A mathematical model is presented that predicts the dimensional and porosity changes in a porous electrode caused by volume changes in the active material during intercalation (e.g., lithium into carbon or silicon). Porosity and dimensional changes in an electrode significantly affect the resistance of the battery during cycling. In addition, volume changes generate stresses in the electrode, which can lead to premature failure of the battery. Here, material conservation equations are coupled with the mechanical properties of the porous electrode to derive governing relations that link dimensional and porosity changes to stresses that occur during the intercalation process. The stress-strain relationships used in this model, which are needed to predict porosity and dimensional changes, have been established by examining the similarities between thermal rock expansion (e.g., the exchange of thermal energy with the rock) and electrode expansion due to intercalation. In order to understand and accurately predict the behavior of electrochemical devices, it is necessary to develop sophisticated models that take into consideration transport processes, electrochemical phenomena, mechanical stresses, and structural deformations on the operation of an electrochemical system. There are many models in the literature that can predict the electrochemical performance of these devices (e.g., voltage versus time) under a variety of operating (e.g., current) and design (e.g., electrode thickness) conditions. Porosity of the porous electrode is often assumed constant since the volume change during the intercalation reaction can be small.

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