Solution Control

MPoint uses explicit time integration. The same equations of motion can be used to approach a quasi static state or to calculate a physical dynamic response. The modeling objective determines the appropriate damping, loading rate, timestep, and stopping condition.

Fixed-cycle solution

Use model cycle or model step when the required stage is defined by a number of explicit updates or when equilibrium is not expected.

model cycle 5000
model save 'stage-01'

Fixed-cycle stages are useful for large-deformation flow, runout, progressive conversion, and staged loading. Choose the number of cycles from histories, not only from a previously used example.

Dynamic analysis

Configure the mechanical dynamic process with model mechanical. Define dynamic nodal damping with mpoint node dynamic. The official MPoint beam example uses a fixed mechanical timestep and a specified number of steps.

model configure dynamic
model large-strain on

mpoint node dynamic damping local 0.0
model mechanical timestep fix [dt]
model step [number_of_steps]

Physical time and histories

Record time and response quantities before cycling. Example history commands include model history and mpoint history.

model history name 'Time' dynamic time-total
mpoint history name 'Vertical displacement' ...
    displacement-z position [monitor_position]
history interval 20

model step [number_of_steps]

If the timestep is fixed, the modeled duration is

\[T=N\,\Delta t,\]

where \(N\) is the number of steps and \(\Delta t\) is the timestep.

Quasi-static loading

A quasi-static model should minimize inertial effects while preserving the intended constitutive path. Apply loads in small increments, use suitable static damping, and allow the model to settle between increments. Use local damping for the static process with mpoint node damping. Use dynamic damping for the dynamic process with mpoint node dynamic.

Volume control and particle management

Large distortion may produce excessive material point volume changes or poor particle coverage. If the model uses mpoint volume-limit, mpoint split, or other particle-management controls, activate them from a documented stage and perform a sensitivity study. These controls can improve robustness but may also change the numerical response. The volume limit, splitting, and other particle-management controls can be applied at any stage throughout the analysis.

PIC–FLIP velocity update

The command mpoint pic-fraction controls the blend between FLIP and PIC for the material point translational velocity update.

mpoint pic-fraction 0.0    ; Pure FLIP.
mpoint pic-fraction 1.0    ; Pure PIC.
mpoint pic-fraction 0.01    ; 1% PIC, 99% FLIP. (Default for mechanical models)

For dynamic models, the command mpoint dynamic pic-fraction is used. This allows different values for Mechanical and Dynamic models.

mpoint dynamic pic-fraction 0.0    ; Pure FLIP. (Default value for dynamic models)
mpoint dynamic pic-fraction 1.0    ; Pure PIC.
mpoint dynamic pic-fraction 0.01    ; 1% PIC, 99% FLIP.

FLIP

A PIC fraction of zero selects FLIP. FLIP is less dissipative and is generally preferred when conservation of dynamic motion is important. It can retain particle-level velocity noise and may become unstable in severe deformation, fracture, contact, or failure problems.

PIC

A PIC fraction of one selects PIC. PIC directly filters the material point velocity through the background grid. It is usually smoother and more stable, but it introduces numerical dissipation and can suppress legitimate dynamic content.

Blended PIC–FLIP

A small positive PIC fraction can reduce FLIP noise while limiting PIC dissipation. A reasonable investigation is to compare values such as \(0.0\), \(0.05\), \(0.1\), and \(0.2\), while monitoring energy, velocity noise, deformation, and failure timing.

Do not treat the blend as a universal material parameter. The acceptable value depends on the problem, resolution, timestep, constitutive model, contact, loading rate, and the response quantity of interest.

Nodal damping

The command mpoint node damping controls damping used during the background-node equations of motion for the static process. Local damping is the default form.

mpoint node damping local 0.8

Reduce excessive damping if it changes the loading path, delays instability, or masks oscillatory behavior needed to identify failure.

Combined dampiong is also commonly used in psuedo-static analyses (mpoint node damping combined). See Mechanical Damping for a description of how these different damping schemes.

Dynamic nodal damping

The command mpoint node dynamic controls damping when the dynamic process is active. Local, combined, and Rayleigh forms are available.

mpoint node dynamic damping local 0.0

; Example Rayleigh specification: fraction of critical damping and
; center frequency in cycles per second.
mpoint node dynamic damping rayleigh [damping_fraction] [center_frequency]

Rayleigh stiffness-proportional damping can reduce the stable timestep. Select damping from the physical problem or a documented calibration and verify the frequency range over which it is appropriate.

Transfer and damping study

For important models, run a small sensitivity matrix:

Case

PIC fraction

Static/dynamic damping

Purpose

A

0.0

baseline

Least transfer dissipation

B

0.05

baseline

Mild noise filtering

C

0.10

baseline

Stronger stabilization

D

selected value

reduced/increased

Separate transfer and damping effects

Compare displacement, velocity, energy, stress, plastic strain, and failure mechanism. The selected parameters should be justified by response convergence, not only by visual smoothness.

Stopping a model

Use a stopping condition appropriate to the problem:

  • a force-ratio target for static equilibrium;

  • a target physical time for dynamics;

  • negligible velocity and displacement increments for settlement;

  • a specified displacement, load, or stage number for controlled loading;

  • a steady runout distance or energy decay for flow problems.