sfepy.terms.terms_hyperelastic_ul module¶
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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}
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family_data_names
= ['det_f']¶
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name
= 'dw_ul_bulk_penalty'¶
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static
stress_function
()¶
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static
tan_mod_function
()¶
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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
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arg_shapes
= {'state': 'D', 'state_p': 1, 'virtual': ('D', 'state')}¶
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arg_types
= ('virtual', 'state', 'state_p')¶
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family_data_names
= ['det_f', 'sym_b']¶
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static
family_function
()¶
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get_eval_shape
(virtual, state, state_p, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'dw_ul_bulk_pressure'¶
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static
stress_function
()¶
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static
tan_mod_u_function
()¶
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static
weak_dp_function
()¶
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static
weak_function
()¶
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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)
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arg_shapes
= {'material': '1, 1', 'parameter_u': 'D', 'state': 1, 'virtual': (1, 'state')}¶
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arg_types
= ('material', 'virtual', 'state', 'parameter_u')¶
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family_data_names
= ['mtx_f', 'det_f']¶
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static
function
()¶
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get_fargs
(bulk, virtual, state, parameter_u, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'dw_ul_compressible'¶
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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)
The common (family) data are cached in the evaluate cache of state variable.
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static
family_function
()¶
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fd_cache_name
= 'ul_common'¶
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hyperelastic_mode
= 1¶
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static
weak_function
()¶
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static
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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}
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family_data_names
= ['det_f', 'tr_b', 'sym_b', 'in2_b']¶
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name
= 'dw_ul_he_mooney_rivlin'¶
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static
stress_function
()¶
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static
tan_mod_function
()¶
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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}
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family_data_names
= ['det_f', 'tr_b', 'sym_b']¶
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name
= 'dw_ul_he_neohook'¶
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static
stress_function
()¶
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static
tan_mod_function
()¶
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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}
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arg_shapes
= {'state': 'D', 'virtual': (1, None)}¶
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arg_types
= ('virtual', 'state')¶
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family_data_names
= ['mtx_f', 'det_f']¶
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static
function
()¶
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name
= 'dw_ul_volume'¶