Hybrid Electric Vehicle (HEV) current profiles are dynamic, consisting of repeated charge and discharge pulses. Accurate prediction of the battery response to these inputs requires models with open circuit voltage and Butler-Volmer kinetic nonlinearities. This paper derives a nonlinear, electrolyte-enhanced, single particle model (NESPM) that includes aging due to solid electrolyte interphase layer growth. The model is validated with experimental full charge, discharge, HEV cycle, and aging data from 4.5 Ah graphite/LiFePO4 cells. The NESPM is capable of operating up to 3C constant charge discharge cycles and up to 25C and 10 s charge discharge pulses within 35-65% state of charge (SOC) with less than 2% error. The NESPM aging model is then simplified to obtain explicit formulas for capacity fade and impedance rise that depend on the battery parameters and current input history. The formulas show that aging increases with SOC, operating temperature, time, and root mean square (RMS) current. The formula predicts that HEV current profiles with the (i) same average SOC, (ii) small SOC swing, (iii) same operating temperature, (iv) same cycle length, and (v) same RMS current, will have the same cell capacity fade. (C) 2015 Elsevier B.V. All rights reserved.