sfepy.terms.terms_hyperelastic_ul module

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

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’
static stress_function()
static tan_mod_function()
class sfepy.terms.terms_hyperelastic_ul.BulkPressureULTerm(*args, **kwargs)[source]

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)[source]
family_data_names = [‘det_f’, ‘sym_b’]
static family_function()
get_eval_shape(virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
get_fargs(virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
name = ‘dw_ul_bulk_pressure’
static stress_function()
static tan_mod_u_function()
static weak_dp_function()
static weak_function()
class sfepy.terms.terms_hyperelastic_ul.CompressibilityULTerm(*args, **kwargs)[source]

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’]
static function()
get_fargs(bulk, virtual, state, parameter_u, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
name = ‘dw_ul_compressible’
class sfepy.terms.terms_hyperelastic_ul.HyperElasticULBase(*args, **kwargs)[source]

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)

get_family_data = HyperElasticULFamilyData
hyperelastic_mode = 1
static weak_function()
class sfepy.terms.terms_hyperelastic_ul.HyperElasticULFamilyData(**kwargs)[source]

Family data for UL formulation.

cache_name = ‘ul_common’
data_names = (‘mtx_f’, ‘det_f’, ‘sym_b’, ‘tr_b’, ‘in2_b’, ‘green_strain’)
static family_function()
class sfepy.terms.terms_hyperelastic_ul.MooneyRivlinULTerm(*args, **kwargs)[source]

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’
static stress_function()
static tan_mod_function()
class sfepy.terms.terms_hyperelastic_ul.NeoHookeanULTerm(*args, **kwargs)[source]

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’
static stress_function()
static tan_mod_function()
class sfepy.terms.terms_hyperelastic_ul.VolumeULTerm(*args, **kwargs)[source]

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’]
static function()
get_eval_shape(virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
get_fargs(virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
name = ‘dw_ul_volume’