sfepy.terms.terms_flexo module

Flexoelectricity related terms.

class sfepy.terms.terms_flexo.MixedFlexoCouplingTerm(*args, **kwargs)[source]

Flexoelectric coupling term, mixed formulation.

Definition:

\int_{\Omega} f_{ijkl}\ e_{jk,l}(\ull{\delta w}) \nabla_i p \\ \int_{\Omega} f_{ijkl}\ e_{jk,l}(\ull{w}) \nabla_i q

Call signature:

de_m_flexo_coupling

(material, virtual, state)

(material, state, virtual)

(material, parameter_t, parameter_s)
Arguments 1:

  • material: f_{ijkl}

  • virtual/parameter_t: \ull{\delta w}

  • state/parameter_s: p

Arguments 2:

  • material: f_{ijkl}

  • state : \ull{w}

  • virtual : q

arg_shapes = [{'material': 'D, SD', 'parameter_s': 1, 'parameter_t': 'D2', 'state/dp-w': 'D2', 'state/dw-p': 1, 'virtual/dp-w': (1, None), 'virtual/dw-p': ('D2', None)}]
arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_t', 'parameter_s'))
get_function(mat, tvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
modes = ('dw-p', 'dp-w', 'eval')
name = 'de_m_flexo_coupling'
class sfepy.terms.terms_flexo.MixedFlexoTerm(*args, **kwargs)[source]

Mixed formulation displacement gradient consistency term.

Definition:

\int_{\Omega} v_{i,j} a_{ij} \\ \int_{\Omega} u_{i,j} \delta a_{ij}

Call signature:

de_m_flexo

(virtual, state)

(state, virtual)

(parameter_v, parameter_t)
Arguments 1:

  • virtual/parameter_v: \ul{v}

  • state/parameter_t: \ull{a}

Arguments 2:

  • state : \ul{u}

  • virtual : \ull{\delta a}

arg_shapes = [{'parameter_t': 'D2', 'parameter_v': 'D', 'state/da-u': 'D', 'state/du-a': 'D2', 'virtual/da-u': ('D2', None), 'virtual/du-a': ('D', None)}, {'opt_material': None}]
arg_types = (('virtual', 'state'), ('state', 'virtual'), ('parameter_v', 'parameter_t'))
get_function(vvar, tvar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
modes = ('du-a', 'da-u', 'eval')
name = 'de_m_flexo'
class sfepy.terms.terms_flexo.MixedStrainGradElasticTerm(*args, **kwargs)[source]

Flexoelectric strain gradient elasticity term, mixed formulation.

Additional evaluation modes:

  • ‘strain’ - compute strain from the displacement gradient (state) variable.

Definition:

\int_{\Omega} a_{ijklmn}\ e_{ij,k}(\ull{\delta w}) \ e_{lm,n}(\ull{w})

Call signature:

de_m_sg_elastic

(material, virtual, state)

(material, parameter_1, parameter_2)
Arguments:

  • material: a_{ijklmn}

  • virtual/parameter_1: \ull{\delta w}

  • state/parameter_2: \ull{w}

arg_shapes = {'material': 'SD, SD', 'parameter_1': 'D2', 'parameter_2': 'D2', 'state': 'D2', 'virtual': ('D2', 'state')}
arg_types = (('material', 'virtual', 'state'), ('material', 'parameter_1', 'parameter_2'))
get_function(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
modes = ('weak', 'eval')
name = 'de_m_sg_elastic'
sfepy.terms.terms_flexo.make_grad2strain(dim)[source]