THE STRESSES AROUND A HOLE IN A LINEAR ELASTIC MATERIAL WITH VOIDS

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Abstract
The problems of quasi-static plane strain and plane stress for a linear elastic material with voids are treated in a relatively complete fashion. The formalism developed is applied to the problem of a cylinder of elastic material shrunk-fit into a hollow circular cylinder of linear elastic material with voids. It is suggested that this problem is a model for the determination of the temporal decay of stress in the wood around a nail. The major solution presented here is the stress distribution about a circular hole in a flat plate subjected to uniaxial tension far away from the hole. It is shown that the stress concentration factor for this problem is always greater than or equal to three, and it can be very much greater than three. Three is the value of the stress concentration factor predicted by classical elasticity in the same situation. An interesting feature of the solutions presented is that the stresses, strains and displacements coincide with those predicted by classical elasticity at time t = 0, and as t tends to infinity a new equilibrium solution for the stresses, strains, and displacements is obtained. The transition between these two limiting solutions is monotonic and due to a rate-dependent term in the theory.

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