As lithium-ion batteries are more and more widely used in electrical vehicles and hybrid electrical vehicles, their safety has become a primary concern due to their high energy densities and wide-range working conditions. Previously, experiments such as crush tests, have attempted to mimic the failure process of batteries under abuse conditions, but they usually only give binary pass/fail results and provide limited details of the root causes of failure. Recently, computational modeling has gained a lot of interest because it provides an efficient tool to capture fundamental mechanisms of battery failure. Nevertheless, most of existing models of battery safety either treat the battery as a homogeneous solid and only consider its mechanical response, or focus on the thermal-electrical coupling without consideration of mechanical influence. Here we present a three-dimensional multi-physics model of battery safety that is able to predict coupled mechanical, thermal, electrical and electrochemical responses of automobile lithium-ion batteries under mechanical abuse. This model resolves each component in unit cells of a large format Li-ion cell and applies one-way coupling between mechanical and other types of responses to accommodate the significant differences in time scales. In particular, the mechanical solver predicts the onset of internal or external short circuit at the initial stage of an impact, and then the coupled thermal and electrical solver captures the evolution of temperature and current distribution after short circuit initiation. The electrochemical response is captured by a spatially distributed equivalent circuit model, where empirical parameters are obtained from experimental data. This model has been applied to capture internal and external short circuits and subsequent thermal and electrical responses in different types of cells and modules. Various element formulations have been evaluated to achieve the computational efficiency that will be required for future pack simulations. Model predictions have been compared with experiment data, demonstrating the model capacity and providing insights into the failure mechanisms of batteries during an impact process.