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(out, mat, det_f)¶

static tan_mod_function(out, mat, det_f)¶

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_geometry_types = {('state_p', None): {'facet_extra': 'facet'}}¶

arg_shapes = {'state': 'D', 'state_p': 1, '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(mtx_f, det_f, vec_bs, tr_b, in_2b, vec_es, state, cmap, conn)¶

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(out, pressure_qp, det_f)¶

static tan_mod_u_function(out, pressure_qp, det_f)¶

static weak_dp_function(out, det_f, cmap_s, cmap_v, transpose, mode)¶

static weak_function(out, stress, tan_mod, mtx_f, det_f, cmap, is_diff, mode_ul)¶

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_geometry_types = {('state', None): {'facet_extra': 'facet'}, ('virtual', None): {'facet_extra': 'facet'}}¶

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

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

family_data_names = ['mtx_f', 'det_f']¶

static function(out, coef, val_qp, rcmap, ccmap, is_diff)¶

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(out, stress, tan_mod, mtx_f, det_f, cmap, is_diff, mode_ul)¶

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(mtx_f, det_f, vec_bs, tr_b, in_2b, vec_es, state, cmap, conn)¶

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

General hyperelastic term: the tangent modulus and the stress tensor are calculated by a user defined function $fun$ .

Definition:

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

Call signature:

dw_ul_he_by_fun

(fun, virtual, state)

Arguments:

material : $fun$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = [{'fun': <function HyperelasticByFunULTerm.<lambda>>, 'state': 'D', 'virtual': ('D', 'state')}]¶

arg_types = ('fun', 'virtual', 'state')¶

family_data_names = ['mtx_f', 'det_f', 'sym_b', 'tr_b', 'in2_b', 'green_strain']¶

get_fargs(mat_fun, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_ul_he_by_fun'¶

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(out, mat, det_f, tr_b, vec_bs, in_2b)¶

static tan_mod_function(out, mat, det_f, tr_b, vec_bs, in_2b)¶

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(out, mat, det_f, tr_b, vec_bs)¶

static tan_mod_function(out, mat, det_f, tr_b, vec_bs)¶

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_geometry_types = {('virtual', None): {'facet_extra': 'facet'}}¶

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

arg_types = ('virtual', 'state')¶

family_data_names = ['mtx_f', 'det_f']¶

static function(out, det_f, cmap_s, cmap_v, transpose, mode)¶

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'¶