Reference revision · 2026-09-27
Start with one periodic unit cell containing a dry fiber bed and trapped gas. Temperature controls resin viscosity; applied pressure drives transverse resin flow into the void. Gas pressure and fiber-bed resistance oppose compaction. This is a reduction of Simacek, Advani, Gruber and Jensen (2013), not the full interacting-void model.
Set up and run
- Open Models → Void Consolidation. Copy the example or create a model of type void consolidation model. Edit its properties for your material.
- Open a transient Thermal case → Initial conditions → Optional void consolidation. Select the model and use the link button to edit it.
- Set the temperature/pressure boundary schedule as usual. Batch schedules use time. Moving-section schedules can use length and pulling velocity; time equals distance divided by velocity.
- For rollers, choose Total. Both faces use the same global-plus-roller pressure. The shared 1D pressure envelope takes the larger active roller contribution at each position, without adding opposing pressures. Global excludes rollers.
- Run the simulation. In the 2D thermal output dropdown, select Void consolidation profile. With Model defaults, the plot shows the cell at the selected depth. The sampling setting below adds independent node or ply histories. Choose void content, thickness, gas pressure, viscosity or another quantity. Moving runs offer Time/Distance axes; Void CSV exports the full sampled history.
Consolidation is optional and off until linked. Initial gas pressure is defined at the first solved local temperature. A temperature-depth fraction of 0 is the lower face, 0.5 the mid-plane, and 1 the upper face. Interpolation uses saved thermal nodes and times; reduce the thermal output interval to check rapid-heating convergence.
For epoxy, link Castro–Macosko viscosity in the matrix cure model. The local temperature and conversion determine viscosity; flow stops at gel. This replaces the PEEK viscosity and melt threshold below, while cell, permeability and gas inputs remain independently editable.
Controls
| Input | Example | Meaning |
|---|---|---|
| Model family | Void Consolidation Model model | Editable model coefficient; see the equations below. |
| Initial void content | 2 % | Initial gas volume divided by total unit-cell volume. |
| Initial fiber volume fraction | 50 % | Fiber volume divided by initial total cell volume, including voids. |
| Unit-cell thickness | 0.2 mm | Local tape thickness. Does not replace laminate geometry. |
| Void spacing | 0.5 mm | Periodic transverse spacing between identical voids; controls the resin flow distance. |
| Void gas condition | Sealed type | Sealed: trapped ideal gas. Vented: ambient gas pressure. Evacuated: zero gas resistance. |
| Initial gas pressure | 0.1 MPa absolute | Initial absolute pressure at the first solved local temperature; sealed mode only. |
| Ambient pressure | 0.1 MPa absolute | Gauge-pressure offset and vented void pressure. |
| Applied pressure convention | Gauge type | Gauge adds ambient pressure. Absolute uses the existing process pressure unchanged. |
| Consolidation pressure source | Total type | Total is the shared through-thickness pressure: global plus the largest active roller contribution. Opposing nip pressures are not added. Global excludes rollers. |
| Temperature depth | 0.5 fraction | Through-thickness location in solved thermal output: 0 = lower, 1 = upper. Linear interpolation between saved nodes and times. |
| Permeability prefactor | 2.408e-11 m² | Transverse carbon-fiber example: K = A exp(−B Vf). Replace with calibrated material data. |
| Permeability exponent | 10.262 — | Editable model coefficient; see the equations below. |
| Viscosity prefactor | 0.016384 Pa·s | PEEK example: viscosity = A exp(B/(T in kelvin + C)). |
| Viscosity temperature coefficient | 6403 K | Editable model coefficient; see the equations below. |
| Viscosity temperature offset | 30 K | Editable model coefficient; see the equations below. |
| Flow activation temperature | 343 °C | Example PEEK melt threshold. No flow below this temperature; does not solve crystallization or gelation. |
| Fiber-bed modulus | 0 MPa | Compressive resistance = modulus × max(Vf/Vf0 − 1, 0)^exponent. Zero follows the paper’s example. |
| Fiber-bed exponent | 2 — | Editable model coefficient; see the equations below. |
| Fiber-bed effective viscosity | 0 Pa·s | Optional additional resistance to thickness strain rate. |
| Maximum fiber volume fraction | 80 % | Packing limit. The model cannot consolidate below this permitted cell thickness. |
| Maximum integration step | 1 s | Adaptive steps may be smaller. All process/roller events are resolved. |
| Integration tolerance | 0.000001 fraction | Local normalized-volume error relative to initial/current gas volume. |
| Parameter basis | Carbon/PEEK example; calibrate for actual material text | Editable model coefficient; see the equations below. |
Equations and limits
Let q be gas volume divided by initial cell volume, c = 1 − initial porosity, and h/h₀ = c + q. Fiber and resin volumes are conserved. The evolving fiber fraction is Vf₀/(c+q), and porosity is q/(c+q). The compression-positive cell balance gives dq/dt = −(c+q)(Pabs − Pgas − Pbed)/(ηL²/(12K) + ηbed).
Sealed gas follows pV/T = constant, with kelvin temperature. Vented gas stays at ambient absolute pressure; an evacuated cell has zero gas pressure. K = A exp(−B Vf); η = A exp(B/(T[K]+C)). Bed pressure = Ebed max(Vf/Vf₀−1,0)ⁿ. The flow threshold freezes consolidation below the selected temperature. Full closure of a vented/evacuated void is irreversible here; later gas nucleation is not modeled.
The implementation derives force balance from the paper’s Eq. 12 pressure distribution and enforces constituent volume conservation. It does not copy printed Eqs. 14–16 literally, which contain apparent sign, missing-pressure-term and dimensional inconsistencies. The scalar equations are integrated with adaptive implicit steps and a packing limit.
The default carbon/PEEK coefficients are an example, not calibrated properties for other materials. Single-cell uniform spacing is an optimistic special case. Void distributions, migration, gas dissolution, capillarity, crystallization coupling and feedback of compaction into thermal geometry remain outside this version. Pressure represents the selected process face, including any width averaging already used for partial-width rollers; it is not a resolved internal stress field.
Source paper · Composites Part A 46 (2013), 154–165Node, interface and ply sampling
In Thermal → Initial conditions → Material model sampling, choose All thermal nodes or Interfaces and ply averages, then rerun. All thermal nodes evaluates each linked void, interface and PEEK model at every thermal node. Reduced sampling evaluates contact/healing only at internal ply boundaries and evaluates voids/PEEK using each ply's thickness-averaged temperature.
An eight-ply laminate has seven internal interfaces and eight ply histories. The outer surfaces are excluded from the interface count. Ply numbering runs from the lower face to the upper face. The linked model coefficients, initial states and pressure source apply at every sampled location.
Select a material output in the temperature dropdown, then choose All interfaces or All ply results. Each location has a separate trace, a visibility checkbox and a value at the slicer time cursor. Moving runs support distance; Slice CSV exports all traces. With node calculations, the slicer can also show all thermal nodes. Cursor output retains the existing detailed plot; reduced PEEK results use the ply slicer and its time cursor.
Reduced mode averages temperature before running the nonlinear bulk model. In node mode, the ply slicer averages already calculated results, while interface traces interpolate node results. These operations can differ. Compare the two modes when temperature varies strongly across a ply. The thermal mesh, cure/reaction model and saved thermal output interval are unchanged.
Model defaults preserves older studies: void and interface models use their chosen depth; PEEK uses thermal nodes. Older saved runs need a new run with a sampling mode selected to produce material slices. PEEK rate coefficients remain illustrative and require calibration.