A chemo-mechanical model for fully-coupled lithiation reaction and stress generation in viscoplastic lithiated silicon

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Development of stresses in silicon (Si) anodes of lithium-ion batteries is strongly affected by its mechanical properties. Recent experiments reveal that the mechanical behavior of lithiated silicon is viscoplastic, thereby indicating that lithiation-induced mechanical stresses are dependent on the lithiation reaction rate. Experimental evidence also accumulates that the rate of lithiation reaction is conversely affected by the magnitude of mechanical stresses. These experimental observations demonstrate that lithiation reaction and stress generation in silicon anodes are fully coupled. In this work, we formulate a chemo-mechanical model considering the two-way coupling between lithiation reaction and viscoplastic deformation in silicon nanoparticle anodes. Based on the model, the position of the lithiation interface, the interface velocity, and the lithiation-induced stresses can be solved simultaneously via numerical methods. The predicted interface velocity is in line with experimental measurements reported in the literature. We demonstrate that the lithiation-induced stress field depends on the lithiation reaction through two parameters: the migration velocity and the position of the lithiation interface. We identify a stress-mitigation mechanism in viscoplastic silicon anodes: the stress-regulated lithiation reaction at the interface serves as a “brake” to reduce the interface velocity and mitigate the lithiation-induced stresses, protecting the Si nanoparticle anode from being subjected to excessive mechanical stresses.