sfepy.terms.terms_biot module

class sfepy.terms.terms_biot.BiotETHTerm(name, arg_str, integral, region, **kwargs)[source]

This term has the same definition as dw_biot_th, but assumes an exponential approximation of the convolution kernel resulting in much higher efficiency. Can use derivatives.

Definition:

\begin{array}{l}
\int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau}
\right]\,e_{ij}(\ul{v}) \mbox{ ,} \\
\int_{\Omega} \left [\int_0^t
\alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q
\end{array}

Call signature:
dw_biot_eth (ts, material_0, material_1, virtual, state)
(ts, material_0, material_1, state, virtual)
Arguments 1:
  • ts : TimeStepper instance
  • material_0 : \alpha_{ij}(0)
  • material_1 : \exp(-\lambda \Delta t) (decay at t_1)
  • virtual : \ul{v}
  • state : p
Arguments 2:
  • ts : TimeStepper instance
  • material_0 : \alpha_{ij}(0)
  • material_1 : \exp(-\lambda \Delta t) (decay at t_1)
  • state : \ul{u}
  • virtual : q
arg_shapes = {‘virtual/grad’: (‘D’, None), ‘state/div’: ‘D’, ‘state/grad’: 1, ‘material_0’: ‘S, 1’, ‘material_1’: ‘1, 1’, ‘virtual/div’: (1, None)}
arg_types = ((‘ts’, ‘material_0’, ‘material_1’, ‘virtual’, ‘state’), (‘ts’, ‘material_0’, ‘material_1’, ‘state’, ‘virtual’))
get_fargs(ts, mat0, mat1, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
modes = (‘grad’, ‘div’)
name = ‘dw_biot_eth’
class sfepy.terms.terms_biot.BiotStressTerm(name, arg_str, integral, region, **kwargs)[source]

Evaluate Biot stress tensor.

It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as [11, 22, 33, 12, 13, 23], in 2D it has 3 components with the indices ordered as [11, 22, 12].

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition:

- \int_{\Omega} \alpha_{ij} \bar{p}

\mbox{vector for } K \from \Ical_h:
- \int_{T_K} \alpha_{ij} \bar{p} / \int_{T_K} 1

- \alpha_{ij} \bar{p}|_{qp}

Call signature:
ev_biot_stress (material, parameter)
Arguments:
  • material : \alpha_{ij}
  • parameter : \bar{p}
arg_shapes = {‘material’: ‘S, 1’, ‘parameter’: 1}
arg_types = (‘material’, ‘parameter’)
static function(out, val_qp, mat, vg, fmode)[source]
get_fargs(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
name = ‘ev_biot_stress’
class sfepy.terms.terms_biot.BiotTHTerm(name, arg_str, integral, region, **kwargs)[source]

Fading memory Biot term. Can use derivatives.

Definition:

\begin{array}{l}
\int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau}
\right]\,e_{ij}(\ul{v}) \mbox{ ,} \\
\int_{\Omega} \left [\int_0^t
\alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q
\end{array}

Call signature:
dw_biot_th (ts, material, virtual, state)
(ts, material, state, virtual)
Arguments 1:
  • ts : TimeStepper instance
  • material : \alpha_{ij}(\tau)
  • virtual : \ul{v}
  • state : p
Arguments 2:
  • ts : TimeStepper instance
  • material : \alpha_{ij}(\tau)
  • state : \ul{u}
  • virtual : q
arg_shapes = {‘virtual/grad’: (‘D’, None), ‘state/grad’: 1, ‘state/div’: ‘D’, ‘material’: ‘.: N, S, 1’, ‘virtual/div’: (1, None)}
arg_types = ((‘ts’, ‘material’, ‘virtual’, ‘state’), (‘ts’, ‘material’, ‘state’, ‘virtual’))
get_fargs(ts, mats, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
modes = (‘grad’, ‘div’)
name = ‘dw_biot_th’
class sfepy.terms.terms_biot.BiotTerm(name, arg_str, integral, region, **kwargs)[source]

Biot coupling term with \alpha_{ij} given in:

  • vector form exploiting symmetry - in 3D it has the indices ordered as [11, 22, 33, 12, 13, 23], in 2D it has the indices ordered as [11, 22, 12],
  • matrix form - non-symmetric coupling parameter.

Corresponds to weak forms of Biot gradient and divergence terms. Can be evaluated. Can use derivatives.

Definition:

\int_{\Omega}  p\ \alpha_{ij} e_{ij}(\ul{v}) \mbox{ , } \int_{\Omega}
q\ \alpha_{ij} e_{ij}(\ul{u})

Call signature:
dw_biot (material, virtual, state)
(material, state, virtual)
(material, parameter_v, parameter_s)
Arguments 1:
  • material : \alpha_{ij}
  • virtual : \ul{v}
  • state : p
Arguments 2:
  • material : \alpha_{ij}
  • state : \ul{u}
  • virtual : q
Arguments 3:
  • material : \alpha_{ij}
  • parameter_v : \ul{u}
  • parameter_s : p
arg_shapes = [{‘state/grad’: 1, ‘state/div’: ‘D’, ‘material’: ‘S, 1’, ‘virtual/grad’: (‘D’, None), ‘parameter_s’: 1, ‘parameter_v’: ‘D’, ‘virtual/div’: (1, None)}, {‘material’: ‘D, D’}]
arg_types = ((‘material’, ‘virtual’, ‘state’), (‘material’, ‘state’, ‘virtual’), (‘material’, ‘parameter_v’, ‘parameter_s’))
get_eval_shape(mat, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
get_fargs(mat, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]
modes = (‘grad’, ‘div’, ‘eval’)
name = ‘dw_biot’
set_arg_types()[source]