Shape Optimization for Lithium-Ion Battery with Porous Electrodes

In this presentation, we introduce a gradient-based shape optimization framework to design porous electrodes for maximum energy storage. Lithium-ion batteries are becoming an increasingly important energy source and storage device. Large surface area that advocates high reaction rates often leads to small porosities that deteriorate electrochemical transport, which significantly restricts ion penetration depth, limiting the material utilization in planar electrodes. Consequently, architected electrodes are required to optimize performance. We consider a model with two materials, namely porous electrode and pure electrolyte. Density-based topology optimization with continuous material volume fraction has previously been implemented on lithium-ion battery system for both half-cell and full-cell model to maximizes its energy storage. Despite the capability of producing complex interdigitated structures, an appropriate penalization scheme for intermediate materials is required for the optimizer to provide near binary designs. Setting up such a penalization is often time-consuming due to the large number of design-dependent variables that affect the forward model differently. Alternatively, the shape optimization approach used in this work produces binary designs naturally by morphing conformal meshes, circumventing inaccuracies associated with fuzzy interfaces. Shape sensitivities are computed via the adjoint method and leveraging automatic differentiation. The optimization problem is solved using a nonlinear programming technique. In this presentation, we perform shape optimization on a half-cell model to maximize its energy storage when a fixed charging current is applied. We study multiple arrangements of physical parameters and compare their performance against a monolithic electrode. Both 2D and 3D results are presented.