Material data and constitutive state

Converts each calibrated kinetic prefactor and activation energy into a temperature-dependent reaction-rate constant. Absolute temperature must be used.

Model connectionEvaluated from the current thermal iterate before the selected cure law is advanced; it therefore couples cure rate to the transient temperature field.

Theory basisSourour–Kamal cure kinetics

Represents a non-autocatalytic reaction whose rate decreases as the unreacted fraction is consumed.

Model connectionThe nth-order cure law. The returned nonnegative rate is passed to the bounded irreversible state update.

Theory basisThermoset kinetic model basis

Adds an autocatalytic branch that grows with degree of cure to the nth-order branch, allowing an isothermal rate peak after the reaction begins.

Model connectionThe Kamal–Sourour cure law, also used as the base reaction law before vitrification limitation is applied.

Theory basisSourour–Kamal autocatalytic model

Uses a single autocatalytic rate constant with reacted- and unreacted-fraction powers. A small positive numerical floor on α prevents a zero-to-a-negative-power singularity.

Model connectionThe Prout–Tompkins cure law. It shares the same bounded state update, heat source, and shrinkage mapping as the other cure laws.

Theory basisNASA composite cure-process formulation

Suppresses the chemical Kamal–Sourour rate as cure passes a calibrated vitrification threshold. It is an empirical mobility correction, not an independently predicted glass-transition model.

Model connectionThe diffusion-limited cure law. The limited rate, rather than the raw chemical rate, advances α and produces reaction heat.

Theory basisCure-process modeling and vitrification context

Advances cure over one transport step without consuming more than the remaining unreacted fraction. The outer bounds enforce irreversibility and α≤1.

Model connectionApplied independently at every active thermoset node inside each staggered thermal/kinetic iteration. The reported rate is (αⁿ⁺¹−αⁿ)/Δt.

Theory basisNumerical cure-process integration context

Converts cure progress and mass-specific total heat of reaction into a volumetric source for the one-dimensional heat equation.

Model connectionIncluded in the thermal right-hand side only when the cure-exotherm option is enabled and reported separately as cure heat generation.

Theory basisNASA composite cure-process heat balance

Maps the increase in degree of cure into an anisotropic contraction in the ply material axes. Positive calibrated shrinkage magnitudes therefore produce negative free strain.

Model connectionStored at each process node, fitted across each ply, transformed to laminate axes, and optionally included in the process force and moment resultants.

Theory basisNASA cure-induced residual-stress study

Expresses current absolute crystallinity as a fraction of the maximum crystallinity available to the selected thermoplastic grade.

Model connectionThe normalized state is used by both Nakamura branches and the bounded integration rule; the crystallinity history retains the absolute crystallinity X.

Theory basisNakamura nonisothermal crystallization

Combines Arrhenius temperature dependence with a calibrated undercooling function that vanishes at the melting temperature and is evaluated only inside the Tg–Tm process window.

Model connectionEvaluated at every active thermoplastic transport node using the current thermal iterate. Outside Tg<T<Tm, R15 sets the crystallization rate to zero.

Theory basisPEEK dual-mechanism crystallization model

Differentiates the Nakamura form of Avrami crystallization to obtain an instantaneous nonisothermal rate in the normalized state. Numerical floors protect the logarithm near ξ=0 and ξ=1.

Model connectionThe single-branch crystallization law uses its calibrated rate directly. The rate is then advanced using the irreversible bounded update.

Theory basisNakamura rate formulation

Blends two independently calibrated Nakamura branches to represent two-stage crystallization with one bounded weighting factor.

Model connectionThe dual-branch crystallization law. The same combined rate controls crystallinity growth, latent heat release, and the subsequent shrinkage state.

Theory basisVelisaris–Seferis dual-mechanism PEEK model

Integrates the normalized rate over the process step without consuming more than the remaining crystallizable fraction, then maps the state back to absolute crystallinity.

Model connectionApplied independently at every active thermoplastic node. The crystallization-rate history reports (Xⁿ⁺¹−Xⁿ)/Δt rather than the normalized branch rate.

Theory basisNonisothermal Nakamura state evolution

Converts absolute crystallinity growth and the calibrated heat of crystallization into a volumetric heat source.

Model connectionIncluded in the heat equation only when the crystallization-exotherm option is enabled and reported as crystallization heat generation.

Theory basisPEEK crystallization calorimetry basis

Maps crystallinity gained after the initial state into an anisotropic contraction in each ply material direction.

Model connectionStored in the process-shrinkage history, fitted through each ply, and optionally added to the laminate process resultants and local failure-stress recovery.

Theory basisProcess-shrinkage residual-stress framework