In order to 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 (i.e. strain) on the operation of an electrochemical system. There are many different models in use that can predict the electrochemical performance of these devices under a variety of operating and design conditions. However, many of these models assume a constant porosity and do not take into consideration the effects of a variable porosity on the porous electrode during cycling and what effects that may have on performance. In recent years, electrodes have been developed that show significant volume changes during intercalation and deintercalation, which are unable to be accurately predicted using these constant porosity models.

Here, a mathematical battery model is presented that incorporates the dimensional and porosity changes in porous electrodes caused by volume changes in the active material during intercalation (e.g., lithium into carbon or silicon). Porosity and dimensional changes in an electrode can 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 were coupled with the mechanical properties of porous electrodes to link dimensional and porosity changes to stresses and the resulting resistances that occur during the intercalation process. The stress-strain relationships used in this model are from previous works, which are used to predict porosity and dimensional changes, and were established by comparing thermal rock expansion and electrode expansion due to intercalation. Several different cases modeled after new battery electrode technologies are examined and operating curves are predicted based off of standard equilibrium potentials.