A good spatial discretization is of prime interest in the accuracy of the Finite Element Method. This paper presents a new refinement criterion dedicated to an h-type refinement method called Conforming Hierarchical Adaptive Refinement MethodS (CHARMS) and applied to solid mechanics. This method produces conformally refined meshes and deals with refinement from a basis function point of view. The proposed refinement criterion allow adaptive refinement where the mesh is still too coarse and where a strain or a stress field has a large value or a large gradient. The sensitivity of the criterion to the value or to the gradient ca be adjusted. The method and the criteria are validated through 2-D test cases. One limitation of the h-adaptive refinement method is highlighted: the discretization of boundary curves.