We consider the behavior of both internal material lines and free-surface shape near, order O(e-05 L), the upper corner of the punch (width = L) as predicted by computational results obtained from the solution of the bonded punch problem. The mathematical formulation of this problem is stated elsewhere in this web site.
In Figure 2, we show a sequence of frames extracted from the MPEG movie grid (2.25 Mb) (for a short version, see the movie short grid (1.14 Mb) ) which illustrates the self-intersecting behavior of material lines in this neighborhood of the corner for increasing values of the punch displacement U. This sequence of frames and the movie correspond, respectively, to the sequence shown in Figure 1 and the movie free (2.25 Mb) (for a short version, see the movie short free (1.03 Mb) ).
Click on each individual frame to see an enlarged version of the image, or, click anywhere else on the figure to see an enlarged version of the whole image.
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In Figure 2.a (43.1 Kb), we show the cross section of the flat, rigid, bonded punch (thick white line), the free-surface (thick yellow line), and the material lines (thin yellow lines) of an elastic half-space at zero punch displacement. The remainder of the description of this figure follows the description of Figure 1.a (9.9 Kb).
In Figure 2.b (36.5 Kb), material is drawn under the punch and the free-surface intersects with internal material lines of the elastic half-plane. This anomalous intersection characterizes eversion of material in the vicinity of the free-surface; notice from the shades of green and light blue that det F also changes sign near these places of eversion.
In Figure 2.c (34.9 Kb), the cusp-like shape of the free-surface for a moderately large load is clearly intersecting internal material lines of the elastic half-plane and, again, this intersection is correlated to a nearby change of sign of det F.
In Figure 2.d (30.9 Kb), the cusp becomes looped and the free-surface intersects itself inside the elastic region.
In Figure 2.e (33.7 Kb), we change the scale from 2 e-05 L to 8 e-05 L to show the intersection of both the material lines and the free-surface with the punch surface.
Figure 2.f (34.8 Kb) is the last frame of the MPEG movie grid (2.25 Mb) (for a short version, see the movie short grid (1.14 Mb) ) and shows that the intersection of both the material lines and the free-surface with the punch surface persists.
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