sfepy.terms.terms_elastic module¶
- 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',)¶
- integration = ('cell', 'facet_extra')¶
- name = 'ev_cauchy_strain'¶
- 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
instancematerial_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'¶
- 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
instancematerial :
parameter :
- arg_shapes = {'material': '.: N, S, S', 'parameter': 'D'}¶
- arg_types = ('ts', 'material', 'parameter')¶
- name = 'ev_cauchy_stress_th'¶
- 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')¶
- integration = ('cell', 'facet_extra')¶
- name = 'ev_cauchy_stress'¶
- 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'¶
- 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'¶
- class sfepy.terms.terms_elastic.LinearDRotSpringTerm(name, arg_str, integral, region, **kwargs)[source]¶
- Call signature:
dw_lin_dspring_rot
(opt_material, material, virtual, state)
- arg_shapes = [{'material': 'S, 1', 'opt_material': 'D, 1', 'state': 'S', 'virtual': ('S', 'state')}, {'material': 'S, S'}, {'opt_material': None}]¶
- arg_types = ('opt_material', 'material', 'virtual', 'state')¶
- name = 'dw_lin_dspring_rot'¶
- class sfepy.terms.terms_elastic.LinearDSpringTerm(name, arg_str, integral, region, **kwargs)[source]¶
Linear spring element with the stiffness transformed into the element direction.
- Definition:
- Call signature:
dw_lin_dspring
(opt_material, material, virtual, state)
- Arguments:
opt_material :
material :
virtual:
state:
Stiffness matrix is defined by 6 components in 3D and by 3 components , where is the stiffness for the displacement DOF and is for the rotational DOF. Note that the components of are in the local coordinates system specified by a given direction or by the vector for non-coincidental end nodes. The stiffness parameter can also be defined as a 6x6 matrix in 3D or a 3x3 matrix in 2D.
- arg_shapes = [{'material': 'D, 1', 'opt_material': 'D, 1', 'state': 'D', 'virtual': ('D', 'state')}, {'material': 'D, D'}, {'opt_material': None}]¶
- arg_types = ('opt_material', 'material', 'virtual', 'state')¶
- geometries = ['1_2', '2_1_2', '3_1_2']¶
- integration_order = 0¶
- name = 'dw_lin_dspring'¶
- 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
instancematerial_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(out, coef, strain, mtx_d, cmap, is_diff)¶
- get_fargs(ts, mat0, mat1, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
- name = 'dw_lin_elastic_eth'¶
- 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/parameter_1:
state/parameter_2:
- arg_shapes = {'material_1': '1, 1', 'material_2': '1, 1', 'parameter_1': 'D', 'parameter_2': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶
- 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'¶
- 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
instancematerial :
virtual :
state :
- arg_shapes = {'material': '.: N, S, S', 'state': 'D', 'virtual': ('D', 'state')}¶
- arg_types = ('ts', 'material', 'virtual', 'state')¶
- static function(out, coef, strain, mtx_d, cmap, is_diff)¶
- name = 'dw_lin_elastic_th'¶
- 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 = {'material': 'S, S', 'parameter_1': 'D', 'parameter_2': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶
- arg_types = (('material', 'virtual', 'state'), ('material', 'parameter_1', 'parameter_2'))¶
- modes = ('weak', 'eval')¶
- name = 'dw_lin_elastic'¶
- class sfepy.terms.terms_elastic.LinearPrestressTerm(name, arg_str, integral, region, **kwargs)[source]¶
Linear prestress term, with the prestress given either 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 , or in the matrix (possibly non-symmetric) form. 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)}, {'material': 'D, D'}]¶
- arg_types = (('material', 'virtual'), ('material', 'parameter'))¶
- modes = ('weak', 'eval')¶
- name = 'dw_lin_prestress'¶
- class sfepy.terms.terms_elastic.LinearSpringTerm(name, arg_str, integral, region, **kwargs)[source]¶
Linear spring element.
- Definition:
- Call signature:
dw_lin_spring
(material, virtual, state)
- Arguments 1:
material :
virtual :
state :
- arg_shapes = {'material': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶
- arg_types = ('material', 'virtual', 'state')¶
- geometries = ['1_2', '2_1_2', '3_1_2']¶
- integration_order = 0¶
- name = 'dw_lin_spring'¶
- 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(out, mtx_d, mat, cmap)¶
- name = 'dw_lin_strain_fib'¶
- class sfepy.terms.terms_elastic.LinearTrussInternalForceTerm(name, arg_str, integral, region, **kwargs)[source]¶
Evaluate internal force in the element direction. To be used with ‘el_avg’ or ‘qp’ evaluation modes which give the same results. The material parameter is equal to Young modulus times element coss-section. The internal force is given by , where is the element length and , are the nodal displacements and the nodal forces in the element direction.
- Definition:
- Call signature:
ev_lin_truss_force
(material, parameter)
- Arguments:
material :
parameter :
- arg_shapes = {'material': '1, 1', 'parameter': 'D'}¶
- arg_types = ('material', 'parameter')¶
- geometries = ['1_2', '2_1_2', '3_1_2']¶
- integration_order = 0¶
- name = 'ev_lin_truss_force'¶
- class sfepy.terms.terms_elastic.LinearTrussTerm(name, arg_str, integral, region, **kwargs)[source]¶
Evaluate internal force in the element direction. To be used with ‘el_avg’ or ‘qp’ evaluation modes which give the same results. The material parameter is equal to Young modulus times element coss-section. The internal force is given by , where is the element length and , are the nodal displacements and the nodal forces in the element direction.
- Definition:
- Call signature:
dw_lin_truss
(material, virtual, state)
- Arguments:
material :
parameter :
- arg_shapes = {'material': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶
- arg_types = ('material', 'virtual', 'state')¶
- geometries = ['1_2', '2_1_2', '3_1_2']¶
- integration_order = 0¶
- name = 'dw_lin_truss'¶
- 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 = {'material': 'D2, D2', 'parameter_1': 'D', 'parameter_2': 'D', 'state': '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'¶
- class sfepy.terms.terms_elastic.SDLinearElasticTerm(name, arg_str, integral, region, **kwargs)[source]¶
Sensitivity analysis of the linear elastic term.
- Definition:
- Call signature:
ev_sd_lin_elastic
(material, parameter_w, parameter_u, parameter_mv)
- Arguments:
material :
parameter_w :
parameter_u :
parameter_mv :
- arg_shapes = {'material': 'S, S', 'parameter_mv': 'D', 'parameter_u': 'D', 'parameter_w': 'D'}¶
- arg_types = ('material', 'parameter_w', 'parameter_u', 'parameter_mv')¶
- static function(out, coef, grad_v, grad_u, grad_w, mtx_d, cmap)¶
- 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 = 'ev_sd_lin_elastic'¶