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>

  The name of the amplitude which will be used for later assignment to loads and boundary conditions.

• Type = <amplitude type>

  Set this keyword equal to the amplitude type to be used. The subsequent lines <amplitude parameter 1>, ... , <amplitude parameter n> depend on the type chosen. This keyword 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