Wrinkling of a circular elastic plate stamped by a spherical punch

Large deflection theory is used to determine when wrinkling occurs in a simply supported circular elastic plate loaded at the center by a spherical punch. If the edges are free to displace radially, thin plates stamped by intermediate radius punches will develop radial wrinkles near the edge at a central deflection approximately equal to four plate thicknesses, w₀ h ≈ 4. Initially, there are either three or four wrinkles, but the number increases if the central deflection is increased. With larger radius punches, thin plates do not wrinkle. It is calculated that elastic wrinkling occurs in thin plates ( a h > 80) when a² Rh > 8, where a is the plate radius and R is the punch radius.