Battery electrode particle fracture due to stress generation is a critical mechanism causing capacity fade, and thus reducing battery life. This paper develops a nonlinear adaptive observer for lithium-ion battery state of charge (SOC), electrode particle stress, and solid phase diffusivity estimation using a high-fidelity coupled single particle-mechanical stress model, where the stress submodel captures stress development during lithium-ion intercalation and deintercalation. Simultaneous state and parameter estimation based on coupled single particle and mechanical stress model is extremely challenging because the coupled model is given by highly nonlinear partial differential equations. We address this problem by reducing the coupled model to a nonlinear finite dimensional system. The key novelty of this paper is a nonlinear internal state and parameter estimation methodology, from which the internal stress and the state of health-related parameters are monitored from real-time electric current and terminal voltage measurements. Numerical studies on simulation and experimental data have been conducted to illustrate the performance of the proposed estimation scheme.