Enabled local free strains
Equation detailsExplanation · variables · model connection · reference+
Adds the unconstrained strain caused by temperature change, moisture change, thermoset chemical shrinkage, and thermoplastic crystallization shrinkage. Independent binary switches let each contribution enter or leave the structural solve without changing the process solution.
Model connectionEvaluated at mapped bottom, middle, and top structural recovery points for every ply. These are the same free strains subtracted during stress recovery and failure evaluation.
Theory basisNASA hygrothermal laminate mechanics
Equation detailsExplanation · variables · model connection · reference+
Rotates each local engineering free-strain vector from material axes 1–2 into laminate axes x–y using the ply orientation.
Model connectionThe transformed field is multiplied by the ply’s damaged transformed stiffness Q̄d when process force and moment resultants are integrated.
Theory basisClassical lamina transformation relations
Mapping the process mesh to three structural nodes per ply
The transport mesh may contain any user-selected number of cells per ply, whereas structural visualization and field output retain exactly three recovery nodes per ply. R15 least-squares fits each process field to a linear function within its owning physical ply, then evaluates that fit at the bottom, middle, and top coordinates.
Equation detailsExplanation · variables · model connection · reference+
Finds the best constant and gradient for temperature, moisture, cure shrinkage, and crystallization shrinkage within one ply from all transport cells belonging to that ply.
Model connectionPreserves both the ply-average process state and its first through-thickness gradient while keeping the stress/strain field histories and animation mesh fixed at three structural nodes per ply.
Theory basisReduced-order process-to-structure mapping
Damaged laminate stiffness and process resultants
Equation detailsExplanation · variables · model connection · reference+
Integrates the current transformed stiffness of every ply through the laminate thickness. Progressive failure changes Q̄d and therefore rebuilds A, B, and D.
Model connectionThe same damaged stiffness used for mechanical equilibrium also weights the process resultants, so a new ply failure changes load redistribution and residual-stress restraint at the same accepted load.
Theory basisNASA classical laminate ABD formulation
Equation detailsExplanation · variables · model connection · reference+
Converts an otherwise free process strain into equivalent in-plane forces and moments representing the restraint imposed by the bonded laminate. A gradient contributes directly to process bending moment.
Model connectionRecomputed after any new damage state before same-load re-equilibration. The process-resultant history reports each component over the structural increments.
Theory basisHygrothermal force and moment resultants
Combined generalized equilibrium
Equation detailsExplanation · variables · model connection · reference+
Solves simultaneously for mid-plane strains and curvatures under the sum of enabled mechanical and process-equivalent resultants. This is the governing superposition step, not a postprocessed stress offset.
Model connectionUsed for a static mechanical state or at every progressive load increment. The mechanical-load flag may remove Nmech and Mmech while retaining process-only residual response.
Theory basisNASA generalized laminate equilibrium
Equation detailsExplanation · variables · model connection · reference+
Recovers the compatible global strain at any z and subtracts the enabled free strain before applying the current damaged stiffness. The result is the actual constrained ply stress used by failure criteria.
Model connectionEvaluated at the bottom, middle, and top of every ply and then transformed to local 1–2 axes. Top and bottom surface states govern the progressive failure check.
Theory basisClassical laminate stress recovery with hygrothermal strain
Equation detailsExplanation · variables · model connection · reference+
Reports total fields together with separately evaluated mechanical, thermal, moisture, cure-shrinkage, and crystallization-shrinkage contributions at the same increment and damaged material state.
Model connectionSupports the global, local, principal, and process-only field histories so CDS can display each contribution without reconstructing it outside the solver.
Theory basisProcess-induced residual-response decomposition
Progressive same-load update
At each accepted increment the solver recovers all three structural nodes per ply; checks both surfaces; evaluates the independent criterion assigned to that ply; degrades only newly activated stiffness families; rebuilds damaged ABD and process resultants; and re-equilibrates at the same combined mechanical–process load until no new event occurs.
Coupling boundary. The process solver is one-way with respect to structural damage in r15: process fields create structural strains and stresses, while ply damage changes the stiffness that restrains those fields. Damage does not yet change k3, cp, diffusivity, cure kinetics, or crystallization kinetics.
Auditable outputs
- Stress and strain histories: total, mechanical, thermal, and moisture contributions.
- Transport histories: mesh, fields, state, rates, heat, shrinkage, and surface interpolation.
- Structural process mapping: mapped states and active physical components.
- Process-only fields: global and local stress and strain.
- Process resultants: force and moment components at every structural increment.
Theory references
- Nettles, Basic Mechanics of Laminated Composite Plates, NASA RP-1351, including ABD and hygrothermal effects.
- NASA, Composite Cure Process Modeling and Simulations using Finite Element Analysis (2016).
- NASA/TM–20205009287, cure-induced residual stress development.
Workbench availability: released models, inputs and compatible study paths. The wider theory library includes reference formulations not available in every Workbench solve.