cratepy.material.materialmodeling.VonMises¶

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

Bases: ConstitutiveModel

Von Mises constitutive model with isotropic strain hardening.

_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()[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 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 material constitutive model state update.

Methods

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

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()[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 >
    ...
isotropic_hardening < option > < n_hardening_parameters >
    hard_parameter < value >
    hard_parameter < 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.
isotropic_hardening - Isotropic strain hardening type and number of parameters.
hard_parameter - Isotropic strain hardening type parameter.

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()[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: \(\boldsymbol{\varepsilon^{e}}\) / \(\boldsymbol{\varepsilon^{e}}\)
acc_p_strain
- Accumulated plastic strain.
- Symbol: \(\bar{\varepsilon}^{p}\)
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_plastic
- Plastic step flag.
is_su_fail
- State update failure flag.

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

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

Perform material constitutive model state update.

Parameters:

inc_strain (numpy.ndarray (2d)) – Incremental strain second-order tensor.
state_variables_old (dict) – Last converged material constitutive model 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.