sfepy.terms.terms_elastic module¶
-
class
sfepy.terms.terms_elastic.
CauchyStrainSTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Evaluate Cauchy strain tensor on a surface region.
See
CauchyStrainTerm
.Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
Definition: Call signature: ev_cauchy_strain_s (parameter)
Arguments: - parameter :
-
arg_types
= (‘parameter’,)¶
-
integration
= ‘surface_extra’¶
-
name
= ‘ev_cauchy_strain_s’¶
- parameter :
-
class
sfepy.terms.terms_elastic.
CauchyStrainTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Evaluate Cauchy strain tensor.
It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as
, in 2D it has 3 components with the indices ordered as
. The last three (non-diagonal) components are doubled so that it is energetically conjugate to the Cauchy stress tensor with the same storage.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
Definition: Call signature: ev_cauchy_strain (parameter)
Arguments: - parameter :
-
arg_shapes
= {‘parameter’: ‘D’}¶
-
arg_types
= (‘parameter’,)¶
-
name
= ‘ev_cauchy_strain’¶
- parameter :
-
class
sfepy.terms.terms_elastic.
CauchyStressETHTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Evaluate fading memory Cauchy stress tensor.
It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as
, in 2D it has 3 components with the indices ordered as
.
Assumes an exponential approximation of the convolution kernel resulting in much higher efficiency.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
Definition: Call signature: ev_cauchy_stress_eth (ts, material_0, material_1, parameter)
Arguments: - ts :
TimeStepper
instance - material_0 :
- material_1 :
(decay at
)
- parameter :
-
arg_shapes
= {‘material_0’: ‘S, S’, ‘material_1’: ‘1, 1’, ‘parameter’: ‘D’}¶
-
arg_types
= (‘ts’, ‘material_0’, ‘material_1’, ‘parameter’)¶
-
get_eval_shape
(ts, mat0, mat1, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
name
= ‘ev_cauchy_stress_eth’¶
- ts :
-
class
sfepy.terms.terms_elastic.
CauchyStressTHTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Evaluate fading memory Cauchy stress tensor.
It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as
, in 2D it has 3 components with the indices ordered as
.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
Definition: Call signature: ev_cauchy_stress_th (ts, material, parameter)
Arguments: - ts :
TimeStepper
instance - material :
- parameter :
-
arg_shapes
= {‘material’: ‘.: N, S, S’, ‘parameter’: ‘D’}¶
-
arg_types
= (‘ts’, ‘material’, ‘parameter’)¶
-
name
= ‘ev_cauchy_stress_th’¶
- ts :
-
class
sfepy.terms.terms_elastic.
CauchyStressTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Evaluate Cauchy stress tensor.
It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as
, in 2D it has 3 components with the indices ordered as
.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
Definition: Call signature: ev_cauchy_stress (material, parameter)
Arguments: - material :
- parameter :
-
arg_shapes
= {‘material’: ‘S, S’, ‘parameter’: ‘D’}¶
-
arg_types
= (‘material’, ‘parameter’)¶
-
name
= ‘ev_cauchy_stress’¶
- material :
-
class
sfepy.terms.terms_elastic.
ElasticWaveCauchyTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Elastic dispersion term involving the wave strain
,
, with the wave vector
and the elastic strain
.
is given in the usual matrix form exploiting symmetry: in 3D it is
with the indices ordered as
, in 2D it is
with the indices ordered as
.
Definition: Call signature: dw_elastic_wave_cauchy (material_1, material_2, virtual, state)
(material_1, material_2, state, virtual)
Arguments 1: - material_1 :
- material_2 :
- virtual :
- state :
Arguments 2: - material_1 :
- material_2 :
- state :
- virtual :
-
arg_shapes
= {‘material_1’: ‘S, S’, ‘material_2’: ‘.: D’, ‘state’: ‘D’, ‘virtual’: (‘D’, ‘state’)}¶
-
arg_types
= ((‘material_1’, ‘material_2’, ‘virtual’, ‘state’), (‘material_1’, ‘material_2’, ‘state’, ‘virtual’))¶
-
geometries
= [‘2_3’, ‘2_4’, ‘3_4’, ‘3_8’]¶
-
modes
= (‘ge’, ‘eg’)¶
-
name
= ‘dw_elastic_wave_cauchy’¶
- material_1 :
-
class
sfepy.terms.terms_elastic.
ElasticWaveTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Elastic dispersion term involving the wave strain
,
, with the wave vector
.
is given in the usual matrix form exploiting symmetry: in 3D it is
with the indices ordered as
, in 2D it is
with the indices ordered as
.
Definition: Call signature: dw_elastic_wave (material_1, material_2, virtual, state)
Arguments: - material_1 :
- material_2 :
- virtual :
- state :
-
arg_shapes
= {‘material_1’: ‘S, S’, ‘material_2’: ‘.: D’, ‘state’: ‘D’, ‘virtual’: (‘D’, ‘state’)}¶
-
arg_types
= (‘material_1’, ‘material_2’, ‘virtual’, ‘state’)¶
-
geometries
= [‘2_3’, ‘2_4’, ‘3_4’, ‘3_8’]¶
-
name
= ‘dw_elastic_wave’¶
- material_1 :
-
class
sfepy.terms.terms_elastic.
LinearElasticETHTerm
(name, arg_str, integral, region, **kwargs)[source]¶ This term has the same definition as dw_lin_elastic_th, but assumes an exponential approximation of the convolution kernel resulting in much higher efficiency. Can use derivatives.
Definition: Call signature: dw_lin_elastic_eth (ts, material_0, material_1, virtual, state)
Arguments: - ts :
TimeStepper
instance - material_0 :
- material_1 :
(decay at
)
- virtual :
- state :
-
arg_shapes
= {‘material_0’: ‘S, S’, ‘material_1’: ‘1, 1’, ‘state’: ‘D’, ‘virtual’: (‘D’, ‘state’)}¶
-
arg_types
= (‘ts’, ‘material_0’, ‘material_1’, ‘virtual’, ‘state’)¶
-
static
function
()¶
-
get_fargs
(ts, mat0, mat1, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
name
= ‘dw_lin_elastic_eth’¶
- ts :
-
class
sfepy.terms.terms_elastic.
LinearElasticIsotropicTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Isotropic linear elasticity term.
Definition: Call signature: dw_lin_elastic_iso (material_1, material_2, virtual, state)
(material_1, material_2, parameter_1, parameter_2)
Arguments: - material_1 :
- material_2 :
- virtual :
- state :
Arguments 2: - material :
- parameter_1 :
- parameter_2 :
-
arg_shapes
= {‘virtual’: (‘D’, ‘state’), ‘state’: ‘D’, ‘parameter_2’: ‘D’, ‘material_1’: ‘1, 1’, ‘material_2’: ‘1, 1’, ‘parameter_1’: ‘D’}¶
-
arg_types
= ((‘material_1’, ‘material_2’, ‘virtual’, ‘state’), (‘material_1’, ‘material_2’, ‘parameter_1’, ‘parameter_2’))¶
-
geometries
= [‘2_3’, ‘2_4’, ‘3_4’, ‘3_8’]¶
-
get_eval_shape
(mat1, mat2, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
name
= ‘dw_lin_elastic_iso’¶
- material_1 :
-
class
sfepy.terms.terms_elastic.
LinearElasticTHTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Fading memory linear elastic (viscous) term. Can use derivatives.
Definition: Call signature: dw_lin_elastic_th (ts, material, virtual, state)
Arguments: - ts :
TimeStepper
instance - material :
- virtual :
- state :
-
arg_shapes
= {‘state’: ‘D’, ‘material’: ‘.: N, S, S’, ‘virtual’: (‘D’, ‘state’)}¶
-
arg_types
= (‘ts’, ‘material’, ‘virtual’, ‘state’)¶
-
static
function
()¶
-
name
= ‘dw_lin_elastic_th’¶
- ts :
-
class
sfepy.terms.terms_elastic.
LinearElasticTerm
(name, arg_str, integral, region, **kwargs)[source]¶ General linear elasticity term, with
given in the usual matrix form exploiting symmetry: in 3D it is
with the indices ordered as
, in 2D it is
with the indices ordered as
. Can be evaluated. Can use derivatives.
