An explicit dynamic 2D finite element model of a composite under dynamic tribological loading is proposed. The software used for this kind of application manages contact conditions thanks to the Lagrange multipliers. The kind of contact is a deformable against rigid surface one. First of all due to ill-posedness of the classical Coulomb friction law, a regularized Coulomb friction law that allows local and global convergence of the models even under the presence of contact instabilities is proposed. This friction law is experimentally motivated and is similar to the simplified "Prakash-Clifton" law. In a second time the dynamic tribological behavior of the composite is studied by the mean of different models where the heterogeneities of the material are explicitly introduced. Those heterogeneous models stand for a description of the microscopic scale of the composite. A comparison is made between the results given by these heterogeneous models and the results obtained by the analysis of a homogeneous model. The elastic properties of the homogeneous model are obtained through classical homogenization process which is suitable here because the scale separation, difference between the size of the heterogeneities and the wavelength of the loading, is sufficiently important. The homogeneous model represents the macroscopic scale of the composite. Equivalence between heterogeneous models and the homogeneous one is straightforward if the contrast of Young's modulus between the heterogeneities and the matrix is sufficiently low and if the local contact dynamic is stable. This equivalence has been observed for different contact instabilities like slip-separated, and stick-slip-separated ones. When the equivalence between the models is not ensured, because of high contrast of elastic properties for example, an adaptation of the dynamic parameter of the friction law is necessary to retrieve this equivalence. Finally the determination of the stresses and their evolution along the time in the heterogeneities and in the matrix is performed thanks to the relocalization process. This process is mixing dynamic analysis of the homogeneous models and fast static calculations on heterogeneous model. This process has already been applied to structures submitted to static loading but to our knowledge this is the first attempt to use it for dynamic contact problems. So this work highlights a full multi-scale approach for composite under dynamic contact with friction loading.
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