Inexact Newton is a popular technique for solving large sparse nonlinear system of equations. However,  stagnation in the nonlinear residual curve might occur when the nonlinearities in the system are not balanced. In this talk, we will revisit the convergence results of Newton's method and explain why the nonlinear preconditioning techniques can improve the convergence of Newton iterations under special assumptions.  Based on the preliminary analysis result, we propose a nonlinear elimination preconditioned inexact Newton method for the numerical simulation of diseased human arteries with a heterogeneous hyperelastic model. We show numerically that the method performs quite well for solving this nonlinearly difficult problem.