5. Theory Documentation

5.1. Solver

The solver is based on Darcy’s law.

\[\overline{u} = -\frac{k}{\mu} * \nabla{}p\]

The variable \(k\) refers to the fabric permeability set for the material. \(μ\) refers to the resin viscosity, \(p\) is the pressure, and \(\overline{u}\) is the flow velocity.

At each increment, Darcy’s law is used to calculate the pressure of each node. The pressure gradient is then used to calculate the rate of flow, which is then used to propogate the flow front.

5.2. Cure Kinetic Equations

The solver supports three Cure Kinetic Equations for the modelling of resin cure. These are Nth Order, Kamal Sourour and Autocatalytic. See Cure Kinetics Equations for thermosets for more information.

Warning

In versions prior to 2025R2, only Kamal Sourour equation is fully supported.

5.3. Viscosity

When cure dependent viscosity is defined, the viscosity of the resin will update at every iteration. In this case, the viscosity of the resin is dependent on both the temperature and the degree of cure. This relationship is expressed using the following equation:

\[v = v_0 \times{} (\frac{X_g}{X_g-X})^{(A+B \times{} X)}\]

where:

\(v_0\) is the initial viscosity at the start of the simulation,

\(X\) is the current degree of cure, which is determined by the selected cure kinetic equation for the resin,

\(X_g\) represents the degree of cure at gelation, and

\(A\) and \(B\) are temperature and cure-dependent parameters.

The parameters A and B are defined as:

\[A = a_1 \times{} T + a_2,\]

\[B = b_1 \times{} T + b_2.\]

where \(T\) is temperature

Here \(a_1\), \(a_2\), \(b_1\), \(b_2\) are constants fitted from resin rheometer test results. These parameters characterise how the resin’s viscosity evolves with temperature and curing progression.

Note

Ensure that the rheometer test results are always fitted in Kelvin.