Mechanical failure and its interference with electrochemistry are a roadblock in deploying high-capacity electrodes for Li-ion batteries. Computational prediction of the electrochemomechanical behavior of high-capacity composite electrodes is a significant challenge because of (i) complex interplay between mechanics and electrochemistry in the form of stress-regulated Li transport and interfacial charge transfer, (ii) thermodynamic solution non-ideality, (iii) nonlinear deformation kinematics and material inelasticity, and (iv) evolving material properties over the state of charge. We develop a computational framework that integrates the electrochemical response of batteries modulated by large deformation, mechanical stresses, and dynamic material properties. We use silicon as a model system and construct a microstructurally resolved porous composite electrode model. The model concerns the effect of large deformation of silicon on charge conduction and electrochemical response of the composite electrode, impact of mechanical stress on Li transport and interfacial charge transfer, and asymmetric charging/discharging kinetics. The study captures the rate-dependent, coupled electrochemomechanical behavior of high-capacity composite electrodes that agrees well with experimental results.