sfepy.terms.terms_biot module¶
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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
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arg_shapes
= {}¶
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arg_types
= (('ts', 'material_0', 'material_1', 'virtual', 'state'), ('ts', 'material_0', 'material_1', 'state', 'virtual'))¶
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modes
= ('grad', 'div')¶
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name
= 'dw_biot_eth'¶
- ts :
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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}
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arg_shapes
= {'material': 'S, 1', 'parameter': 1}¶
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arg_types
= ('material', 'parameter')¶
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name
= 'ev_biot_stress'¶
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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
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arg_shapes
= {}¶
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arg_types
= (('ts', 'material', 'virtual', 'state'), ('ts', 'material', 'state', 'virtual'))¶
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modes
= ('grad', 'div')¶
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name
= 'dw_biot_th'¶
- ts :
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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]. 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
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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)}¶
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arg_types
= (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_v', 'parameter_s'))¶
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modes
= ('grad', 'div', 'eval')¶
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name
= 'dw_biot'¶