In the analysis of instrumented indentation data, it is common practice to incorporate the combined moduli of the indenter (Ei) and the specimen (E) in the so-called reduced modulus (Er) to account for indenter deformation. Although indenter systems with rigid or elastic tips are considered as equivalent if Er is the same, the validity of this practice has been questioned over the years. The present work uses systematic finite element simulations to examine the role of the elastic deformation of the indenter tip in instrumented indentation measurements and the validity of the concept of the reduced modulus in conical and pyramidal (Berkovich) indentations. It is found that the apical angle increases as a result of the indenter deformation, which influences in the analysis of the results. Based upon the inaccuracies introduced by the reduced modulus approximation in the analysis of the unloading segment of instrumented indentation applied load (P)–penetration depth (δ) curves, a detailed examination is then conducted on the role of indenter deformation upon the dimensionless functions describing the loading stages of such curves. Consequences of the present results in the extraction of the uniaxial stress–strain characteristics of the indented material through such dimensional analyses are finally illustrated. It is found that large overestimations in the assessment of the strain hardening behavior result by neglecting tip compliance. Guidelines are given in the paper to reduce such overestimations.

We give a first contribution to the homogenization of many-body structures that are exposed to large deformations and obey the noninterpenetration constraint. The many-body structures considered here resemble cord-belts like they are used to reinforce pneumatic tires. We establish and analyze an idealized model for such many-body structures in which the subbodies are assumed to be hyperelastic with a polyconvex energy density and shall exhibit an initial brittle bond with their neighbors. Noninterpenetration of matter is taken into account by the Ciarlet-Nečas condition and we demand deformations to preserve the local orientation. By studying Γ-convergence of the corresponding total energies as the subbodies become smaller and smaller, we find that the homogenization limits allow for deformations of class special functions of bounded variation while the aforementioned kinematic constraints are conserved. Depending on the many-body structures’ geometries, the homogenization limits feature new mechanical effects ranging from anisotropy to additional kinematic constraints. Furthermore, we introduce the concept of predeformations in order to provide approximations for special functions of bounded variation while preserving the natural kinematic constraints of geometrically nonlinear solid mechanics.

Une prise en compte simplifiée et macroscopique de l’usure des matériaux abradables dansles moteurs d’avion est proposée. Ces revêtements sont positionnés sur les carters auniveau des sommets d’aubes. Plus spécifiquement, il s’agit d’inclure, au sein d’uneprocédure d’intégration en temps explicite dédiée à l’étude de l’interaction aube-carterpar contact mécanique, la prise en compte de l’évolution du profil d’usure en temps réel.Ce profil est mis à jour grâce à une loi de comportement plastique de l’abradable. Afin demaintenir des temps de calcul adaptés à des analyses paramétriques, les équations dumouvement de l’aube étudiée sont projetées sur un espace réduit construit selon laprocédure de synthèse modale de Craig-Bampton. Ce choix est motivé par la possibilité detraiter les contraintes de contact et les conditions d’usure directement dans l’espaceréduit. Il est montré que le comportement de ce matériau est à l’origine de zonesd’interaction dangereuses vis-à-vis de la stabilité de l’aube. Sous certaines conditions,l’utilisation de revêtements abradables semble très défavorable.

This work presents a rigorous three-dimensional finite element procedure to analyze belt transmission systems. The frictional contact behavior between the belt and the pulley, which accounts for the power loss of the system and the wear of the belt, is investigated in detail. In addition to adopting the transformation matrix to satisfy the geometric conditions on the contact surfaces, the proposed procedure also uses the modified elements with incremental Wilson displacement modes to improve the accuracy due to bending at the end zones of the contact area for the belt. To demonstrate the accuracy and feasibility of the proposed procedure, the analyses for flat and V belt drives are carried out. Excellent correlations between the calculated results and referenced theoretical/experimental solutions are found. The influences of friction coefficients on the deformation, normal and tangential contact forces on the contact surfaces are studied as well. Those will be helpful for the estimation of wear properties and operation efficiency for belt transmission systems.