Geodesic
On some models of indentation for functionally-graded coatings
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 4, pp. 421-432

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The paper presents approximate models of deformation for an inhomogeneous elastic strip. Approximate models reflect the distribution features of the inhomogeneous structure properties over the thickness. The models are based on hypotheses about the nature of the change in the components of the displacement field, which allows to consider arbitrary laws of heterogeneity: continuous, as well as discontinuous or having a strong gradient. Solutions of the contact problem for different inhomogeneity laws are constructed. Comparative analysis of the models is carried out. The results of the solutions are compared with the solution based on the FE model. 
@article{ISU_2018_18_4_a5,
     author = {A. O. Vatulyan and D. K. Plotnikov and A. A. Poddubny},
     title = {On some models of indentation for functionally-graded coatings},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {421--432},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2018_18_4_a5/}
}
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A. O. Vatulyan; D. K. Plotnikov; A. A. Poddubny. On some models of indentation for functionally-graded coatings. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 4, pp. 421-432. http://geodesic.mathdoc.fr/item/ISU_2018_18_4_a5/