The dual-primal finite-element tearing and interconnecting (FETI-DP) method is combined with the Newton-Raphson method to expand the capability and improve the efficiency of 3-D finite-element analysis (FEA) of nonlinear electromechanical problems. Despite its modeling capability and high degree of accuracy, FEA has high computational complexity, especially for nonlinear analysis. The FETI-DP method is a robust domain decomposition method, which has been enhanced and applied to solve electromechanical problems involving linear materials. In this paper, the FETI-DP method is extended with the Newton-Raphson method to address problems involving nonlinearity and saturation. Using parallel computing techniques, the total computation time is reduced significantly. Linear and nonlinear regions are separated using the FETI-DP method. This further improves simulation efficiency and flexibility. Cubic splines and relaxation techniques are adopted to ensure stable and fast convergence of the Newton-Raphson method. The performance of the proposed method is compared with infolytica's MagNet, a commercial 3-D FEA solver.