Application of PGD separation of space to create a reduced order model of a lithium-ion cell structure

Lithium-ion cells can be considered a laminate of thin plies comprising the anode, separator, and cathode. Lithium-ion cells are vulnerable toward out-of-plane loading. When simulating such structures under out-of-plane mechanical loads, subordinate approaches such as shells or plates are sub-optimal because they are blind toward out-of-plane strains and stresses. On the other hand, the use of solid elements leads to limitations in terms of computational efficiency independent of the time integration method. In this paper, the bottlenecks of both (implicit and explicit) methods are discussed, and an alternative approach is shown. Proper generalized decomposition (PGD) is used for this purpose. This computational method makes it possible to divide the problem into the characteristic in-plane and out-of-plane behaviors. The separation of space achieved with this method is demonstrated on a static linearized problem of a lithium-ion cell structure. The results are compared with conventional solution approaches. Moreover, an in-plane/out-of-plane separated representation is also built using proper orthogonal decomposition (POD). This simply serves to compare the in-plane and out-of-plane behaviors estimated by the PGD and does not allow computational advantages relative to conventional techniques. Finally, the time savings and the resulting deviations are discussed.