An efficient reduced simulation of residual stresses in composite forming processes

An efficient simulation of thermal and mechanical models involved in thermosetting composites forming needs to overcome some numerical difficulties related to: (i) the multi-scale behaviour; (ii) the complex geometries involved needing too many degrees of freedom; (iii) the large time intervals where the solution has to be computed; (iv) the non-linearity of the involved evolution equations; (v) the numerous couplings… In this work, an efficient strategy based on a separated representation is proposed. This method enables to avoid the use of an incremental strategy and can lead to impressive computing time savings especially when the model involves fine meshes and very small time steps. The local non-linear chemical kinetics and its coupling with the global heat balance equation are naturally introduced in the separated representation algorithm. Moreover, the dependence of the thermal conductivity and the specific heat on the temperature and on the reaction advancement degree are also taken into account. Knowing the history of the temperature field, the separated representation is again used to solve the thermo-mechanical problem in order to determine the residual stresses.