sfepy.terms.terms_hyperelastic_ul module

class sfepy.terms.terms_hyperelastic_ul.BulkPenaltyULTerm(*args, **kwargs)

Hyperelastic bulk penalty term. Stress \tau_{ij} = K(J-1)\; J \delta_{ij}.

Definition:

\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J

Call signature:

dw_ul_bulk_penalty

(material, virtual, state)

Arguments:

• material : K
• virtual : \ul{v}
• state : \ul{u}

family_data_names = ['det_f']

name = 'dw_ul_bulk_penalty'

stress_function()

tan_mod_function()

class sfepy.terms.terms_hyperelastic_ul.BulkPressureULTerm(*args, **kwargs)

Hyperelastic bulk pressure term. Stress S_{ij} = -p J \delta_{ij}.

Definition:

\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J

Call signature:

dw_ul_bulk_pressure

(virtual, state, state_p)

Arguments:

• virtual : \ul{v}
• state : \ul{u}
• state_p : p

arg_shapes = {'state_p': 1, 'state': 'D', 'virtual': ('D', 'state')}

arg_types = ('virtual', 'state', 'state_p')

compute_data(family_data, mode, **kwargs)

family_data_names = ['det_f', 'sym_b']

family_function()

get_eval_shape(virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs)

get_fargs(virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs)

name = 'dw_ul_bulk_pressure'

stress_function()

tan_mod_u_function()

weak_dp_function()

weak_function()

class sfepy.terms.terms_hyperelastic_ul.CompressibilityULTerm(*args, **kwargs)

Compressibility term for the updated Lagrangian formulation

Definition:

\int_{\Omega} 1\over \gamma p \, q

Call signature:

dw_ul_compressible

(material, virtual, state, parameter_u)

Arguments:

• material : \gamma
• virtual : q
• state : p
• parameter_u : \ul(u)

arg_shapes = {'state': 1, 'material': '1, 1', 'parameter_u': 'D', 'virtual': (1, 'state')}

arg_types = ('material', 'virtual', 'state', 'parameter_u')

family_data_names = ['mtx_f', 'det_f']

function()

get_fargs(bulk, virtual, state, parameter_u, mode=None, term_mode=None, diff_var=None, **kwargs)

name = 'dw_ul_compressible'

class sfepy.terms.terms_hyperelastic_ul.HyperElasticULBase(*args, **kwargs)

Base class for all hyperelastic terms in UL formulation family.

The subclasses should have the following static method attributes: - stress_function() (the stress) - tan_mod_function() (the tangent modulus)

The common (family) data are cached in the evaluate cache of state variable.

compute_family_data(state)

family_function()

fd_cache_name = 'ul_common'

hyperelastic_mode = 1

weak_function()

class sfepy.terms.terms_hyperelastic_ul.MooneyRivlinULTerm(*args, **kwargs)

Hyperelastic Mooney-Rivlin term.

Definition:

\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J

Call signature:

dw_ul_he_mooney_rivlin

(material, virtual, state)

Arguments:

• material : \kappa
• virtual : \ul{v}
• state : \ul{u}

family_data_names = ['det_f', 'tr_b', 'sym_b', 'in2_b']

name = 'dw_ul_he_mooney_rivlin'

stress_function()

tan_mod_function()

class sfepy.terms.terms_hyperelastic_ul.NeoHookeanULTerm(*args, **kwargs)

Hyperelastic neo-Hookean term. Effective stress \tau_{ij} = \mu J^{-\frac{2}{3}}(b_{ij} - \frac{1}{3}b_{kk}\delta_{ij}).

Definition:

\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J

Call signature:

dw_ul_he_neohook

(material, virtual, state)

Arguments:

• material : \mu
• virtual : \ul{v}
• state : \ul{u}

family_data_names = ['det_f', 'tr_b', 'sym_b']

name = 'dw_ul_he_neohook'

stress_function()

tan_mod_function()

class sfepy.terms.terms_hyperelastic_ul.VolumeULTerm(*args, **kwargs)

Volume term (weak form) in the updated Lagrangian formulation.

Definition:

\begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array}

Call signature:

dw_ul_volume

(virtual, state)

Arguments:

• virtual : q
• state : \ul{u}

arg_shapes = {'state': 'D', 'virtual': (1, None)}

arg_types = ('virtual', 'state')

family_data_names = ['mtx_f', 'det_f']

function()

get_eval_shape(virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)

get_fargs(virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)

name = 'dw_ul_volume'