Numerical prediction of the foam structure of polymeric materials by direct 3D simulation of their expansion by chemical reaction based on a multidomain method

The quality of thermosetting polymer foams (like polyurethane foam, used for example in automotive industry) mainly depends on the manufacturing process. At a mesoscopic scale, the foam can be modelled by the expansion of gas bubbles in a polymer matrix with evolutionary rheological behaviour. The initial bubbles correspond to germs, which are supposed quasi-homogeneously distributed in the polymer. An elementary foam volume (∼1 mm3) is phenomenologically modelled by a diphasic medium (polymer and immiscible gas bubbles). The evolution of each component is governed by equations resulting from thermodynamics of irreversible processes: the relevant state variables in gas, resulting from chemical reaction creating carbon dioxide (assimilated then to a perfect gas), are pressure, temperature and conversion rate of the reaction. The number of gas moles in each bubble depends on this conversion rate. The foam is considered as a shear-thinning viscous fluid, whose rheological parameters evolve with the curing reaction, depending on the process conditions (temperature, pressure). A mixed finite element method with multidomain approach is developed to simulate the average growth rate of the foam during its manufacture and to characterize the influence of the manufacturing conditions (or initial rheological behaviour of the components) on macroscopic parameters of the foam (cell size, heterogeneity of porosity, wall thickness).