Abstract
An integral representation is found for the solution of a two-dimensional difference problem of elasticity theory for a plane cut along the negative semi-axes Ox, under the action of forces which produce a solution characteristic of a normal tear fracture. An asymptotic expansion of the solution is found and it is shown that the difference between the solutions of the difference problem and the exact problem is O(h/r1/2). Where r is the distance from the vertex of the tear. The results are generalized to the case of a longitudinal shear fracture and to schemes of the finite element method for both types of fracture.
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