Continuum energy balance
Equation detailsExplanation · variables · model connection · reference+
Balances local sensible-energy storage with through-thickness conduction and volumetric heat released by thermoset cure and thermoplastic crystallization. Material coefficients may change abruptly at ply interfaces.
Model connectionThe micromechanics stage supplies ρ, cp, and k3 for every ply; the material kinetics pages supply qc and qx. The resulting T(z,t) feeds thermal strain and temperature-dependent diffusion.
Theory basisNASA composite cure-process heat model
Cell-centered finite-volume form
Every active ply is divided into a user-selected number of cell-centered control volumes. Each cell belongs to exactly one physical ply, so its storage and conductivity are taken from that ply. Flux continuity is enforced at every shared face.
Equation detailsExplanation · variables · model connection · reference+
Collapses volumetric heat capacity across the thickness of one unit-area finite volume, producing the storage coefficient used in the semidiscrete equations.
Model connectionForms the diagonal capacity matrix C used by the theta time integrator. Refining nodes per ply reduces Δzi while conserving total areal heat capacity.
Theory basisConservative finite-volume heat discretization
Equation detailsExplanation · variables · model connection · reference+
Adds the two half-cell thermal resistances in series. This is essential when adjacent plies have different conductivities because an arithmetic average does not preserve the correct interface heat flux.
Model connectionPopulates the tridiagonal conduction operator. The same resistance construction is reused for the heterogeneous moisture-diffusion operator.
Theory basisFinite-volume interface-flux treatment
Equation detailsExplanation · variables · model connection · reference+
States that heat stored in a cell equals net conductive inflow plus the local volumetric reaction source integrated through the cell thickness.
Model connectionAssembled for every transport cell into C dT/dt + K T = Q before application of surface boundary terms.
Theory basisConservative cell energy balance
Independent top and bottom boundary histories
Top and bottom use separate seven-column tables. Continuous temperature, moisture, and coefficient/flux fields are linearly interpolated to the transport time grid; integer boundary IDs are held piecewise constant. A five-row schedule can therefore drive a thousand-step solve without changing the intended boundary mode between schedule breakpoints.
Equation detailsExplanation · variables · model connection · reference+
Linearly interpolates continuous boundary data while selecting the last declared discrete boundary type until the next table time is reached.
Model connectionApplied separately to both surfaces. Temperature, moisture, and coefficients/fluxes use y(t); thermal and moisture type columns use b(t).
Theory basisProcess-cycle boundary-history context
Equation detailsExplanation · variables · model connection · reference+
Expresses prescribed temperature, adiabatic, convection, and custom inward heat-flux conditions in the same linear source form used by the finite-volume matrix.
Model connectionThe selected pair (Gs,Ss) modifies only the first or last transport equation. Top and bottom types, temperatures, and coefficients remain independent.
Theory basisFinite-volume Dirichlet, Neumann, and Robin boundaries
| Column | Surface-table field | Interpolation |
|---|---|---|
| 1–3 | Time, surface temperature, surface moisture | Continuous fields linear in time |
| 4 | Thermal ID: prescribed, adiabatic, convection, custom inward heat flux | Previous-value hold |
| 5 | Moisture ID: prescribed, insulated, film, custom inward concentration flux | Previous-value hold |
| 6–7 | Thermal and moisture coefficient or signed custom flux | Linear in time |
Theta time integration and coupling
Current Workbench implementation. The general theta equation below describes the theory family, not a selectable theta control in WB. The current transient Workbench solver uses backward Euler with a full-step/two-half-step error estimate. It stops at schedule changes and requested outputs; output spacing is not the integration accuracy target. Rejected trials do not commit temperature or reaction state. If the computation budget or supported schedule size is exceeded, the run fails explicitly rather than accepting a coarser result. Through-thickness mesh convergence, calibration and experimental validation must still be checked separately.
Linked thermal tables use the same property convention in Micro and Process: Micro reports the 23 °C reference, while Process evaluates the table at local temperature without extrapolation. Constituent-based through-thickness closure uses transverse fiber conductivity and matrix conductivity; a stored homogenized ply retains its own through-thickness conductivity.
Equation detailsExplanation · variables · model connection · reference+
Advances the matrix heat balance between old and new time levels. θ=1 is backward Euler; θ=0.5 is Crank–Nicolson. The source includes both interpolated boundaries and enabled reaction heat.
Model connectionSolved repeatedly within each process step while kinetics and heat sources are updated. Convergence is checked using the largest normalized temperature or moisture change.
Theory basisImplicit theta-method discretization
Solver modes. Bypassing transport uses the prescribed temperature for each ply. A process-only study calculates the temperature field. A coupled study also maps the field into structural residual stress and progressive failure. Temperature inputs may be entered in kelvin or Celsius, but the internal kinetics evaluation always uses kelvin.
Theory references
- NASA, Composite Cure Process Modeling and Simulations using Finite Element Analysis (2016).
- NASA composite cure-process heat-transfer formulation and material-state coupling.
- CDS micromechanics theory: effective thermal conductivity, density, and heat capacity supplied to the ply transport cells.
Workbench availability: released models, inputs and compatible study paths. The wider theory library includes reference formulations not available in every Workbench solve.