On contact problem of an elastic laminated half-plane with a boundary normal to layering

This paper deals with the plane contact problem of an infinite long cylinder pressured into an elastic laminated semi-space. The nonhomogeneous body is composed of periodically repeated two constituent laminae and its boundary is assumed to be normal to the layering. The homogenized model with microlocal parameters given by Woźniak [Woźniak C. A nonstandard method of modelling of thermoelastic periodic composites. Int J Eng Sci 1987;25:483–99]. Matysiak and Woźniak [Matysiak SJ, Woźniak C. Micromorphic effects in a modeling of periodic multilayered elastic composites. Int J Eng Sci 1987;25:549–59.] are applied to find an approximate solution to the problem. The problem is reduced to well-known dual integral equations and the stresses are obtained in the form of Fourier integrals. Numerical results, which show the influence of geometrical and mechanical properties of composite constituents on stress distributions, are presented in figures.