On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics

This study concerns the local character of the elastostatic field in plane strain near a point that separates a free from an adjoining fixed segment of a rectilinear boundary-component. The well-known singular field behavior predicted by the linear theory, as such a point is approached, exhibits oscillatory deformations and stresses. It is shown here by means of an asymptotic analysis that the foregoing anomalous behavior does not occur within the nonlinear theory of harmonic elastic materials. In preparation for this task certain general aspects of the latter theory are reviewed. The results obtained in the nonlinear asymptotic treatment of the class of mixed boundary-value problems considered are discussed in detail with particular attention to the problem of a bonded flat-ended rigid punch.