One of the most important requirements in modern engines design is the minimization of the clearance between rotating and static components. It has been shown in several studies that this clearance minimization increases the aerodynamic efficiency of the internal flow leading to significative improvement of the engine performances. During engine operation due to several phenomena such as thermal dilatations of the parts, misalignment of the shaft due to centrifugal effects, gravity effects during manouvers and unbalanced parts, contact interactions between the rotating blades and the abradable seal of the surrounding casing can occur. It has been observed that these contact interactions can lead to undesirable consequences that can affect significantly the performances of the engine. This thesis is concerned with the modeling of wear phenomena on an engine blade proposing an alternative approach for the geometry update. The basic idea of this approach is instead of re-meshing or eliminating at each iteration the worn out elements such as it is performed in the traditional remeshing and killing element methods for wear treatment problems, is to interpolate by a polynomial function the structural matrices in correspondence of a small subset of interpolating points that correspond to different amounts of wear and recover the structural matrices for all other configurations by the build polynomial function. The advantage of this technique is the simplicity of the operations involved at each iteration. Indeed at each iteration a simple algebraic sum is performed on the constant interpolating matrices to recover the solution for all the blade configurations due to wear evolution. Thus, there is no need to keep memory of the whole wear evolution history and the simplicity of the involved operations leads to significant decrease in the computational effort and memory storage. In the performed analysis this proposed approach is fully validated in case of a 1D structure. To perform such analysis a FEM model of a clamped beam has been exploited. In the test conditions the beam undergoes to contact interactions with a rigid moving wall. The wall is moving both in normal direction penetrating the blade tip and transversally with a constant upward velocity inducing blade vibrations in both the directions. The contact interactions are modelled with both Lagrange multipliers and Penalty methods. In a second moment the wear is added to the analysis. Before implementing the proposed approach, traditional re-meshing techniques have been applied to the problem in order to recover reliable results to use as term of comparison and validation for the proposed approach results. Accuracy and reliability of the proposed approach is demonstrated by different test case results involving different conditions, such as soft contact interactions and severe interactions. A focus have been reserved also to the discussion of the important savings in the computational cost registered. Finally, some suggestions and ideas for future developments and extension of such technique to 2D structures are given. All the above mentioned algorithms and simulations have been implemented exploiting Python language.