A polynomial approach to determine stress in an elastic body of circular section indented by conformable contact

A polynomial of degree greater than two that describes the indenter concavity shape is proposed. From the proposed polynomial, the gradient of the displacement is derived and combined with that one determined by Timoshenko and Goodier to obtain the polynomial distribution of the pressure in the cross direction of wire. By using the polynomial pressure in the "stress function" proposed by Flamant, a set of equations serving to know the stresses state in the wire section is obtained. To extend the analysis to two opposite indenters, all contributions to total stress are considered, to knowing: the stresses being produced by each one of the indenters; the biaxial tension to balance the free area of pressure. Finally, by using all contributions to total stress and determining the principal stresses, the magnitude of maximum-shear-stress at each point of elastic body it could be obtained. In order to confront the model with the reality, by associating to each point its maximum-shear-stress respective, patterns of lines representing isostresses were obtained; such patterns were compared with a photo-elasticity image, showing a good agreement.