Amplitude

*Amplitude, Name = <amplitude name> , Type = <amplitude type>
<amplitude parameter 1>, ..., <amplitude parameter n>

This option enables the user to define amplitudes for later use (e.g. loading or boundary conditions).

Name=<amplitude name>

Set this parameter equal to the name of the material set to which the properties are defined. This parameter is mandatory.
Type = <amplitude type>

Set this parameter equal to the amplitude type to be used. The subsequent lines <amplitude parameter 1>, ... , <amplitude parameter n> depend on the type chosen. This parameter is mandatory. The following amplitude types are available:
- ramp Linear increasing amplitude with variable starting ($\sqcup_0$) and ending ($\sqcup_1$) time. The subsequent lines take the following form:
  t0, v0, t1, v1
- periodic Amplitude as a Fourier series of N number of terms:
  
  $f(t) = \begin{cases} A_0 + \sum_i^N \Big( A_i \cos i \omega (t - t_0) + B_i \sin i \omega (t - t_0) \Big) & \text{~for: }~ t \geq t_0 \\ A_0 & \text{~for: }~ t < t_0 \end{cases}$
  
  The subsequent lines take the following form:
  N, A0, t0, $\omega$ A1, B1
  ...
  AN, BN
- rising_cosine Periodic function with increasing amplitude of the following form:
  
  $f(t) = \begin{cases} \frac{A_1}{t_1} \cdot t \cdot \cos(\omega t) & \text{~for: }~ t \leq t_1 \\ A_1 \cdot \cos(\omega t) & \text{~for: }~ t > t_1 \end{cases}$
  
  The subsequent line takes the following form:
  t1,$\omega$, A1
- rising_sine Periodic function with increasing amplitude of the following form:
  $f(t) = \begin{cases} \frac{A_1}{t_1} \cdot t \cdot \sin(\omega t) & \text{~for: }~ t \leq t_1 \\ A_1 \cdot \sin(\omega t) & \text{~for: }~ t > t_1 \end{cases}$
  The subsequent line takes the following form:
  t1,$\omega$, A1
- equally_spaced Choose the equally spaced definition method to give a list of amplitude values vi at fixed time intervals dx beginning at a specified value of time. If needed, numgeo interpolates linearly between these values. The subsequent lines take the following form:
  dx
  v1, v2, ..., v8,
  v9, ...
- tabular Choose the tabular definition to define the amplitude curve as a table of values at convenient points (e.g. t1 = 0 s, v1 = 0, t2 = 1 s, v2 = 2) on the time scale. If needed, numgeo interpolates linearly between these values. The subsequent lines take the following form:
  t1, v1
  t2, v2
  ...
- user The amplitude is defined in a user-defined file described here. The user may specify as many amplitude parameters in the input file as needed in the user file
- lab-cyclic-stress-strain-control An amplitude specially designed for cyclic triaxial tests. For a defined element set <elset> a signal is generated with constant rate <rate>. The direction of the signal is reversed when target stress <stress1> or <stress2> is reached in the element of <elset>. The procedure is continued until <N> load reversals are performed. This amplitude is best combined with a displacement-controlled simulation. The command takes the following form:
  *Amplitude, name = ..., Type = lab-cyclic-stress-strain-control
  <elset>, <stress component>, <stress1>, <stress2>, <rate>, <N> The following stress components are available:
  - s11: stress in $x_1$ direction, i.e. $\sigma_{11}$
  - s22: stress in $x_2$ direction, i.e. $\sigma_{22}$
  - s33: stress in $x_3$ direction, i.e. $\sigma_{33}$
  - s11-s22: "triaxial" deviatoric stress, i.e. $\sigma_{11} - \sigma_{22}$
- lab-triaxial-constant-pressure An amplitude specially designed for axially loaded triaxial tests with constant mean effective stress (<target pressure>, $p=\sigma_{ii}/3$). For a defined element set <elset> an updated horizontal stress $\sigma_{11}$ is calculated that enforces $\dot{p}=0$:
  $\sigma_{11} = \dfrac{2p^{target}-\sigma_{22,0}}{2}$
  
  Example:
  *Amplitude, name = updated-s11, Type = lab-triaxial-constant-pressure
  <elset>, <target pressure>
  Best combined with a distributed surface load, e.g.
  *DSload, name = ..., amplitude = updated-s11
  <surface name>, P, 1