PSI - Issue 59

Hryhorii Habrusiev et al. / Procedia Structural Integrity 59 (2024) 494–501 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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The fig. 6 illustrates the dependence of the radius a of the contact area on the parameter 1  , ie on the characteristics of the initial deformation field. Graphs are built for case 2 R  , 0 a r  .

Fig. 6. Dimensions of the contact area

5. С onclusions The shape of the indenter significantly affects the magnitude and nature of the distribution of stresses and displacements. In particular, for indenters without a plane domain at the footing the extreme values of contact stresses occur in the center of the contact area. The appearance of a flat area causes the extremum points to shift to the edge of the contact area and reduces their absolute value. Regardless of the shape of the indenter and the presence of residual deformations, the distribution of contact stresses for a layer with a thickness at least twice the radius of the contact area is similar to the corresponding distribution for the half-space. The presence of residual tensile deformations in the layer causes a narrowing of the contact area, an increase in the absolute value of the contact forces and a decrease in vertical displacements. The magnitude of the induced changes depends on the type of elastic potential. The presence of residual compression deformations in the layer, in turn, causes the expansion of the contact area, reducing the absolute value of contact stresses and increasing vertical displacements. Guz’ N., Rudnitskii V., 2006. Foundations of the Theory of Contact Interaction of Elastic Bodies with Initial (Residual) Stresses. In: PP Mel’nik, Khmel’nitskii , pp. 710. Habrusiev H., Habrusieva І. and Shelestovskyi B., 2022. Contact Interaction of a Prestrained Thick Plate with Parabolic Punch. Journal of Mathematical Sciences 263, 129 – 137. Jesenko M., Schmidt B., 2021. Geometric linearization of theories for incompressible elastic materials and applications. Mathematical Models and Methods in Applied Sciences, Volume 31, Issue 4, 829 – 860. Lapusta Y., Harich J., Wagner W., 2008. Three-dimensional FE model for fiber interaction effects during microbuckling in composites with isotropic and anisotropic fibers. Comm. Numer. Meth. Eng., 24, No. 12, 2206 – 2215. Mahesh S., Selvamani R., Ebrahami F., 2021. Assessment of hydrostatic stress and thermo piezoelectrici-ty in a laminated multilayered rotating hollow cylinder. Mechanics of Advanced Composite Structures, Volume 8, Issue 1. 77 – 86. References