Abstract
A body with a hole in it has a thin ligament if the boundary of the hole approaches the outer surface of the body. The asymptotic form of the stress-deformation state of two- and three-dimensional bodies with ligaments is determined, using the width of the ligament as a small parameter. A boundary-layer effect arises near the ligament and can be described, in the two-dimensional case, by a system of ordinary differential equations which can be solved explicitly. The stress-deformation state turns out to depend closely both on the value characterizing the degree to which the ligament has narrowed, and on the overall geometric structure of the body. Analysis of the asymptotic formulae indicates that the collapse of a ligament cannot be a quasistatic process (the Griffith energy balance is destroyed). In the three-dimensional case, the boundary layer is described by an elliptic system of equations in the plane.
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