On the Validation of the Proper Generalized Decomposition Method with Finite Element Method: 3D Heat Problem Under Cyclic Loading

Polymers are widely used in machine design, biomedical engineering, aircraft, and mechatronics. Certainly, these products are subjected to thermo-mechanical loading. For this reason, dealing with the fatigue criteria for viscous polymers is essential. In fact, this requires a large number of cycles to reach the accommodated cycle. These materials have a thermoviscoelastic behavior that has already been studied within the Finite Element Method (FEM). However, a very large computation time or a non-convergence has been noticed. In this paper, we considered a 3D thermal problem under cyclic load in which three main parts are considered. Firstly, the problem is studied using the Proper Generalized Decomposition method (PGD) where it shows a gain in the computation time compared to the classical FEM with a relative error less than 5%. Secondly, different time scales are taken into consideration: the cyclic time (load) and the characteristic one (material properties), where different relaxation times lead to various responses of the polymer. A link between these times should be established. Finally, the effect of the spatial point position on the evolution of the temperature within the domain is investigated.