Fickian continuum model
Equation detailsExplanation · variables · model connection · reference+
Applies Fick’s second law through the laminate thickness. The divergence form permits temperature- and ply-dependent diffusivity while preserving concentration flux at material interfaces.
Model connectionSolved on the same cell-centered mesh and time grid as heat transfer. The current temperature field updates D before the moisture equation is advanced.
Theory basisNASA moisture diffusion in composites
Equation detailsExplanation · variables · model connection · reference+
Adjusts each ply’s reference diffusivity for the current absolute temperature using a calibrated activation energy.
Model connectionEvaluated after the thermal solve in each staggered process iteration; different plies may use different D0 and ED values.
Theory basisTemperature-dependent environmental diffusion
Heterogeneous finite-volume form
Equation detailsExplanation · variables · model connection · reference+
Adds the adjacent half-cell diffusion resistances in series, conserving interfacial moisture flux across dissimilar ply materials.
Model connectionPopulates the moisture transport operator. A zero diffusivity on either side closes that interface in the current reduced-order model.
Theory basisLayered-composite diffusion treatment
Equation detailsExplanation · variables · model connection · reference+
Balances concentration storage in a cell with the moisture flux entering and leaving through its two faces.
Model connectionAssembled into the same theta-family integrator as the thermal equation, but with cell thickness rather than heat capacity as the storage matrix.
Theory basisFickian layered finite-difference/volume balance
Independent moisture boundaries
Equation detailsExplanation · variables · model connection · reference+
Writes prescribed concentration, insulated, film-transfer, and custom inward-flux conditions as a conductance and source on the surface control volume.
Model connectionTop and bottom selections are independent and are interpolated from columns 3, 5, and 7 of their respective surface tables.
Theory basisComposite environmental-exposure boundary modeling
Equation detailsExplanation · variables · model connection · reference+
Advances the heterogeneous diffusion system while allowing fully implicit or Crank–Nicolson weighting of the old and new operators and boundary sources.
Model connectionExecuted only when the moisture-diffusion flag is active. The solved field is clipped to nonnegative values and, where supplied, each node’s ply saturation limit.
Theory basisTransient Fickian diffusion solution
Equation detailsExplanation · variables · model connection · reference+
Prevents negative concentration and limits each node to its calibrated saturation concentration when a positive saturation value is supplied.
Model connectionApplied node-by-node after each moisture solve. When Csat is zero or omitted, only the nonnegative lower bound is imposed.
Theory basisEquilibrium moisture-content context
Hygroscopic strain coupling
Concentration is stored in percentage points to match the coefficient of moisture expansion used by the laminate model. Every ply may carry its own β1, β2, and β3.
Equation detailsExplanation · variables · model connection · reference+
Maps moisture change relative to the ply reference state into unconstrained hygroscopic strain in each local material direction.
Model connectionThe nodal field is fitted across each ply and optionally included in process resultants, local/global field recovery, and ply failure checks.
Theory basisNASA hygrothermal laminate mechanics
Scope boundary. The model is one-dimensional and Fickian. Edge drying, damage-assisted transport, two-stage sorption, concentration-dependent diffusivity, imperfect ply-interface partitioning, and stress-assisted diffusion require extension or calibrated effective parameters.
Theory references
- NASA composite moisture-diffusion formulation and environmental response reference.
- NASA, Prediction of moisture and temperature changes in composites during atmospheric exposure.
- Nettles, Basic Mechanics of Laminated Composite Plates, NASA RP-1351, including hygrothermal effects.
Workbench availability: released models, inputs and compatible study paths. The wider theory library includes reference formulations not available in every Workbench solve.