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}](../../../_images/math/21f2955cb96181c5d10bb4de66c8c6b82a3d5fd8.png)
| Call signature: |
|---|
| dw_biot_eth | (ts, material_0, material_1, virtual, state) |
| (ts, material_0, material_1, state, virtual) |
| Arguments 1: |
|
|---|---|
| Arguments 2: |
|
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
, in
2D it has 3 components with the indices ordered as
.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
| Definition : |
|---|



| Call signature: |
|---|
| ev_biot_stress | (material, parameter) |
| Arguments : |
|
|---|
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}](../../../_images/math/21f2955cb96181c5d10bb4de66c8c6b82a3d5fd8.png)
| Call signature: |
|---|
| dw_biot_th | (ts, material, virtual, state) |
| (ts, material, state, virtual) |
| Arguments 1: |
|
|---|---|
| Arguments 2: |
|
Biot coupling term with
given in vector form exploiting symmetry: in 3D it has the
indices ordered as
, in 2D it has
the indices ordered as
. Corresponds to weak
forms of Biot gradient and divergence terms. Can be evaluated. Can
use derivatives.
| Definition : |
|---|

| Call signature: |
|---|
| dw_biot | (material, virtual, state) |
| (material, state, virtual) | |
| (material, parameter_v, parameter_s) |
| Arguments 1: |
|
|---|---|
| Arguments 2: |
|
| Arguments 3: |
|