In this paper an adaptive multilevel mesh refinement method, coupled with the Zienkiewicz and Zhu a posteriori error estimator, is applied to solid mechanics with the objective of conduct reliable nonlinear studies in acceptable computational times and memory space. Our automatic approach is first verified on linear behaviour, on 2D and 3D simulations. Then a nonlinear material behaviour is studied. Advantages and limitations of the local defect correction method in solid mechanics problems in terms of refinement ratio, error level, CPU time and memory space are discussed. This kind of resolution is also compared to a global h-adaptive resolution.