Moisture diffusion describes the evolution of water stored inside a material. Environmental relative humidity and internal moisture concentration are distinct quantities, linked by an equilibrium sorption relation. A boundary condition must state which quantity is imposed and how it maps to the selected material.
Different materials can hold different water mass fractions at the same equilibrium moisture potential. A heterogeneous model must state its transported variable, storage basis and interface conditions. Do not infer correct skin–core partitioning simply because each layer has its own diffusivity. Verify that the chosen solver supports the intended material transition.
A conditioned specimen generally starts with material-specific equilibrium moisture. Report whether uptake is relative to dry mass or to the initial conditioned state. Layer densities and thicknesses are needed to convert concentration fields into water mass. Check the integral mass balance against the two surface fluxes.
Sealed-edge, intact-skin assumptions exclude ingress through cracks, holes and open edges. Diffusion alone does not represent capillary flow, dissolution, salt transport or material degradation. Hygroscopic strain requires expansion coefficients and a reference moisture state in addition to the diffusion solution.
6.1 Moisture transport and environmental conditioning governing relation
Equation details — explanation, variables and reference
Water storage and flux must use consistent mass units. This balance does not prescribe a sorption relation, interface partition coefficient or constitutive flux law; those must be supplied and supported separately.
cw: water mass per material volume (kg/m³); Jw: water mass flux (kg/m²/s); z: through-thickness position (m); t: time (s). This notation is not the percentage-point concentration input used by every CDS branch.
Theory basis6.2 Heterogeneous moisture diffusion
06.1 Manuals · read online, preview or download →
05.5.1 / Moisture
Predict water uptake or release through a multi-material laminate using per-ply diffusivity, saturation, independent moisture boundaries, and the same interpolated process time grid used by heat transfer. Expand any equation for its physical meaning, variables, units, model connection, and theory source.
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
6.3 Connect moisture transport to stress response.
06.1 Manuals · read online, preview or download →
Theories / Moisture
Generate concentration histories, recover moisture expansion, assemble environmental resultants, and carry the coupled response into progressive laminate assessment.
Theory map
Models, equations, figures, and cross-referencesConcentration through thickness
Resolve uptake or release with temperature-dependent diffusivity and independent surface conditions.
Open diffusion theory →Hygroscopic free strain
Transform directional moisture-expansion coefficients and integrate environmental force and moment resultants.
Open hygrothermal CLT →Coupled properties and limits
Connect effective properties, recovered ply fields, calibration boundaries, and progressive failure assumptions.
Open effective properties →Complete reference
One continuous sequenceChapter review
Sealed-edge, intact-skin assumptions exclude ingress through cracks, holes and open edges. Diffusion alone does not represent capillary flow, dissolution, salt transport or material degradation. Hygroscopic strain requires expansion coefficients and a reference moisture state in addition to the diffusion solution.
References and source sections
References are retained with the formulations they support. Software instructions describe implementation scope; a cited source does not establish independent validation of a CDS calculation.
- 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.