Axisymmetric Indentation Of An Elastic Layer On A Rigid Foundation With A Circular Hole
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M. Sakamoto & K. Kobayashi
The axisymmetric indentation problem of an elastic layer overlaid on a rigid foundation with a circular hole is investigated. An infinite rigid punch is pressed onto the upper surface of the elastic layer causing a small deformation mode. The problem is equivalent to a mixed boundary-value problem of the three-dimensional theory of elasticity, and an analytical solution is obtained through an infinite system of simultaneous equations by expressing the normal displacement in the circular hole as an appropriate series. Significant effects of the layer thickness and circular hole on the stress fields are demonstrated with numerical results. Keywords: elasticity, contact problem, indentation, rigid punch, elastic layer, theoretical analysis. 1 Introduction Contact problems have attracted considerable attention due to possible application to various important problems and have constituted one of the fields in the theory of elasticity since the work of Hertz . Hertz theory of contact has been expanded by Boussinesq  and has been developed to important applications by numerous authors. These problems are equivalent to mixed boundary-value problems where stresses and displacements induce in an elastic half-space. However, the mixed boundary-value problem of an elastic layer has been dealt with in a relatively few publications. The axisymmetric indentation problems of an elastic layer resting without friction on a rigid foundation, or attached to a rigid foundation by a frictionless rigid punch, have been considered
elasticity, contact problem, indentation, rigid punch, elastic layer,theoretical analysis.