In this study, we have performed density functional theory calculations and ab initio molecular dynamic simulations to investigate the kinetics and dynamics of the lithiation processes of the doped and undoped c-Si anodes for their application in Li-ion batteries.  Our ab initio molecular dynamic simulations showed that the lithiation process of c-Si can be remarkably improved by phosphorus-doping while that for the boron-doped Si is simply comparable to the performance of the undoped Si electrode.  To explore the physical origins of the enhanced rate capability of the phosphorus-doped Si anode, we calculated the insertion and migration energy barriers of Li ions in c-Si, and then simulated the mechanical response of the Li-inserted Si matrix under different hydrostatic stresses.  Our calculated results showed that boron-doping can effectively lower down the insertion barrier of a Li atom into the Si-matrix but phosphorus-doping may lead to the increment of the Li insertion energy in c-Si.  Furthermore, although the diffusion energy barriers of Li may slightly decrease (increase) by ~0.2 eV in the phosphorus (boron)-doped Si matrix, these changes were found to be highly localized within the range of the nearest-neighbor distance.  Accordingly, the enhanced lithiation rate in the phosphorus-doped Si electrode cannot be attributed to the increased Li diffusion rate or the reduction of the insertion energy barriers of Li atom into the c-Si electrode.  On the other hand, our calculated mechanical response of the Li-inserted Si matrix showed that the phosphorus-doped Si matrix can become more ductile and more easily undergo plastic deformation upon hydrostatic stresses, but on the contrary, the Si matrix may become more brittle and stiffer as it was doped with boron atoms.  Our ab initio molecular dynamic simulations also showed that the phosphorus-doped Li-inserted Si matrix can easily undergo structure amorphorization within 10 ps, but the boron-doped and undoped Si matrices can still or mostly hold in the diamond structures within the same elapsed time of MD simulations.  These results clearly indicate that mechanical softening of the Si bond network can be one of the major reasons that leads to the enhanced lithiation rate of the phosphorus-doped Si electrode.