Example Stress generated when islands impinge

2 Example Stress generated when islands impinge 

Consider an array of islands on a substrate in which all the islands are identical hemispheres of radius R. The centers of the islands are fixed at the intersection points of the square grid of lines with uniform spacing 2R on the growth surface. It is assumed that the islands otherwise behave like free spheres with surfaces having 

The islands are formed in this pattern with radii smaller than R, and they grow until they achieve radii of R. The constraint of the substrate is assumed to be negligible for purposes of this discussion, so the islands behave exactly as did the spheres in the preceding section, but only one-half of the volume of each is taken into account. Once the radius of each island reaches R, contact areas with cohesion form spontaneously between each island and its four immediate neighbors. Again, as a result of this cohesive contact, a tensile force is generated across each island which could be sensed by means of substrate curvature measurement. 

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