The contact problem of the motion of a punch with a parabolic base shape along a heterogeneous fluid-saturated half-space is considered in a quasi-static formulation, taking into account friction in the contact area. A multiphase heterogeneous medium is described by the Biot-Frenkel model, and within the framework of the concept of effective homogeneity, an equivalent homogeneous medium is considered. The boundary value problem for the Biot medium is reduced to an integral equation of the 1st kind with a difference kernel having a logarithmic singularity using the Fourier transform. The solution of the integral equation is constructed by the boundary element method. The solution of the boundary value problem for an equivalent medium is implemented by the finite element method in the ANSYS software package. Based on the constructed solution of the contact problem, the influence of the mechanical properties of a heterogeneous medium, the friction coefficient on the stress state in the contact area and in its projection along the base depth is studied, which is of great practical importance in the design of new nanomodified antifriction composite materials. For this purpose, numerical experiments are carried out on the example of a nanomodified composite with a matrix of phenylone modified with an ultrafine additive of aluminum-magnesium spinel and cylinder oil. The effect of porosity, fluid saturation, the friction coefficient on the stress state of the base is studied.

Рассмотрена квазистатическая контактная задача о скольжении штампа с параболическим основанием по границе изотропной пористоупругой флюидонасыщенной полуплоскости при учете трения в области контакта. Микроструктура основания учтена в рамках двух подходов — модели Био-Френкеля и концепции эквивалентной гомогенности. Исследованы зависимости напряжений в области контакта и в ее проекции по глубине основания от пористоупругости и флюидонасыщенности гетерогенной среды, коэффициента трения.