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
instancematerial_0 : \alpha_{ij}(0)
material_1 : \exp(-\lambda \Delta t) (decay at t_1)
virtual : \ul{v}
state : p
- Arguments 2
ts :
TimeStepper
instancematerial_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'))¶
- 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')¶
- integration = 'volume'¶
- 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
instancematerial : \alpha_{ij}(\tau)
virtual : \ul{v}
state : p
- Arguments 2
ts :
TimeStepper
instancematerial : \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'))¶
- 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', 'virtual/grad': ('D', None), 'state/grad': 1, 'virtual/div': (1, None), 'state/div': 'D', 'parameter_v': 'D', 'parameter_s': 1}, {'material': 'D, D'}]¶
- arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_v', 'parameter_s'))¶
- modes = ('grad', 'div', 'eval')¶
- name = 'dw_biot'¶