The volume fractions of polymer and gas, φp and φg respectively, are taken as uniform within an element. Material properties, such as density, specific heat, and thermal conductivity, are defined at the nodes, and may depend on temperature.
During each timestep, chemical reactions convert some portion of the polymer contained within each element to gas. The mass of this exchanged material is obtained by integrating the rate of change of polymer mass within an element i over the total element volume and multiplying by the time increment Δt:
This calculation applies the polymer mass balance equation (2) holding the element volume constant (and thus polymer velocity Wp set to zero) over the timestep.
Next, the volume of the polymer that has been lost from element i during this timestep is obtained by dividing the mass by polymer density. Assuming that the polymer density ρp is uniform within element i, the rate of loss of polymer volume is
 | (34) |
where T is a linear or quadratic function of r from Ti to Ti+1, depending on the basis functions chosen for the analysis. The rate of gain of gas volume by element i during this timestep is
 | (35) |
and the rate of change of total volume of this element is
 | (36) |