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 = {'material_0': 'S, 1', 'material_1': '1, 1', 'state/div': 'D', 'state/grad': 1, 'virtual/div': (1, None), 'virtual/grad': ('D', 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:

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

Call signature:

ev_biot_stress

(material, parameter)

Arguments:

material : $\alpha_{ij}$
parameter : $p$

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]¶

integration = 'cell'¶

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 = {'material': '.: N, S, 1', 'state/div': 'D', 'state/grad': 1, 'virtual/div': (1, None), 'virtual/grad': ('D', 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 = [{'material': 'S, 1', 'parameter_s': 1, 'parameter_v': 'D', 'state/div': 'D', 'state/grad': 1, 'virtual/div': (1, None), 'virtual/grad': ('D', 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]¶