A phenomenological Li-ion cell degradation model, pertaining to charge-discharge cyclic fatigue, is proposed and validated. It is known that Solid Electrolyte Inter-phase (SEI) formation on the particle surfaces consumes active Li leading to capacity loss. The problem is further aggravated by the creation of fresh surfaces by the fracture that develops as a result of intercalation induced stresses. In addition, fracture could result in isolation of chunks of electrode material or SEI could electronically isolate certain electrode material zones, both essentially rendering the active Li or electrode material ineffective. The degradation leads to increase in electronic resistance and decrease of ionic conductivity as well as diffusivity. Central to the model is a parameter expressed as the normalized reaction surface area, diminishing with charge-discharge cycles. Here, we develop phenomenological evolution expressions for the Fracture, SEI formation and Isolation, and incorporate them in Newman's Porous Composite Electrode framework. The model is implemented in the battery module of COMSOL. Notably, the utility of a lumped parameter ‘ΔSOC*SOCmean’, based on the State of Charge (SOC) is brought out.

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We develop novel closed-form empirical relations to estimate the dynamic pull-in parameters of electrostatically actuated linearly tapered microcantilever beams driven by a step-function voltage. A computationally efficient single degree-of-freedom model is employed in the setting of an energy-based technique to characterize the dynamic pull-in of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The model exploits the fundamental mode shape of the respective nonprismatic geometry obtained using the differential transform technique. A unique surface fitting model is proposed to characterize the variations of both pull-in displacement and pull-in voltage over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. The empirical estimates of dynamic pull-in parameters are validated against 3D finite element simulations and available data in the literature. Excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the preliminary design of tapered microcantilever beams.

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