Formation of a contact zone during compression of a plate with an elliptic hole

The problem of compression of a thin plate with an elliptic hole is considered. It is assumed that increasing the distant compressive load can lead to contact of opposite regions of the boundaries of the ellipse. The problem is solved within the framework of a modified Leonov–Panasyuk–Dugdale model and an elastoplastic analog of the Griffith problem for an ellipse using the Goodier and Kanninen model. The critical fracture parameters providing an equilibrium configuration of the system are determined from a sufficient strength criterion representing a system of two equations, one of which specifies the absence of partial overlapping of the upper and lower surfaces of the contact zone, and the other is a deformation criterion of critical opening of the ellipse. The compression-induced deformation of the boundaries of ellipses with various curvature radii at the top is shown by the example of annealed copper having nanostructure.