e}}\) / \(\boldsymbol{\varepsilon^{e}}\)
strain_mf
- Infinitesimal strains: Infinitesimal strain tensor (matricial form).
- Finite strains: Spatial logarithmic strain tensor (matricial form).
- Symbol: \(\boldsymbol{\varepsilon}\) / \(\boldsymbol{\varepsilon}\)
stress_mf
- Infinitesimal strains: Cauchy stress tensor (matricial form).
- Finite strains: Kirchhoff stress tensor (matricial form) within state_update(), first Piola-Kirchhoff stress tensor (matricial form) otherwise.
- Symbol: \(\boldsymbol{\sigma}\) / (\(\boldsymbol{\tau}\), \(\boldsymbol{P}\))
is_su_fail
- State update failure flag.

Returns:: state_variables_init – Initialized constitutive model material state variables.
Return type:: dict

state_update(inc_strain, state_variables_old, su_max_n_iterations=20, su_conv_tol=1e-06)[source]¶

Perform constitutive model state update.

Parameters:

inc_strain (numpy.ndarray (2d)) – Incremental strain second-order tensor.
state_variables_old (dict) – Last converged constitutive model material state variables.
su_max_n_iterations (int, default=20) – State update maximum number of iterations.
su_conv_tol (float, default=1e-6) – State update convergence tolerance.

Returns:

state_variables (dict) – Material constitutive model state variables.
consistent_tangent_mf (numpy.ndarray (2d)) – Material constitutive model consistent tangent modulus in matricial form.