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This paper proposes an analytical model for the Boussinesq problem between a tilted rigid punch and an elastic half space to enable the analysis of elastic deformations inside and outside a contact area. Inside the contact area, two types of pressure distributions are applied: one generates a flat elastic deformation, and the other produces a tilte...
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Citations
... However, these models are also based on the phenomenological approach developed in [17,18]. At the same time, the continuum mechanics papers devoted to contact interaction are mostly focused on study of the contact and internal stress distribution and the energy losses for various loading conditions and type of motion [19][20][21][22][23], thermo-effects [24] and wear [25]. This lack between the fields indicates that it is necessary to use the contact mechanics models for analysis of the system dynamics. ...
This paper investigates the influence of the material properties on the deceleration dynamics of a deformable cylinder rolling with slipping on a half-space of the same material. The interaction of the cylinder and the half-space is described by the 2D quasistatic contact problem of viscoelasticity (Goryacheva: J Appl Math Mech 37(5):877–885, 1973; Contact mechanics in tribology. Kluwer, Dordrecht 1998) which includes as limiting cases the absolutely rigid and elastic materials. Full dynamical analysis of the problem including the phase portrait, the dependence of the deceleration distance on the mechanical properties of the contacting bodies and on the friction coefficient is provided. The qualitative features of deceleration are justified by asymptotic analysis.
Contact usually results in stress concentration which can easily cause the yield of materials and structures. The classic elastic–plastic yield criterion needs to utilize stress or strain field for calculation. However, most advanced full-field measurement methods output the displacement as the original data, and the fitting from displacement to strain will induce error accumulation in applications. In this paper, a plastic domain characterization method is developed that can directly judge the elastic–plastic state of materials based on the full-field displacement and neural network. By establishing and training a three-layer-based neural network, the relationship between the displacement and the elastic/plastic stage of the sampling points is modeled. A physical model is formulated based on the yield criterion and embedded in the layer of the network, which can increase the convergence rate and accuracy. Only the displacements of the contact member are required in this method, which can be easily measured by the optical metrologies. The performances of the developed method are carefully discussed through simulated data and real-world tests. Results show that the method can accurately identify the plastic domain during the tests.
This paper considers the receding contact problem between an exponentially graded layer and a homogeneous layer under the indentation of a tilted rigid flat-ended punch. In the presence of an offset load deviated from the symmetry axis of the rigid punch, the contact pressures both under the rigid punch and along the receding contact interface between the layers lose symmetry. Depending on the magnitude of eccentricity, either complete or incomplete contact may take place under the rigid flat-ended punch, whereas a receding type of contact always occurs along the interface separating the graded and the homogeneous layers. Fourier integral transforms help to convert the governing equations and mixed boundary conditions of the double-contact problem into dual Fredholm integral equations of the second kind with Cauchy-type singular kernels. Gauss–Chebyshev and Gauss–Jacobi numerical quadratures are subsequently employed to discretize and collocate the dual singular integral equations, together with the four force and moment equilibrium equations, for the complete and incomplete contact, as well as the transitional status corresponding to the critical load eccentricity. Extensive parametric studies indicate that the critical load eccentricity depends on the property gradation of the graded layer and the layer-thickness ratio, but not on the magnitude of the indentation load. The extent of contact both under the rigid flat-ended punch and along the receding contact interface is also independent of the magnitude of the indentation load. The results suggest reasonable departures from the contact properties of a homogeneous half-plane under a tilted rigid flat-ended punch, indicating the valuable information on optimizing the double-contact properties in terms of the property gradation and layer-thickness ratio under a given eccentricity.