Computational Analysis of Porous Structures Considering Coupled Diffusion Law With Large Volume Expansion


August 2023

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The increasing interest of silicon anodes for lithium-ion batteries (LIBs) can be attributed to their high charge capacity and recharge speed. Severe volume expansion from the lithiation process, however, results in pulverization and mechanical failure of the silicon anode. To both improve charge capacity and mechanical stability, designers have tested multiple geometries of nanostructures varying from nanotubes to silicon hollow-spheres. Although failure analysis can be performed by observing the surface morphology of these structures, the physical model of lithiation and corresponding stress analysis is highly limited, not only because geometries of these structures are quite complex to mode, but also because it requires modification of the diffusion law due to large volume expansion which could alter the chemical potential. In this work, we will formulate a modified coupled diffusion law to consider large volume expansion which the Si anode experiences during lithiation and delithiation. We incorporate this generalized diffusion equation into commercial package (ABAQUS) using user-subroutines, in order to develop a physical model under various environments. Through a series of test cases, we can analyze the effects of large deformation on the diffusion profile, as well as the effects of changing geometries on the stress profile. Deformations and stress gradients are shown to be able to expedite the diffusion process, while drastically decreasing the area along the diffusion path is shown to result in stress concentrations. Based on these physical insights, we apply it to models with realistic porous geometries to investigate general design guidelines: columnar void structures along parallel to the diffusion path could alleviate stress concentration, compared to misaligned voids. Structures with gradual area changes such as spherical voids could have a more relaxed stress field. This multi- physical modeling technique could allow us to analyze structural stability and also serve as a standard to develop nanostructures for optimal design.



Engineering, Mechanical