Definition: Call signature: dw_lin_elastic (material, virtual, state)
(material, parameter_1, parameter_2)
Arguments 1: - material :
- virtual :
- state :
Arguments 2: - material :
- parameter_1 :
- parameter_2 :
-
arg_shapes
= {‘parameter_2’: ‘D’, ‘state’: ‘D’, ‘material’: ‘S, S’, ‘parameter_1’: ‘D’, ‘virtual’: (‘D’, ‘state’)}¶
-
arg_types
= ((‘material’, ‘virtual’, ‘state’), (‘material’, ‘parameter_1’, ‘parameter_2’))¶
-
modes
= (‘weak’, ‘eval’)¶
-
name
= ‘dw_lin_elastic’¶
- material :
-
class
sfepy.terms.terms_elastic.
LinearPrestressTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Linear prestress term, with the prestress
given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as
, in 2D it has 3 components with the indices ordered as
. Can be evaluated.
Definition: Call signature: dw_lin_prestress (material, virtual)
(material, parameter)
Arguments 1: - material :
- virtual :
Arguments 2: - material :
- parameter :
-
arg_shapes
= {‘material’: ‘S, 1’, ‘parameter’: ‘D’, ‘virtual’: (‘D’, None)}¶
-
arg_types
= ((‘material’, ‘virtual’), (‘material’, ‘parameter’))¶
-
modes
= (‘weak’, ‘eval’)¶
-
name
= ‘dw_lin_prestress’¶
- material :
-
class
sfepy.terms.terms_elastic.
LinearStrainFiberTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Linear (pre)strain fiber term with the unit direction vector
.
Definition: Call signature: dw_lin_strain_fib (material_1, material_2, virtual)
Arguments: - material_1 :
- material_2 :
- virtual :
-
arg_shapes
= {‘material_1’: ‘S, S’, ‘material_2’: ‘D, 1’, ‘virtual’: (‘D’, None)}¶
-
arg_types
= (‘material_1’, ‘material_2’, ‘virtual’)¶
-
static
function
()¶
-
name
= ‘dw_lin_strain_fib’¶
- material_1 :
-
class
sfepy.terms.terms_elastic.
NonsymElasticTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Elasticity term with non-symmetric gradient. The indices of matrix
are ordered as
in 3D and as
in 2D.
Definition: Call signature: dw_nonsym_elastic (material, virtual, state)
(material, parameter_1, parameter_2)
Arguments 1: - material :
- virtual :
- state :
Arguments 2: - material :
- parameter_1 :
- parameter_2 :
-
arg_shapes
= {‘parameter_2’: ‘D’, ‘state’: ‘D’, ‘material’: ‘D2, D2’, ‘parameter_1’: ‘D’, ‘virtual’: (‘D’, ‘state’)}¶
-
arg_types
= ((‘material’, ‘virtual’, ‘state’), (‘material’, ‘parameter_1’, ‘parameter_2’))¶
-
geometries
= [‘2_3’, ‘2_4’, ‘3_4’, ‘3_8’]¶
-
modes
= (‘weak’, ‘eval’)¶
-
name
= ‘dw_nonsym_elastic’¶
- material :
-
class
sfepy.terms.terms_elastic.
SDLinearElasticTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity analysis of the linear elastic term.
Definition: Call signature: d_sd_lin_elastic (material, parameter_w, parameter_u, parameter_mesh_velocity)
Arguments: - material :
- parameter_w :
- parameter_u :
- parameter_mesh_velocity :
-
arg_shapes
= {‘parameter_mesh_velocity’: ‘D’, ‘material’: ‘S, S’, ‘parameter_w’: ‘D’, ‘parameter_u’: ‘D’}¶
-
arg_types
= (‘material’, ‘parameter_w’, ‘parameter_u’, ‘parameter_mesh_velocity’)¶
-
function
()¶
-
geometries
= [‘2_3’, ‘2_4’, ‘3_4’, ‘3_8’]¶
-
get_eval_shape
(mat, par_w, par_u, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
name
= ‘d_sd_lin_elastic’¶
- material :