cratepy.material.models.stvenant_kirchhoff.StVenantKirchhoff

class StVenantKirchhoff(strain_formulation, problem_type, material_properties)

Bases: ConstitutiveModel

St.Venant-Kirchhoff hyperelastic 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

_comp_order_nsym

Strain/Stress components nonsymmetric order.

Type:

list

get_required_properties()

Get constitutive model material properties and constitutive options.

state_init(self)

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)

Perform material constitutive model state update.

Constitutive model 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

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.
state_init	Get initialized material constitutive model state variables.
state_update	Perform constitutive model state update.

Methods

__init__(strain_formulation, problem_type, material_properties)

Constitutive model 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}).

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()

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’}

state_init()

Get initialized material constitutive model state variables.

Constitutive model state variables:

• e_strain_mf

  • Elastic deformation gradient (matricial form).

  • Symbol: \(\boldsymbol{F}^{e}\)

• strain_mf

  • Deformation gradient (matricial form).

  • Symbol: \(\boldsymbol{F}\)

• stress_mf

  • First Piola-Kirchhoff stress tensor (matricial form).

  • Symbol: \(\boldsymbol{P}\)

• 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)

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.